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https://www.arxiv-vanity.com/papers/cond-mat/0505350/

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arXiv Vanity renders academic papers from arXiv as responsive web pages so you don’t have to squint at a PDF. Read this paper on arXiv.org. Voter model on Sierpinski fractals Krzysztof Suchecki and Janusz A. Hołyst Corresponding author. Tel.: +48 22 660 7133; fax: +48 22 628 2171 Faculty of Physics and Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland August 14, 2020 Abstract We investigate the ordering of voter model on fractal lattices: Sierpinski Carpets and Sierpinski Gasket. We obtain a power law ordering, similar to the behavior of one-dimensional system, regardless of fractal ramification. PACS numbers: 89.75.-k, 05.45.Df, 05.50.+q 1 Introduction The Ising model is a well known dynamical model that was investigated in complex networks and fractal structures [1, 2, 3, 4, 5]. However, aside from that model, there are many other possible dynamics, sharing little in common with behavior of the Ising model. The voter model is an example of such a model, that exhibits different qualities at a very basic level. Unlike the Ising model, the voter model has no surface tension and defines a broad universality class [6]. While the Ising model dynamics has been studied on fractal lattices [3, 4, 5] little is known about the behavior of voter model in such geometries. We have investigated the behavior of the voter model on Sierpinski carpets and on Sierpinski gasket. It is known [7] that the evolution of the voter model depends on the dimensionality of the lattice. For a large time the ordering process obeys the following equations ρ(t)∼⎧⎪⎨⎪⎩t−α,D<2(lnt)−1,D=21,D>2 (1) where is a fraction of links that form interfaces, i.e. they connect opposite spins, is dimensionality and is time. The predicted exponent was calculated for a lattice with integer dimensionality (). We will focus on the question, whether the dynamics on the fractal lattices is the same, or are there other rules governing them. 2 Models The voter model is a very simple model of opinion formation. Nodes in the network are agents, each one having an opinion. There are only two possible opinions, and typically they are considered as +1 and -1, just as Ising spins. The dynamic rule is simple — the node opinion changes to an opinion of one randomly chosen neighbor. The implementation is following: we choose one node at random, and then one of its neighbors randomly. The first node assumes the state of the second. One time step of the dynamics corresponds to the number of individual node updates equal to the number of nodes in the network, so on average each node is updated once every time step. We investigate the voter model behavior on two fractal networks: Sierpinski Carpet (SC) and Sierpinski Gasket (SG). The SC is constructed according to a chosen basic pattern. The pattern is a square, divided into squares that could be full or empty (Fig.1). First, single nodes are taken, and arranged into the pattern, putting nodes into full positions and skipping empty positions. In the next step, the resulting structures are arranged into the same pattern. All neighboring nodes in the resulting pattern are connected creating the fractal network. The fractal dimension of SC depends on the basic pattern. Classical SC has pattern with all the squares full except the central one. Such SC has a fractal dimension . We have investigated SC of dimensions ranging from to . Since it is impossible to numerically investigate true, infinite fractals, we will call the number of steps in what the network was made a level of fractal. We have investigated SC with different patterns, that all have full squares along the pattern edges and empty interior, but differ in size. All SC fractals have infinite ramification. The ramification is the minimal number of links that one has to remove to separate a part of any chosen size from a network. The finite ramification means that the structure has some ”weak points” where only a finite number of links connect together two parts of an infinite network. The infinite ramification means that infinite parts of infinite network are connected by infinite number of links. For example, a regular square lattice has an infinite ramification, while a tree has a finite ramification order. The SG network is created in the following way (Fig.2). Three nodes are taken and connected into a triangle. In the middle of each edge a node is created and the three new nodes are connected between themselves. This way the whole triangle is divided into four smaller ones. In the next step all three non-central triangles are treated in the same way, adding nodes in middle of the triangle edges and linking them toghether. SG has the fractal dimension and it possesses a finite ramification. While in the case of SC, it was easy to create a general class of SC fractals with different fractal dimensions, we are not aware of any generalization of SC model that allows easy tuning of fractal dimensions. 3 Results We have investigated ordering of the voter model in SC and SG fractals. To measure the disorder, we have used the fraction of interfaces , where is a number of interfaces – links connecting nodes with different spins, is the total number of links in the network. The system orders (Fig.3) with the interface fraction decreasing as a power of time . However, due to the finite system size, there are fluctuations around the power-law. Since the power-law decay becomes slower with time, the fluctuations become more significant, and they push the system into a completely ordered absorbing state after some time. To extract the power-law trend, we have averaged the results of many simulations, but to avoid the exponential decay due to complete ordering of the individual simulations, in a given time step we have averaged only over the simulations that were not completely ordered at that time. This way we have circumvented the fluctuations ordering the system and have obtained an approximation of an infinite network (Fig.4). We observe the evolution of the interface fraction in time for networks with various fractal dimensions between and . We have measured the exponent of that power-law, and compare to the theoretical value [7] (Eq.1). 4 Conclusions The results (Fig.5) we have obtained show that the theoretical predictions [7] (Eq.1) correctly describe the power-law ordering for a voter model on fractals, but the exponents obtained through simulations differ significantly from those obtained from the analytic formula. Moreover, the fact that the voter model in SC and SG behaves in the same fashion suggests that the ramification of the fractal does not influence the voter dynamics, unlike the Ising model case [3]. This work was partially supported by a EU Grant Measuring and Modelling Complex Networks Across Domains (MMCOMNET) and by State Committee for Scientific Research in Poland (Grant No. 1P03B04727). References • [1] A. Aleksiejuk, J.A. Hołyst, D. Stauffer, Physica A 310 (2002), 260-266. • [2] G. Bianconi, Phys. Lett. A 303 (2002), 166-168. • [3] Y. Gefen, B.B. Mandelbrot, A. Aharony, Phys. Rev. Lett. 45 (1980), 855. • [4] J.M. Carmona, U.M.B. Marconi, J.J. Ruiz-Lorenzo, A. Tarancón, Phys. Rev. B 58 (1998), 14387. • [5] T. Stošic, B.D. Stošic, S. Milošević, H.E. Stanley, Physica A 233 (1996), 31-38. • [6] I. Dornic, H. Chaté, J. Chave, H. Hinrichsen, Phys. Rev. Lett 87 (2001), 045701. • [7] L. Frachenbourg, P.L. Krapivsky, Phys. Rev. E 53 (1996), 3009.

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Edit Article # wikiHow to Calculate the Volume of a Rectangular Prism Calculating the volume of a rectangular prism is easy once you know its width, length, and height. Read this wikiHow to learn how. ## 10 Second Summary 1. Find the length, width, and height of the rectangular prism. 2. Multiply the length, width, and height. 3. Write the answer in cubic units. For example: 60 inches3. ## Steps 1. 1 Find the length of the rectangular prism. The length is the longest side of the flat surface of the rectangle on the top or bottom of the rectangular prism. • Ex: Length = 5 in. 2. 2 Find the width of the rectangular prism. The width is the shorter side of the flat surface of the rectangle on the top or bottom of the rectangular prism. • Ex: Width = 4 in. 3. 3 Find the height of the rectangular prism. The height is the part of the rectangular prism that rises up. Imagine that the height is what stretches up a flat rectangle until it becomes a three-dimensional shape. • Ex: Height = 3 in. 4. 4 Multiply the length, the width, and the height. You can multiply them in any order to get the same different result. The formula for finding the volume of a rectangular prism is the following: Volume = Length * Height * Width, or V = L * H * W. • Ex: V = 5 in. * 4 in. * 3 in. = 60 in. 5. 5 State your answer in cubic units. Since you're calculating volume, you're working in a three-dimensional space. Just take your answer and state it in cubic units. Whether you're working in feet, inches, or centimeters, you should state your answer in cubic units. • 60 will become 60 in3. ## Community Q&A Search • Can you give me another example? I still don't get it. wikiHow Contributor Remember that length x width x height. A rectangular prism that is five inches high, ten inches long, and two inches deep will have a volume of 100 square in. 5x10x2=100. • How do I calculate the width when I have the volume, length and height? wikiHow Contributor Multiply the length by the height, and then divide that by the volume. • How can I calculate the dimension when I know the volume? wikiHow Contributor The rectangle's area, times the prism's height vertical to the rectangle, gives the volume; various combinations of dimensions give the same volume, so if you know the volume, and want the dimensions, you will find many sets of dimensions. For example volume 24 could give the length, width, and height of 2, 2, and 6; or 2, 3, 4; or 1, 1, 24; and so on. • How do I find the volume of a rectangular box that is missing some cubes at the top? wikiHow Contributor Find the volume of one cube, then multiply that by the number of cubes. You could also find the volume of the rectangular prism, including the missing cubes, then subtract the volume of the cubes missing. • What does volume mean? wikiHow Contributor It refers to the three-dimensional space that an object occupies. • What is the area of a rectangular prism? wikiHow Contributor There are three different faces on a rectangular prism. Calculate each by multiplying the length by width, add the three results together and multiply by 2 to work out the total area. • How do I calculate the volume with just the length and width? wikiHow Contributor You can't. You have to know the height, otherwise it's only going to give you the area for one side. • How many cubic inches in a gallon? 231. No. Volume is expressed in units cubed. • How do I find the volume of a triangle? wikiHow Contributor You can either find the area of a triangle or the volume of a triangular prism or pyramid. Triangles are 2d, so you find the area. To find the area of a triangle, multiply length by height and divide by two (l x h /2). To find volume of a triangular prism, you take the area of the face (triangle) and multiply it by the width. • How do you solve if it has no variable • How many ways are there to find volume in a rectangular prism? • What is the formula in finding the volume of a cube in a rectangular prism? 200 characters left ## Article Info Categories: Volume In other languages: Français: calculer le volume d'un prisme rectangulaire, Español: calcular el volumen de un prisma rectangular, Italiano: Calcolare il Volume di un Prisma Rettangolare, Português: Calcular o Volume de um Prisma Retangular, Nederlands: De inhoud berekenen van een rechthoekig prisma, Deutsch: Das Volumen von einem Quader berechnen, Русский: найти объем прямоугольной призмы, Bahasa Indonesia: Menghitung Luas Prisma Segi Empat, 中文: 计算长方体的体积, ไทย: คำนวณหาปริมาตรของปริซึมสี่เหลี่ยมมุมฉาก, Tiếng Việt: Tính thể tích hình hộp chữ nhật, العربية: كيفية حساب حجم متوازي المستطيلات Thanks to all authors for creating a page that has been read 565,485 times.

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## ::Normal mode ### ::concepts Modes::normal    Omega::waves    Right::number    System::align    Begin::energy    Pmatrix::which {{#invoke:Hatnote|hatnote}} {{ safesubst:#invoke:Unsubst||\$N=No footnotes |date=__DATE__ |\$B= {{#invoke:Message box|ambox}} }} Vibration of a single normal mode of a circular disc with a pinned boundary condition along the entire outer edge. See other modes. A flash photo of cup of black coffee vibrating in normal modes A normal mode of an oscillating system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at the fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions. When relating to music, normal modes of vibrating instruments (strings, air pipes, drums, etc.) are called "harmonics" or "overtones". The most general motion of a system is a superposition of its normal modes. The modes are normal in the sense that they can move independently, that is to say that an excitation of one mode will never cause motion of a different mode. In mathematical terms, normal modes are orthogonal to each other. The concept of normal modes also finds application in wave theory, optics, quantum mechanics, and molecular dynamics. Normal mode sections Intro  Mode numbers  Nodes   Coupled oscillators    Standing waves    Elastic solids    Quantum mechanics   Earth   See also    References    External links PREVIOUS: Intro NEXT: Mode numbers << >>

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In a working chute, the quarters are a little cramped. If a person inside the chute needs to move from one place to another, he (or she) has to pass by the calves in order to get to his (or her) destination. Squeezing through on either side of the calves sometimes works, when you’re trying to move from the front to the back. But moving from back to front, it doesn’t work as well. Plus, you get your feet stepped on, and no cowboy boot in existence will lessen that amount of pain. On the flip-side, crawling underneath the calves is also ill-advised. Just in case you were wondering. My twelve-year-old punk will now demonstrate the proper method. As the cowboys and kids moved the cattle through the chute, after awhile there turned out to be way more calves between my girl and Cowboy Pete (not shown, far left) than there were between my girl and her sister (right). It’s best to have an even distribution of people throughout the line of calves so they keep moving forward and remain more controlled, so my girl pulled herself up and scooted along the top bars of the chute so she could get up there and help. I realize it’s a little strange for a mother to be bragging on her twelve-year-old daughter’s biceps. It’s like some mutated, cattle-ranch form of “My daughter made the honor roll” or “My daughter got into Dartmouth.” Check out those GUNS, man!” I can’t help it. This is the life I’m living. Sidenote: See the little pile of fuzzy nut sacs lying on the ground? They’re there for a reason. When the crew is finished working calves and they turn them all back out into the pasture, Cowboy Tim will count the number of sacs one by one in order to determine how many heifer calves we have in that herd. Here’s the top-secret scientific formula: Total number of calves – Total number of nutsacs = Total number of heifer calves in the herd Doesn’t that sound like a great job? The nut sac counter? My biceps are stronger than yours.” She’s grounded. Which reminds me…do you remember the old elementary school playground cheer? Sing it with me, folks. With meaning. Firecracker! Firecracker! Boom boom boom! Firecracker! Firecracker! Boom boom boom! Girls got the muscles Teachers got the brains Boys got the sexy legs And we won the game YAY! I just love that cheer. Especially the “teachers got the brains” part…considering I’m the teacher in this family.

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Contents Previous Next Subchapters Current Chapters-> mlmode_assignment multiplestatement mlmode_same mlmode_if mlmode_for mlmode_while mlmode_colon mlmode_numbers mlmode_building mlmode_character mlmode_quote mlmode_matrixdivision mlmode_logicalop mlmode_numericop mlmode_realpart mlmode_matrixindex mlmode_logicalindex mlmode_grow Parent Chapters-> Omatrix6 mlmode mlmode_language mlmode_grow Search Tools-> contents reference index search Automatic Growing of Matrices on Assignment (Mlmode) Syntax x`(`index`) = `expression x`(`row`, `column`) = `expression O-Matrix Mode indices Description If you assign to an index that does not exist, the matrix will grow to be just large enough to include the new index. The undefined entries in the larger matrix are initialized to zero. Example One Index If in Mlmode you enter ```      x = [ 1 2 ];      x(4) = 4 ``` O-Matrix will reply ```      x = [ 1 , 2 , 0 , 4 ] ``` Two Indices If enter ```      x = [ 1 2 0 4 ];      x(2, 2) = 4 ``` O-Matrix will reply ```      {      [ 1 , 2 , 0 , 4 ]      [ 0 , 4 , 0 , 0 ]      } ``` By Rows If in Mlmode you enter ```      x      = 1;      x(3,:) = 3 ``` O-Matrix will reply ```      {      1      0      3      } ``` By Columns If in Mlmode you enter ```      x      = 1;      x(:,3) = 3 ``` O-Matrix will reply ```      [ 1 , 0 , 3 ] ```

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How to calculate strength of Wire Wrapped Screen filter on pressure January 31, 2018 Water Well Filter Pipe,Water Well Screen Pipe February 7, 2018 Wire Wrapped Screen How to calculate the strength of a Wire Wrapped Screen filter on pressure pressure = Force area (f=ps), pressure = stress/Compression area (P=F/S). The physical pressure is the force that occurs on the contact surface of two objects, or the vertical force of a gas on a solid or liquid surface, or the vertical force of a liquid on a solid surface. Traditionally, in mechanics and most engineering disciplines, the term “stress” is synonymous with pressure in physics. The pressure on the surface of a solid is usually the result of elastic deformation, which generally belongs to the contact force. 479 Pressure on the surface of liquids and gases is usually the result of gravitational and molecular motions. The direction of the pressure is usually perpendicular to the contact surface of the object. Pipe base screen Screen API Pipe ID(mm) OD(mm) SLOT(mm) Normal size(inch) OD(mm) 63 73 0.10-3 2-3/8” 60.3 74 85 0.10-3 2-7/8” 73 92 102 0.10-3 3-1/2” 88.9 103 127 0.10-3 4” 101.6 116 130 0.10-3 4-1/2” 114.3 129 142 0.10-3 5” 127 142 154 0.10-3 5-1/2” 139.7 172 184 0.15-3 6-5/8” 168.3 183 195 0.15-3 7” 177.8 220 232 0.15-3 8-5/8” 219.1 246 260 0.25-3 9-5/8” 244.48 276 290 0.25-3 10-3/4” 273.05 342 355 0.25-3 13-3/8” 339.70 Length of screen 5m*1 Length of pipe( m) 5.8 Length of screen 4.5 m * 2 9.3~9.6 Length of screen 5 m * 2 11~12 If the observed pressure is not perpendicular to the contact surface, it is usually the result of the interaction of pressure and friction. Wire Wrapped Screen filter pipe Material: 201, 205, 304, 304L, 316, 316L, 321, such as stainless steel wire. Features: Wire Wrapped Screen filter is also a kind of screen. The winding screen is composed of “V” type stainless steel wire and stainless steel support bar, which is connected together by welding and supporting strip, and the strict continuity and integrity make the full welded wire-mesh liner have the same gap and bear small performance. Compared with other existing filtration elements, it has the characteristics of strong structure, high tensile strength, strong compressive strength, corrosion resistance, high temperature resistance, easy to jam and easily flush. Product specifications and raw materials can be customized according to customer production testing to ensure product quality, so as to ensure the interests of the vast number of customers to the most economic input to obtain the highest production efficiency. Usage: The Wire Wrapped Screen filter is a kind of water-filtering equipment with perforations. Can be with deep pump, submersible pump supporting the use, can also be used for water treatment equipment, environmental protection, seawater conversion for industrial water and water desalination treatment, water treatment, softening treatment, petrochemical industry, petroleum products, terminal filtration and chemical acid, alkali liquid filtration, alcohol and other organic solution recovery filtration. well screen/water well screen filter/sand control oilwell screen 1. GENERAL REQUIREMENTS : The quality of stainless steel should be such that its life once installed will not be less than 20 years. 1.1 The screen shall be able to withstand without deterioration normal handling from the place of manufacture to the place of erection and of being stored in the open yard in any weather to which these may be exposed. The components separately and together shall neither progressively corrode nor suffer deterious change of property in the presence of the materials and bacteria which may encountered below the formation surface at the place of erection or by exposure to weather of by immersion. The stainless steel screen shall be so manufactured that these will not suffer significant damage due to impact or abrasion such as may occur when a sand bailer is used for well maintenance. 2. MATERIALS : AISI Type-304 3. CONSTRUCTION : The screen shall be manufactured in the all welded continuous slot wedge wire or support rod construction, with the latest electronically controlled welding system, ensuring greater fusion strength between the profile wedge wire and support rods maintaining accurate slot opening. The shape of the wedge wire shall be such that when welded to support rods, it will increase the slot openings inwards. The wedge wire shall firmly be attached to the supporting rods which will, in turn, be attached to the coupling adapter. The bidders shall give details of the size and shape of wires and the number of support rods with size and shape. 4. JOINTS : Each end of the screen shall be threaded as per BS-21-1973 (11TPI). Each screen length shall be provided with a coupler to the same standard. 5. CIRCULARITY AND STRAIGHTNESS : The bores of the screen and joints separately and when jointed shall be rounded, smooth and straight. 6. STRENGTH OF COMPONENTS : The components separately and jointed together shall be able to withstand without deterioration the following conditions :-

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Present Remotely Send the link below via email or IM Present to your audience • Invited audience members will follow you as you navigate and present • People invited to a presentation do not need a Prezi account • This link expires 10 minutes after you close the presentation • A maximum of 30 users can follow your presentation Do you really want to delete this prezi? Neither you, nor the coeditors you shared it with will be able to recover it again. Connect your Facebook account to Prezi and let your likes appear on your timeline. You can change this under Settings & Account at any time. Thesis No description by Jessica Whalen on 28 November 2012 Report abuse Transcript of Thesis The Mathematics behind lacings your shoes Definitions Mathematical Shoe: a pair of vertical lines in a plane that are one unit apart and n horizontal lines that intersect with the two vertical lines and are h units apart. Eyelets: represented by the intersections of the vertical and horizontal lines in the mathematical shoe Lacing Rules Every eyelet must be visited once, and only once. Every eyelet must contribute to pulling the two sides of the shoe together, which means at least one of the two segments of shoelace that end in each eyelet also ends in the other column so that there are no gaps. Types and Classes There are are four different types of lacings and six different family types. The classes are Dense, Straight, Superstraight, and Simple. One-Column Lacings One-Column n-lacings are closed paths within a plane containing a single column of n eyelets that are equally spaced apart and form a single vertical column. They can be formed by creating permutations of the n eyelets or by a process called contraction. When creating the one-column n-lacing contraction of a two-column n-lacing, horizontal lacings are disregarded and diagonal lacings are considered the same as vertical lacings. One-Column Lacings (Cont.) One-column n-lacings are made by permutations of the eyelets. They always start in the first eyelet, but after that the order doesn't matter as long as each eyelet is visited exactly once and the lacings returns to the first eyelet. Thus, there are (n-1)! different permutations of the eyelets for all n≥2. However, each permutation is exactly the same as the permutation in which the order that the eyelets are visited is reversed. One-column lacings will make certain calculations much simpler later on. Counting Laces - General Lacings Assume n is an odd number. There are 2k verticals, k in column A and k in column B where 0 ≤ k ≤ (n-1)/2. Let G(k, n) denote the number of oriented n-lacings with 2k verticals. The number of oriented n-lacings is the sum of G(k,n) from k=0 to k=(n-1)/2. To calculate G(k, n) consider the permutation of an oriented n-lacing with 2k verticals. If the last element in the permutation is in column A, move it to the beginning of the permutation. The permutation should now alternate between groups of elements in column A and elements in column B, where each group is either a single or a double and the first group is an A group. ABABAABBABBABAAB There is a total of k double A’s, k double B’s, n-2k single A’s, and n-2k single B’s. Counting General Lacings Let GA(k, n) be the number of permutations starting with a single A group, and GAA(k, n) be the number of permutations starting with a double A group. Thus: GA(k, n) = ((n-k-1)C(k))((n-k)C(k)) and GAA(k, n) = ((n-k-1)C(k-1))((n-k)C(k)) where k = 0, 1, 2, …, (n-1)/2. Given one of the sequences that start with a single A group, all of the oriented lacings that arise from it can be reconstructed by adding indices to the elements in the permutation. As long as the index of the first A is 1 and all of the indices are represented exactly once, this can be done arbitrarily. There are n!(n-1)! ways of doing this. (n-1)! ways of assigning indices to the A's and n! ways of assigning indices to the B's. Counting General Lacings The same thing can be done for permutations that start with a double A group with the additional requirement that the index of the second A is 2. There are 2n!(n-1)! ways of doing this. Combining all of this gives us: n!(n-1)! ∑(from k=0 to k=(n-1)/2) GA(k,n)+GAA(k,n) = n!(n-1)! ∑(from k=0 to k=(n-1)/2) ((n-k-1)C(k))((n-k)C(k))+2((n- k-1) C(k-1))((n-k)C(k)) = n!(n-1)! ∑(from k=0 to k=(n-1)/2) ((n-k)C(k))[((n-k-1)C(k))+2((n- k-1)C(k-1))] = n!(n-1)! ∑(from k=0 to k=(n-1)/2) [(n-k)C(k)^2 (1+ k/(n-k))] = (n!)^2 ∑(from k=0 to k=(n-1)/2) [1/(n-k)((n-k)C(k))^2 ] oriented n-lacings. Therefore, ((n!)^2)/2 ∑(from k=0 to k=(n-1)/2) [1/(n-k)((n-k)C(k))^2] is the total number of (unoriented) n-lacings when n is odd. When n is even it is dealt with in a similar manner and comes out to: ((n!)2 )/2∑(from k=0 to k=(n-1)/2) 1/(n-k)((n-k)C(k))^2 . Counting Dense Lacings Without including the indices of the elements, the permutation of an oriented dense n-lacing is always ABAB…AB. While the first A always has an index of 1, the remaining n-1 A’s and the n B’s can be in any order as long as they are all used exactly once. This means there are (n-1)! ways to arrange the remaining A’s and n! ways to arrange the B’s. Dividing by 2 to remove duplicates caused by the orientations gives us ½(n!)(n-1)! dense n-lacings. Counting Straight Lacings This is where our work with one-column n-lacings comes in useful. A straight n-lacing contains every possible horizontal segment, so when attempting to undo the contraction on a one-column n-lacing there is no question as to whether or not there is a horizontal segment at any given eyelet. If it is an n-lacing, then there are n-1 segments that must be either a vertical or a diagonal, meaning there are 2^(n-1) combinations of verticals and diagonals for each one-column n-lacing. As we previously found, there are ½(n-1)! different one-column n-lacings. Thus, taking into account the fact that each one-column n-lacing has two orientations, the total number of straight n-lacings is: 2*2^(n-1)*1/2(n-1)! = (n-1)!2^(n-1) Counting Simple Lacings Simple lacings always contain the top and bottom horizontal segments. There are six different simple configurations that use the top horizontal, and as such every simple lacing begins with one of these configurations. They are the Fishtail, Box, Zee, Mirror Zee, Cee, and Mirror Cee. Every simple lacing contains one of these configurations at the top of the lacing. Fishtale: deleting the configuration and connecting the two resulting “loose ends” with a horizontal segment creates a simple (n-1)-lacing. Alternately, deleting the top horizontal of any simple (n-1)-lacing and replacing it with a Fishtail will create a simple n-lacing. Counting Simple Lacings Zee/Mirror Zee: deleting this configuration n-lacing leaves one “loose end” in the top row where it used to connect to the top horizontal and one in the other column, one row down. Moving the top “end” down one row and connecting it to the other “end” with a horizontal segment forms an (n-1)-lacing. Inverting this process turns a simple (n-1)-lacing into a simple n-lacing. Box: deleting this configuration does not just give a simple (n-1)-lacing, it gives a simple (n-1)-lacing where top segments are diagonals. If these segments were not both diagonals, then the n-lacing would have contained an invalid lacing. Any simple (n-1)-lacing that has only diagonals connecting to the top horizontal can easily be transformed into a simple n-lacing by deleting the top horizontal and replacing it with a Box. n-lacing: a closed path on a mathematical shoe representing the path of the shoelace Counting Simple Lacings n-diagonaldiagonals (d-d): simple n-lacings with diagonal segments ending in both of the top two eyelets; s_n^dd represent the number of such lacings. n-verticalverticals (v-v): simple n-lacings with verticals ending in both of the top two eyelets; s_n^vv represent the number of such lacings. n-diagonalverticals (d-v) and n-verticaldigonals (v-d): simple n-lacings with one vertical and one diagonal ending in the top two eyelets; s_n^dv and s_n^vd represent the number of such lacings respectively. It should be fairly obvious that s_n^dv = s_n^vd. Ceediagonals (Cee-d) and Ceeverticals (Cee-v): simple n-lacings that contain a Cee configuration and a diagonal or vertical respectively that ends in the remaining top eyelet; the number of such lacings is represented by s_n^Ceed and s_n^Ceev. Mirror Cee’s: s_n^Ceed = s_n^mCeed and s_n^Ceev = s_n^mCeev. Cee/Mirror Cee: If a simple n-lacing does contain a Cee, then the Cee is part of one of the six configurations seen below. Counting Simple Lacings Using these we can form an equation to find the total number of simple n-lacings. The equation is: s_n = s_n^dd + s_n^vv + 2s_n^dv Cee-ds are extended by Cee1s, Cee2s, Cee3s, and Cee4s. Cee-vs are extended by Cee1s, Cee4s, Cee5s, and Cee6s. D-ds are extended by Fishtails, Zees, and Mirror Zees. D-v's are extended by Zees, Cee-d's, and Mirror Cee-d's, and v-v's are extended by Boxes, Cee-v's, and Mirror Cee-v's. Counting Simple Lacings This gives the following system of recursive equations: s_n^Ceed = s_(n-2)^dd+s_(n-2)^dv+s_(n-1)^Ceed+s_(n-1)^Ceev+ s_(n-1)^Ceed + s_(n-2)^dd + s_(n-2)^dv s_n^Ceev = s_(n-2)^dd + s_(n-2)^dv + s_(n-1)^Ceev + s_(n-2)^dd + svvn-2 + 2s_(n-2)^dv + s_(n-2)^dv + s_(n-2)^vv s_n^dd = s_(n-1)^dd + s_(n-1)^vv + 2s_(n-1)^dv + 2(s_(n-1)^dd + s_(n-1)^dv) s_n^dv = s_(n-1)^dv + svvn-1 + s_n^Ceed s_n^vv = s_(n-1)^dd + 2s_n^Ceev Using s_d^dd=1, s_2^vv = 1, s_2^dv = 0, s_2^Ceed = 0, s_2^Ceev = 0, s_3^dd = 4, s_3^vv = 3, s_3^dv = 2, s_3^Ceed = 1, s_3^Ceev = 1, and standard generating function techniques we can come up with the final equation: ∑(i from 1 to 5) [(2-3r_(i )-5r_i^3+4r_i^4)/(r_i^(n-1) (7-20r_i+27r_i^2-84r_i^3 +60r_i^4))] where r_i, i = 1, 2, …, 5 roots of 12r^5-21r^4+9r^3-10r^2+7r-1. Counting Summary Shortest Lacings The shortest lacings is a simple lacing. Simple lacings go from top to bottom, and bottom to top exactly once. All non-simple lacings travel up and down more than once, adding length. The shortest possible lacing is the Bowtie. The Crisscross is the shortest dense lacings. When n is even, then the Serpent lacing is the shortest straight lacing. When n is odd, the Zigsag is the shortest straight lacing. There are three types of lacings: horizontal, diagonal, and vertical. The family classes are Crisscross, Zigzag, Star, Bowtie, Serpent, and Zigsag. Because these two permutations form the same diagram, we do not differentiate between the two orientations. As such, the total number of one-column n-lacings is ½(n-1)!. Shortest General Explanation Horizontals add length without adding vertical distance, so the shortest n-lacing will not contain any horizontal except for the top and bottom horizontal. The rest of the lacing will be a combination of vertical and diagonal segments. Because a vertical segment is shorter than diagonal segment, the lacing should contain as many vertical segments as possible. There cannot be two vertical segments in a row and still be a valid lacing, so the vertical and diagonal segments will have to alternate. This is the description of a Bowtie lacing. Shortest Dense Explanation This requires some shortening rules. In the image below it should be obvious that a straight line from A to C and from B to D would be shorter that the lines connecting A to D and B to C, and that replacing lacing segments like those on the left with segments like those on the right will result in a shorter overall lacing. All other shortening rules are variations of this one. A lacing is reduced when the shortening rules do not affect it and it cannot be shortened any further. If the shortening rules can still be applied, then the lacing is considered to be reducible. The crisscross lacing is the only dense n-lacing that is reduced, which automatically makes it the shorted dense n-lacing. Shortest Straight Explanation Unlike the shortest general lacing, the shortest straight lacing will contain every horizontal segment. Like the shortest general lacing, vertical segments are still shorter than diagonal segments and should be included as often as possible. Relearning Your Lacings Strongest Lacings The purpose of a shoelace is to pull the two sides of a shoe together, and different types of lacings do this with carrying levels of success. When laced and tied properly, the tension on the shoelace should be constant over the entire shoelace. The ability of a shoelace to pull the sides of a shoe together is measured by the horizontal component of the tension on the shoelace. Horizontal segments have the most horizontal tension (obviously). Vertical segments have no horizontal tension. The amount of horizontal tension in diagonal segments is inversely proportional to their length. The shorter it is, the more horizontal tension it has. Strongest Lacings (Cont.) With this in mind, it is easy to see which lacing classes have a high level of horizontal tension, and which do not. Bowtie, Serpent, and Zigsag lacings obviously have very little horizontal tension, making them weak. Crisscross, Zigzag, and Star lacings are the strongest classes of lacings. Tieing The Ends There are enough ways to lace a shoe, there's no reason your shoes can't be unique. A Bowtie lacing will save you from a broken shoelace. The more back and forth, the stronger the lacing. When n is even it is possible to create a superstraight (Serpent) lacing and avoid using diagonal segments entirely. When n is odd, it is impossible to create a lacing without using a diagonal. A Zigsag lacing is a straight lacing with exactly one diagonal segment. Full transcript

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#### Finding Different Shapes Area Worksheet Using this Finding Different Shapes Area Worksheet, students find the area of rectangles, squares, triangles, and trapezoids using the provided formula. Free #### Drawing Circles Worksheet Using Drawing Circles Worksheet, students trace and color the circle outlines to build their fine motor and shape recognition skills. Free #### Drawing Triangles Worksheet Using Drawing Triangles Worksheet, students trace and color the triangle outlines to build their fine motor and shape recognition skills. Free #### Comparing 2D and 3D Shapes Worksheet Using this Comparing 2D and 3D Shapes Worksheet, students sort shapes based on different shape attributes to build shape recognition skills. Free #### Volume, Surface Area Rectangular Prisms Worksheet Using this Volume, Surface Area Rectangular Prisms Worksheet, students find the surface area and volume of a rectangular prism . Free #### Finding Shape Perimeter Worksheet Using Finding Shape Perimeter Worksheet, students find the perimeter of two-dimensional shapes when one or all side lengths are given. Free #### 2-Dimensional and 3-Dimensional Shapes Worksheet This 2-Dimensional and 3-Dimensional Shapes Worksheet teaches students how to determine if a shape is considered 2D or 3D to build shape recognition skills. Free #### Drawing 3D Shapes Worksheet This Drawing 3D Shapes Worksheet teaches students how use  straws and twist ties to create 3D shapes with faces, angles, and sides. Free #### 3D Shapes Matching Worksheet Using this 3D Shapes Matching Worksheet, students match 2D or 3D to their names to build shape recognition skills. Free #### Classifying Shapes Worksheet Using this Classifying Shapes Worksheet, students sort real life objects into categories based on what shape is primarily being shown. Free #### Drawing Squares Worksheet Using Drawing Squares Worksheet, students trace and color the square  outlines to build their fine motor and shape recognition skills. Free Free #### Constructing Shapes Worksheet This Constructing Shapes Worksheet teaches students how use  straws and twist ties to create 2-D and 3D shapes with faces, angles, and sides. Free #### Perimeter Worksheet Using Perimeter Worksheet, students find the perimeter of two-dimensional shapes by counting squares on a grid. Free #### 3 Dimensional Shapes Worksheet This 3 Dimensional Shapes Worksheet teaches students more about identifying 3D shapes in the real world situations and giving names to them. Free #### Circumference of Circles Worksheet Using this Circumference of Circles Worksheet, students find the circumference of circles using the radius or diameter. Free #### Volume Rectangular Prisms Worksheet Using this Volume Rectangular Prisms Worksheet, students find the  volume of  3D shapes. Free #### Volume of 3D Shapes Worksheet Using this Volume of 3D Shapes Worksheet, students find the  volume of regular 3D shapes. Free

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http://examcrazy.com/diode-rectifier-circuits

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# Diode Rectifier Circuits We saw in the previous lecture that Zener diodes can be used in circuits that provide (1) voltage overload protection, and (2) voltage regulation. An important application of “regular” diodes is in rectification circuits. These circuits are used to convert AC signals to DC in power supplies. A block diagram of this process in a DC power supply is shown below In this DC power supply, the first stage is a transformer: An ideal transformer changes the amplitude of time varying voltages as This occurs even though there is no direct contact between the input and output sections. This “magic” is described by Faraday’s law: By varying the ratio N2/N1 in (1) we can increase or decrease the output voltage relative to the input voltage: • If N2> N1 , have a step-up transformer • If N2 For example, to convert wall AC at ~120 VRMS to DC at, say, 13.8 VDC, we need a step down transformer with a ratio of: We choose s v1 ˜ V5DC for a margin. For the remaining stages in this DC power supply: • Diode rectifier. Gives a “unipolar” voltage, but pulsating with time. • Filter. Smoothes out the pulsation in the voltage. • Regulator. Removes the ripple to produce a nearly pure DC voltage. We will now concentrate on the rectification of the AC signal. We’ll cover filtering in the next lecture. Diode Rectification We will discuss three methods for diode rectification: 1. Half-cycle rectification. 2. Full-cycle rectification. 3. Bridge rectification. (This is probably the most widely used.) Half-Cycle Rectification We’ve actually already seen this circuit before in this class! We will use the PWL model for the diode to construct the equivalent circuit for the rectifier: From this circuit, the output voltage will be zero if Conversely, if vs(t ) >vds we can determine vO by superposition of the two sources (DC and AC) in the circuit sources since we have linearized the diode: Notice that we’re not making a small AC signal assumption here. Rather, we have used the assumption of the PWL model to completely linearize this problem when ( ) 0 S D v t V > and then used superposition of the two sources, which just happen to be DC and AC sources. (Consequently, we should not use rd here.) The total voltage is the sum of the DC and AC components: In many applications, A sketch of this last result is shown in the figure below. There are two important device parameters that must be considered when selecting rectifier diodes: 1. Diode current carrying capacity. 2. Peak inverse voltage (PIV). This is the largest reverse voltage across the diode. The diode must be able to withstand this voltage without shifting into breakdown. For the half-cycle rectifier with a periodic waveform input having a zero average value PIV = Vs where Vs is the amplitude of vS. Full-Cycle Rectification One disadvantage of half-cycle rectification is that one half of the source waveform is not utilized. No power from the source will be converted to DC during these half cycles when the input waveform is negative. The full-cycle rectifier, on the other hand, utilizes both the positive and negative portions of the input waveform. An example of a full-cycle rectifier circuit is: Notice that the transformer has a center tap that is connected to ground. On the positive half of the input cycle 0 S v > , which implies that D1 is “on” and D2 is “off.” Conversely, on the negative half of the input cycle, 0 S v < which implies that D1 is “off” and D2 is “on.” In both cases, the output current i0(t ) >0 and the output voltage V0(t)>0 While this full-cycle rectifier is a big improvement over the halfcycle, there are a couple of disadvantages: 1 PIV = 2Vs - VD), which is about twice that of the half-cycle rectifier. This fact may require expensive or hard-to-find diodes. 1 Requires twice as many transformer windings on the secondary as does the half-cycle rectifier. Bridge Rectification The bridge rectifier uses four diodes connected in the famous bridge pattern: Oftentimes these diodes can be purchased as a single, fourterminal device. Note that the bridge rectifier does not require a center-tapped transformer, but uses four diodes instead. The operation of the bridge rectifier can be summarized as: 1. When are “off”: 2. 3. When 4. are “on”: The bridge rectifier is the most popular rectifier circuit. Advantages include: 1 PIV = Vs - VD), which is approximately the same as the half-cycle rectifier. 2 No center tapped transformer is required, as with the half cycle rectifier.

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CC-MAIN-2019-09

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https://help.scilab.org/docs/2023.0.0/en_US/lqi.html

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# lqi Linear quadratic integral compensator (full state) ### Syntax [K, X] = lqi(P, Q, R) [K, X] = lqi(P, Q, R, S) ### Arguments P The plant state space representation (see syslin) with nx states, nu inputs and ny outputs. Q Real nx+ny by nx+ny symmetric matrix, R full rank nu by nu real symmetric matrix S real nx+ny by nu matrix, the default value is zeros(nx+ny,nu) K a real matrix, the optimal gain X a real symmetric matrix, the stabilizing solution of the Riccati equation ### Description This function computes the linear quadratic integral full-state gain K for the plant P. The associated system block diagram is: The plant P is given by its state space representation The cost function in l2-norm is: where and xi is the integrator(s) state(s); It is assumed that matrix R is non singular. If the full state of the system is not available, an estimator of the plant state can be built using the lqe() function. ### Algorithm The lqi function solves the lqr problem for the augmented plant ### Examples Linear quadratic integral controller of a simplified disk drive using state observer. //Disk drive model G=syslin("c",[0,32;-31.25,-0.4],[0;2.236068],[0.0698771,0]); t=linspace(0,20,2000); y=csim("step",t,G); //State estimator Wy=1; Wu=1; S=0; Q=G.B*Wu*G.B'; R=Wy+G.D*S + S'*G.D+G.D*Wu*G.D'; S=G.B*Wu*G.D'+S; //State estimator [Kf,X]=lqe(G,Q,R,S); Gx=observer(G,Kf); //LQI compensator wy=100; Q= wy*blockdiag(G.C'*G.C,1); R=1/wy; Kc=lqi(G,Q,R); //full controller K=lft([1;1]*(-Kc(1:2)*Gx(:,[2 1])+Kc(3)*[1/%s 0]),1);//e-->u //Full system H=(-K*G)/.(1);// full system transfer function y=csim("step",t,H); clf;plot(t,y)

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https://parts-ring.com/2017/05/07/a-career-in-electronics-beginning-the-sequence/

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# A Career in Electronics – Beginning the Sequence ### In the beginning Steve, Steve, Bill and Paul had an idea…. Part I of the basics to electronic engineering… for the student Many years ago most schoolboys had this desire to build something great to make them famous. It may have been a steam train, a car or an aeroplane.  Girls didn’t talk about this because it was “boy” stuff. Times changed and so many boys went on to build electronic stuff, flashing lights, crystal receivers and audio amplifiers.  Some girls tried this and to the young boy’s embarrassment, were better than them. Many years after this along came Steve Jobs, Steve Wozniak, Paul Allen and Bill Gates.  They built and programmed computers and became multi-billionaires. Many boys and girls went on to become programmers, their soul pursuit was becoming rich and famous, unlike many Electronics entrepreneurs. The Mystery of the Electron and where to begin… I think one of the best places to start an introduction, a beginning, a middle part and never the ending is a good website. There are many around and I would never rate one over the other because I know just how much work, time and effort goes into not only generating HTML but getting the “view and attraction” right. You will need to study electrons, electron current flow and conventional wisdom, much of which came about when scientists did not know an electron existed 🙂 You will need to know some things like DC and AC.  You would have touched sides with this at school if you were lucky enough to have studied science. Then you need to know things like electromagnetism – a very important aspect to electronics and much misunderstood, so don’t worry about getting confused. Things get brighter at the end of the tunnel. Passive components – Resistors, capacitors, inductors, diodes etc Always a good start – why resistors are known as…. resistors.  They resist current flow. Here you will learn about current, voltage and power which is a product of current and voltage or P = I(current) x V(voltage). You will need to know Ohm’s Law, or Voltage = Current x Resistance or V = I x R. You will need to know about series and parallel networks. And of course, Kirchoff’s two laws – current flow in a network and voltage drop across a network components. Capacitors. Charge. Coulomb. Joule.  And of course  Michael Faraday’s Farad, the unit of capacitance. Inductors or Inductance.  Reluctance, again energy, the Joule, induction and of course Joseph Henry’s Henry, the unit of electrical induction. Transformers – learning how to step up or step down voltages Chokes – the inductor Now the diode is an interesting device – it conducts current only one way. But of course this is best understood under thermionic tubes and semiconductors. There are other passive components used in electronics but this becomes just a sequence in your travel. Reactance and Resonance A very interesting subject and one which separates the men from the boys.  Ac you would have learnt, a capacitor is just two plates insulated from each other. Connecting a battery across these two plates causes a surge of current (charge) which slow reduces as the plates discharge. But what happens when you apply an alternating current across these two plates? An inductor will impede the current initially (reluctance) when a voltage is applied across it (you will need to put a resistor in series otherwise you will short out the battery – an inductor is simply a coil of wire). Both a capacitor and an inductance are used to store energy. Reactance – alternating current across an inductor or capacitor The outcome of this is that in an AC circuit the capacitor and inductor provide an interesting phenomena known as Reactance.  As the frequency of the AC voltage applied across a capacitor goes up, the current increases.  In an inductor the opposite occurs, the current reduces. Cx or capacitor reactance = 1/(2 x pi x F x C) Lx or inductive reactance = 2 x pi x F x L The current flowing through a capacitor  “leads” the voltage by 90 degrees, an inductor has the current “lagging” the voltage by 90 degrees. You will read up about this of course?  🙂 Remember the word CIVIL  C = Capacitor, I = Current, V = Voltage CIV – current leading (in front) VIL, current lags (behind) in an L = Inductance. Impedance Impedance is the value in Ohms of the effective resistance of  reactance and purely resistive components measured in an AC circuit. Accept or Reject – RLC resonance circuits In a series network of capacitors and inductors an AC voltage can be applied across the network which has a variable frequency.  When this frequency gets to a certain point (and I use this term very loosely) the reactive components will be equal – the capacitive reactance and the inductive reactance will be equal .  The formula for resonance is 1/ sqrt(2 x pi x  L x C) in both parallel and series networks. For a great lesson or lessons in AC circuits go here to electronics-tutorials. Here one can read up how as the circuit goes into resonance one can reject or accept a range of frequencies, as used in band-pass filters. Am I leaving anything out? Thermionic Tubes My favourite. They’re making a comeback.  Transistors distort painfully, tubes distort beautifully.  Fact or fiction. It’s all in the ear. Learn about the thermionic vacuum tube: • Diodes (2 electrodes, anode and cathode) and the beginning of it all, electron current flow in a thermionic tube, or the Thermionic Effect • Triodes (3 electrodes, anode, cathode and a control grid or G1) • Tetrodes (4 electrodes, anode, cathode, control grid and screen grid or G2) • Pentodes (4 electrodes, anode, cathode, control, screen and suppressor or G3) Oh yes, we have heptodes,  beam tetrodes, hexodes, mixed triode/pentodes plus many others. Common grid, common cathode, common anode. Tubes are great because they tend to be easier than semiconductors to understand.  And no, they are not simple to manufacture. They are also highly inefficent, they need to be heated either directly or indirectly, run on high voltages which makes them dangerous for the average school child wanting to learn more. They are notoriously resilient and reliable and indeed until recently were not affected by electromagnetic pulses of the atom bomb kind. Besides for their inefficiencies in many ways they lend themselves easily to multi-kW power amplifiers used in transmitters, oscillators and nowadays they are much in demand for microphone preamplifiers and high fidelity audio reproduction.  In my mind they make the best vinyl reproducers i.e. vinyl or record pre-amplifiers. Amplifiers Learn about Class A, Class B and Class C Semiconductors The great discovery not that long ago, nearly 60 years to be exact. Learn about holes and electrons.  Doping a substrate. Transistors – NPN and PNP, Germanium and Silicon Transistors used as switches and amplifiers. Common Base, Common Collector, Common Emitter FETs or Field Effect Transistors.  Did you know they were discovered before Bipolar Transistors.  MOSFETs, IGFETS, Unijunctions. Lateral and Vertical. Transistors and Mosfets are commonly used as switches and in amplifiers, low and high power. Amplifiers Learn about Class A, Class B and Class C.  With transistors we now have Class D as well as rail shifting class G audio amplifiers. Class T or Tripath amplifiers were also fairly common not that long back. Tripath was a registered trade name. We called it wireless, then radio now wireless. All the same thing really. We have AM – Amplitude Modulation, FM – Frequency Modulation and PM – Pulse Modulation. Plenty of others of course, different strokes for different folks. • Telex and RTTY • Cellular Technology – what made it possible • Single Sideband Radio or SSB • Detection circuits • Pre-emphasis • De-emphasis Test Equipment Good multimeter with high input impedance – this is to stop loading of the circuit components, possibly causing damage when doing voltage readings. Most modern DMMs are high input impedance but always check. Veer clear of entry level R80.00 jobs for electronic repair.  Amongst many things the patch leads and probes will not be designed for high voltage and can be dangerous. Fluke meters are amongst the best in the world but have become ridiculously expensive in South Africa.  There are other very good meters available for R1 000.00 and above. Some even have cap and inductance checking but may not be all that accurate. Do get one which has a diode testing function. An audio frequency multi-function generator (sine, square and sawtooth) is indispensable.   Most DIYers build their own for about R500.00. An oscilloscope is a definite for design work. Many DIYers are looking a using their PC for audio work – this can serve as a signal generator as well as an audio frequency oscilloscope.  KMeasure in Pretoria have  some very good quality equipment – especially for using your PC on a scope as the Visual Display Unit. Bench power supply, preferably a dual supply of +/- 30V 3A.  Most DIYers build their own. It must be very accurate and rock steady for digital work. Where things become costly is usually frequency related.  Scopes with 200MHz bandwidth may cost you more than R20 000.00. Frequency generators and spectrum analysers are usually out of the reach for the student. Part II Part III Where to now once you know it all Happy 0 % 0 % Excited 0 % Sleepy 0 % Angry 0 % Surprise 0 % Article Rating Subscribe Notify of Inline Feedbacks May 9, 2017 8:28 pm […] Chapter One:  Beginning the Sequence […] May 20, 2017 10:42 am […] Chapter One:  Beginning the Sequence […] November 12, 2017 6:26 am […] A Career in Electronics – Beginning the Sequence […] 3 0

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&= 424 \text{ million} \quad \text{(nearest million)} of our 2019 students achieved an ATAR above 90, of our 2019 students achieved an ATAR above 99, was the highest ATAR achieved by 3 of our 2019 students, of our 2019 students achieved a state ranking. [ii] Prove that ∫(1 / a2 – x2) dx = (1 / 2a) log [(a + x) / (a – x)] + c. = (1 / 2a) ∫[(a + x) / (a – x) / (a + x) / (a – x)] dx, = (1 / 2a) ∫(1 / (a + x)) + (1 / (a – x)) dx, = (1 / 2a) [∫(1 / (a + x)) dx + ∫(1 / (a – x)) dx], = (1 / 2a) [log |a + x| – log |a – x|] + c. [iii] Show that ∫-aa f (x) dx = 2 ∫0a f (x) dx, if f (x) is an even function. \text{therefore} \ P(\sqrt{3},-4\sqrt{3})\\ As $$-1 \leq \cos\left(\frac{2\pi t}{366}\right) \leq 1$$, it is least when $$\cos\left(\frac{2\pi t}{366}\right) = -1$$. \end{gather*}, \begin{gather*} [iii] Find the inverse of the matrix using elementary row transformations. Therefore [i] Using the vector method prove that the medians of a triangle are concurrent. \end{align*}, \begin{align*} Question 27 (a) Criteria Marks • Provides correct answer or correct numerical expression 2 • Calculates correct cost of SMS or data, or equivalent merit 1 . \begin{align*} = 2 cos2 ɑ – 1 + 2 cos2 ꞵ – 1 + 2 cos2 – 1 + 1. = tan-1 (5x + 1) / (1 – (3x + 2) (2x – 1)), = tan-1 ((3x + 2) (2x – 1) / (1 – (3x + 2) (2x – 1)), dy / dx = [3 / 1 + (3x + 2)2] + [1 / 1 + (2x – 1)2], = [3 / 9x2 + 12x + 5] + [1 / 2x2 – 2x + 1]. \begin{gather*} 2\ln(k+3) &= \ln 144 \\ [iii]: The measure of the acute angle between the Lines whose direction ratios are 3, 2, 6 and –2, 1, 2 is ______. \frac{d}{dx}(x^2\tan x) &= 2x\tan x + x^2\sec^2x \quad (\text{product rule}) = 8 [(x / 2) * √1 – x2 + (1 / 2) sin-1 (x / 1)]10. (1.04^{n-1}+…+1.05^{n-1})&=(1.05^{n}-1.04^{n})(100)\\ HSC Comm. &= \left[\frac{9}{2}x^2 – \frac{1}{4}x^4\right]^3_0 \\ Rearrange, [iii] Find the distance of the point (1, 2, -1) from the plane x – 2y + 4z – 10 = 0. P(110) &= 92e^{0.0139(110)} \\ &=3\sqrt{5}\,\,\text{unit}\\ [iii] Examine the continuity of the function f (x) = log 100 + log (0.01 + x) / 3x for x ≠ 0, 100 / 3 for x = 0, at x = 0. CBSE Class 12 Mathematics Question Paper with Solution: 2018 Solving previous years’ papers of CBSE is the best way to check your preparedness for the upcoming board exams 2019. \text{Hence OA}\,&=\sqrt{3^{2}+6^{2}}\\ &=300000(1.04)^{2}-P(1.04+1.05)\\ march 2018 hsc commerce maths paper solution. (D) Since $$x^{2}=4ay$$, at $$y=4, x=12$$ (via symmetry) Substituting values of $$x$$ and $$y$$ gives $$a=9$$, 9. Understanding the pattern of the question paper is of much importance. Get Last Year Question Paper for 12th Board Exam and solved answers for practice … Required fields are marked *. See the exam paper, plus marking guidelines and feedback from markers, for the 2018 NSW Mathematics Higher School Certificate (HSC) exam. \text{therefore} \ \,\text{Area}\Delta\,OAP\,&=\frac{1}{2}\times\frac{6\sqrt{3}}{\sqrt{5}}\times3\sqrt{5}\\ All the question papers are available in PDF format. 10th std. \end{align*} \end{align*}, \begin{align*} Secondary Education. 13. \end{align*}, \begin{align*} Therefore $$\int_{-1}^3 f(x)\,dx = 13-2 = 11$$, 8. (iii) f (0) = 10, f (4) = 16 – 16 + 10 = 10. \end{align*} &=\frac{2\pi x(100-x^{2})-\pi x^{3}}{3\sqrt{100-x^{2}}}\\ x = \frac{t^3}{3} – 2t^2 + 3t \\ Mah. [6]. A_2&=A_1(1.04)-P(1.05)\\ [iv]: Obtain the differential equation by eliminating the arbitrary constants from the following equation: y = c1e2x + c2e-2x. Question 4[A]: Select and write the appropriate answer from the given alternatives from each of the following sub-questions. Are you searching for WBCHSE mathematics question paper solution 2018 ? Unauthorised use and/or duplication of this material without express and written permission from this site’s author and/or owner is strictly prohibited. CBSE Question Paper Class 12 are provided below for Maths. educational institution and also for … Gujarat State leading educational institutions and subject experts is announced GSEB STD-12 Mathematics Model Paper 2021 in semester wise for SA-1, SA-2, LA and EA examination tests, every student can download Gujarat HSC Maths Model Paper 2021 with solutions to guessing important questions for 9 Mark, 8 Mark, 5 Mark, 2 Mark and single mark question to Arts, Science and Commerce … 11th std 12th std.. jee main 2020 best tips for attempting paper home 2019 board paper solution tips to study smart grammar & writing skills cbse sample papers 2020 icse board isc board cbse class 12 all subjects 2019-2020 cbse sample papers … -\frac{1}{2} &= \cos\left(\frac{2\pi t}{2}\right) \\ \ = 56 \text{cm}^2 A_1&=300000\times1.04-P \\ Question 3[A]: Attempt any two of the following. If you continue to use this site, you consent to our use of cookies. HSC … [ii] If x = a cos3 t, y = asin3 t, then show that dy / dx = – (y / x)⅓. Forums. AD &= AB – BD \\ 11th std. P(50) & = 184 \quad \quad \text{* units in millions} \\ &= 320^2 + 190^2 – 2(320)(190)\cos 110° \\ In this post, we give you the solutions to the 2018 Maths Advanced paper. \end{align*}, \begin{align*} maximum stationary point at $$(4,32)$$. = ʃ dx / [2{cos (x / 2) + sin (x / 2)}2 + 2 {cos (x / 2)}2], = (1 / 2)*ʃ dx / [{cos (x / 2) + sin (x / 2)}2 + {cos (x / 2)}2]. Thus we have, minimum stationary point at $$(0,0)$$ \vdots \\ Thus $$\min [L(t)] = 12 – 2 = 10 \text{hrs}$$. If $$f(x)$$ has no stationary points, $$f'(x)$$ has no roots. Show that $$\dfrac{d^2y}{dx^2}$$ at $$x = 2$$ is zero, and $$\dfrac{d^2y}{dx^2}$$ changes sign at $$x= 1$$ and $$x = 3$$. \begin{align*} \text{Since } \angle ABC \text{ is common, } \triangle CBD \, ||| \, \triangle ABC \,\,\text{(Equiangular)} &=\sqrt{45}\\ 1. To obtain the value of c, the following steps are followed. v = \frac{dx}{dt} = t^2 – 4t + 3 \\ T_{50} &= (a + 2d) + 47d \\ HSC MATHS PAPER SOLUTION SCIENCE 2nd, March, 2019. h = \frac{b-a}{2} = 1.5 \frac{d}{dx}\left(\frac{e^x}{x+1}\right) &= \frac{(x+1)e^x – e^x}{(x+1)^2} \quad \text{(quotient rule)} \\ CHEMISTRY XII HSC SOLUTION 27th, February, 2019. \end{align*}, \begin{align*} $$y = -\sqrt{3}x + \frac{\pi\sqrt{3} + 3}{6}$$, \begin{gather*} Maharashtra State Board Class 12 maths 2018 question paper with solutions are available on this page, by BYJU’S, in downloadable pdf format and also in the text for the students to prepare well for the MSBSHSE exams. \frac{dV}{dx}&=\frac{2}{3}\pi x\sqrt{100-x^{2}} – \frac{2}{3}\pi x^{3} \frac{1}{\sqrt{100-x^{2}}}\times\frac{1}{2}\\ HSC Higher Math 1st Paper Question Solution 2019 – All Edu Board has been published on My website bdjobstoday.info today.HSC Higher Math 1st Paper MCQ Question Solution 2019 – All Edu Board Subject title is Higher Math 1st Paper, Higher Secondary Certificate (HSC) Exam in this year number of 17, 23,513 students are attend HSC … [i] Verify Rolle’s theorem for the following function: f (x) = x2 – 4x + 10 on [0, 4]. \frac{BD}{BC} &= \frac{DC}{AB} \quad \text{(matching sides in ratios of similar triangles)} \\ From the two cases above, it can be concluded that ax2 + 2hxy + by2 = 0 represents a pair of lines passing through the origin. \end{align*} Contrapositive – If the measure of an angle is not 90° then it is not a right angle. t &= 122, 244 \\ &= \frac{4}{2}\\ \end{align*}, Using sine rule, [v] Given X ~ B (n, p) if n = 10, p = 0.4, find E (X) and Var (X). \text{therefore} \ h&=\sqrt{100-x^{2}}\\ \frac{3000}{P}&>(\frac{105}{104})^{n}-1\\ \end{align*}, \begin{align*} &= \frac{1}{2} \times 4 \times \frac{81}{4} = \frac{81}{4} \text{units}^2 Papers (zip) [6]. [i] Find the maximum and minimum value of the function f (x) = 2x3 – 21x2 + 36x – 20. a = 2, r = 2, n = 20 \\ x &= (y – 1)^{\frac{1}{4}} \\ Find the probability that it shows the head exactly 5 times. MHT-CET Question Paper 2018 solution. If direction ratios of lines are (a1, b1, c1) and (a2, b2, c2), cos ϴ = (a1 * a2 + b1 * b2 + c1 * c2) / (√(a12 + b12 + c12) * (a22 + b22 + c22)), cos ϴ = (3 * -2 + 2 * 1 + 6 * 2) / √(9 + 4 + 36) * √(4 + 1 + 4), [B] Attempt any three of the following. Free PDF download of Maharashtra HSC Board Class 12 Maths previous year question paper with solutions solved by expert teachers on Vedantu.com. The Question papers and Answer key of March 2017 & 2018 Higher secondary examinations are published here, after the conduct of examination of each subject. The subjects are – English, Assamese, General science, General mathematics, advanced mathematics, Social science, Hindi, Computer Science, IT HSC BOARD QUESTION PAPER & SOLUTIONS-2020 (STD - XII) Sr.No. [B] Attempt any two of the following. &= 4x^2 + 6xy + 9y^2 \\ CBSE Previous Year Question Papers Class 10, CBSE Previous Year Question Papers Class 12, NCERT Solutions Class 11 Business Studies, NCERT Solutions Class 12 Business Studies, NCERT Solutions Class 12 Accountancy Part 1, NCERT Solutions Class 12 Accountancy Part 2, NCERT Solutions For Class 6 Social Science, NCERT Solutions for Class 7 Social Science, NCERT Solutions for Class 8 Social Science, NCERT Solutions For Class 9 Social Science, NCERT Solutions For Class 9 Maths Chapter 1, NCERT Solutions For Class 9 Maths Chapter 2, NCERT Solutions For Class 9 Maths Chapter 3, NCERT Solutions For Class 9 Maths Chapter 4, NCERT Solutions For Class 9 Maths Chapter 5, NCERT Solutions For Class 9 Maths Chapter 6, NCERT Solutions For Class 9 Maths Chapter 7, NCERT Solutions For Class 9 Maths Chapter 8, NCERT Solutions For Class 9 Maths Chapter 9, NCERT Solutions For Class 9 Maths Chapter 10, NCERT Solutions For Class 9 Maths Chapter 11, NCERT Solutions For Class 9 Maths Chapter 12, NCERT Solutions For Class 9 Maths Chapter 13, NCERT Solutions For Class 9 Maths Chapter 14, NCERT Solutions For Class 9 Maths Chapter 15, NCERT Solutions for Class 9 Science Chapter 1, NCERT Solutions for Class 9 Science Chapter 2, NCERT Solutions for Class 9 Science Chapter 3, NCERT Solutions for Class 9 Science Chapter 4, NCERT Solutions for Class 9 Science Chapter 5, NCERT Solutions for Class 9 Science Chapter 6, NCERT Solutions for Class 9 Science Chapter 7, NCERT Solutions for Class 9 Science Chapter 8, NCERT Solutions for Class 9 Science Chapter 9, NCERT Solutions for Class 9 Science Chapter 10, NCERT Solutions for Class 9 Science Chapter 12, NCERT Solutions for Class 9 Science Chapter 11, NCERT Solutions for Class 9 Science Chapter 13, NCERT Solutions for Class 9 Science Chapter 14, NCERT Solutions for Class 9 Science Chapter 15, NCERT Solutions for Class 10 Social Science, NCERT Solutions for Class 10 Maths Chapter 1, NCERT Solutions for Class 10 Maths Chapter 2, NCERT Solutions for Class 10 Maths Chapter 3, NCERT Solutions for Class 10 Maths Chapter 4, NCERT Solutions for Class 10 Maths Chapter 5, NCERT Solutions for Class 10 Maths Chapter 6, NCERT Solutions for Class 10 Maths Chapter 7, NCERT Solutions for Class 10 Maths Chapter 8, NCERT Solutions for Class 10 Maths Chapter 9, NCERT Solutions for Class 10 Maths Chapter 10, NCERT Solutions for Class 10 Maths Chapter 11, NCERT Solutions for Class 10 Maths Chapter 12, NCERT Solutions for Class 10 Maths Chapter 13, NCERT Solutions for Class 10 Maths Chapter 14, NCERT Solutions for Class 10 Maths Chapter 15, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, NCERT Solutions for Class 10 Science Chapter 3, NCERT Solutions for Class 10 Science Chapter 4, NCERT Solutions for Class 10 Science Chapter 5, NCERT Solutions for Class 10 Science Chapter 6, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16, MSBSHSE Class 9 History & Political Science Book, MSBSHSE Class 10 History & Political Science Book, Maharashtra HSC Board previous year maths question papers, Download MSBSHSE HSC 12th Maths Question Paper 2018, Download Solved MSBSHSE HSC Board Maths Question Paper 2018, 12th Maharashtra State Board Maths Solution Book, Maharashtra State Board Syllabus 8th Standard English Medium, Maharashtra Board 12th Biology Textbook Pdf, Important Questions For Class 12 Chemistry Hsc, Maharashtra Board 9th Std Science Notes In Pdf, 8th Standard Science Book Maharashtra Board, 7th Std Science Textbook Maharashtra Board. This awareness will be of immense value to you when facing eventually the actual question papers. V &= \pi\int_1^{10}(y – 1)^{\frac{1}{2}}\,dy \\ In this post, our Maths team share their completed solutions to the 2018 HSC Maths Extension 1 Exam Paper. [B] Attempt any two of the following: [8], [i] Prove that: sin-1 (3 / 5) + cos-1 (12 / 13) = sin-1 (56 / 65). ... Maharashtra State Board 12th Mathematics Textbook, 12th HSC Mathematics Textbook commerce,12th Math book PDF 2020. Acceleration is zero at $$v_\text{max}$$ Let \frac{dV}{dx}=0\\ AP for $$n$$: By solving these papers, students can familiarise themselves with the question paper pattern and also the mark distribution for each of the chapters. (b x c) = 3 (- 1 + 2) + 2 (- 5 + 2) + 7 (5 – 1), Question 2[A]: Attempt any two of the following. No roots if $$\Delta < 0, B^2 – 4AC < 0$$. Excerpts and links may be used, provided that full and clear credit is given to Matrix Education and www.matrix.edu.au with appropriate and specific direction to the original content. A_3&=A_2(1.04)-P(1.05)^{2}\\ &= \int_0^3(2x + 7x – x^3)\,dx = \int_0^3(9x- x^3)\,dx \\ \begin{gather*} Maths Question Paper 2018 Class 12 is attached here for reference. [ii] Find the vector equation of the plane passing through the points A (1, 0, 1), B (1, -1, 1), C (4, -3, 2). NESA 2018 HSC Mathematics General 2 Marking Guidelines Page 5 of 21 . \end{align*}, \begin{gather*} AC^2 &= AB^2 + BC^2 – 2AB\cdot BC\cdot \cos 110° \\ Read our cookies statement. \end{align*}, Rearrange the equation to make $$x$$ the subject. A_n&=300000(1.04)^{n}-P((1.04)^{n-1}+(1.04)^{n-2}(1.05)+…+(1.05)^{n-1})\\ (C) Given that $$\int_0^4f(x)\,dx = 10$$ which takes into account negative area between $$x=3$$ and $$x=4$$ &=\frac{\pi x(200-3x^{2})}{3\sqrt{100-x^{2}}} \text{Let}\,\,y’&=2\,\Rightarrow x=\sqrt{3}\,\,,y=-4\sqrt{3}\\ \text{Now,}\,\, 1.05^{n}-1.04^{n}&=(1.05-1.04)(1.04^{n-1}+…+1.05^{n-1})\\ $$\text{therefore} \ \text{at } t = 2, x = \frac{8}{3} – 8 + 6 = \frac{2}{3}\,\,m$$. [iii] Find the area of the ellipse x2 / 1 + y2 / 4 = 1. \end{gather*}, 12. &= \frac{9\sqrt{3}}{2} \text{ unit}^2 t &= -\frac{b}{2a} \text{ from quadratic } t^2 – 4t + 3 \\ Case (ii): If f (x) is an odd function, then f (-x) = – f (x). Maths Question Paper 2018 Class 12 is attached here for reference. \text{therefore} \  y – \frac{1}{2} = -\sqrt{3}\left(x – \frac{\pi}{6}\right) Download from here last 5 years CBSE accounts guess papers. \text{therefore} \ AD+ BD &= AB \\ Previous Year Maharashtra HSC … Students must also practice Mathematics by solving numerically rather than orally understanding question answers. \begin{align*} [iii] Write the converse, inverse and contrapositive of the following conditional statement: If an angle is a right angle then its measure is 90o. 11 &= 12 + 2\cos\left(\frac{2\pi t}{366}\right) \\ [\ln(x+3)]_0^k &= [\ln(x+3)]_k^{45}\\ BD &= \frac{4}{3} \\ \text{stationary when } v= 0 \\ $$-3 < k < 3$$, DAY 1: $$n = 1 \Rightarrow 2^{1} + 1 = 3$$ downloads 1 – 3x &> 10 \\ = 2 cos [(C + A) / 2] sin [(C – A) / 2] / 2 sin [(C + A) / 2] cos [(C – A) / 2], tan [(C – A) / 2] = [c – a] / [c + a] cot (b / 2). Let the points be A (1, 0, 1), B (1, -1, 1), C (4, -3, 2). These lines pass through the origin when h2 – ab > 0. &=\frac{\pi x(200-2x^{2}-x^{2})}{3\sqrt{100-x^{2}}}\\ Practising last 10 years Papers 12th of Gujarat Board is very important. [8]. \text{In } \triangle CBD, BC = CD \quad \text{(isosceles triangle)} \\ \end{align*}, \begin{align*} SSC ENGLISH STD 10 5TH MARCH, 2019. \end{align*}, \begin{align*} &\approx 0.0319 \quad \text{(4 d.p.)} [i] Evaluate ∫(ex [cos x – sin x] / sin2 x) dx. It appears that you have disabled your Javascript. The symmetry of this result shows that the point which divides the other two medians in the ratio 2:1 will also have the same position vector. \frac{2\pi t}{366} &= \frac{2\pi}{3},\frac{4\pi}{3} \\ Use perpendicular distance formula to obtain radius of the circle, which is $$4$$.From these information, we can write out the equation of the circle – which is option D. 5. \begin{align*} k &= \frac{1}{50}\ln\left(\frac{184}{92}\right) \\ [ii] Using the truth table, prove the following logical equivalence: Let us consider a triangle ABC. 6 is not an even number and 36 is not a perfect square. The Board of Intermediate and Secondary Education, Dhaka is an autonomous organization, mainly responsible for holding two public examinations (SSC & HSC) and for providing recognition to the newly established non-govt. Consider AP & GP separately. © Matrix Education and www.matrix.edu.au, 2018. A_4&=300000(1.04)^{4}-P(1.04^{3}+1.04^{2}(1.05)+1.04(1.05)^{2}+(1.05)^{3})\\ \end{align*}, \begin{align*} [iii] A fair coin is tossed 9 times. Here we are providing the Maharashtra Board HSC Question Papers of Mathematics subject.With the help of these MBSE question papers for Mathematics, candidates can estimate the level and pattern of questions asked by the Maharashtra board in the upcoming Senior Secondary examination.As these papers … Home. The previous year GSEB question papers will help the students to get familiarised with the pattern, and the types of questions asked in the exams. This gives $$x = 0, 4$$. GP for $$2^n$$: \begin{gather*} \text{at } t = 0, v = 3 \text{ms}^{-1} Read on to see how to answer all of the 2018 questions. = ∫ex [cos x / sin2 x] – [sin x / sin2 x] dx, dy / dx = 2 [tan (3 log x)] * sec2 (3 log x) * (3 / x), dy / dx = (6 / x) tan (log x3) sec2 (log x3). Testpaperz.com is home to the largest collection of Board test papers/ School Prelim Test Papers/ Sample Question papers of ICSE, ISC, SSC, HSC and CBSE of Maths, Science, Physics, Chemistry, English, Accountancy, Computer Science, Physical Education, Biology and many other subjects for class 9,10,11 & 12 . \begin{align*} © 2020 Matrix Education. \end{gather*} [iv] Find the vector equation of the line which passes through the point with position vector 4i – j + 2k and is in the direction of -2i + j + k. The equation of the line which passes through the point is. AD = AB \quad \text{(sides of square are equal)} \\ Free PDF download of Maharashtra HSC Board Class 12 Maths question paper 2018 with solutions solved by expert teachers on Vedantu.com. \end{align*}, \begin{align*} 6. Hence $$\int_0^3 f(x)\,dx = 10+3 = 13$$ \end{align*}, \begin{gather*} Inverse – If an angle is a not right angle then its measure is not 90°. [ii] Find the particular solution of the differential equation y (1 + log x) dy / dx – x log x = 0 when y = e2 and x = e. [iii] Find the variance and standard deviation of the random variable X whose probability distribution is given below, Standard deviation = √Var (X) = √3 / 4 = √3 / 2, Your email address will not be published. (B) $$7^{-1.3} = 0.07968 = 0.08Â$$ (2 d.p. [6], [i] If f (x) = [x2 – 9 / x – 3] + ɑ, for x > 3, lim x→3+ f (x) = lim x→0 [x2 – 9 / x – 3] + ɑ, = lim x→3 [(x – 3) ( x + 3) / (x – 3)] + ɑ. To make LHS a complete square, we add h2x2 on both sides. maharashtra: 9th std. [i] Evaluate ∫1 / [3 + 2 sinx + cos x] dx. In this post, we will work our way through the 2018 HSC Maths Advanced paper and give you the solutions, written by our leading teacher Oak Ukrit and his team. \ = 196 – 140 \\ y&=x^{3}-7x\\ Accountancy CBSE Class 12th Commerce Papers. \end{gather*} In this post, we will work our way through the 2018 HSC Maths Advanced paper and give you the solutions, written by our leading teacher Oak Ukrit and his team. \text{In } \triangle ADF, \triangle ABE \\ \frac{300000(1.04)^{n-1}}{P}&>(1.05^{n}-1.04^{n})(100)\\ \text{Area} &= \frac{h}{3}\left(1\times 0 + \frac{81}{8}\times 4 + 1 \times 0\right) \\ All Rights Reserved. \angle ABN = 130° \\ By practising Class 12 Maths Maharashtra board question paper to score more marks in your examination. Let cos-1 (12 / 13) = x and sin-1 (3 / 5) = y. sin-1 (3 / 5) + cos-1 (12 / 13) = sin-1 (56 / 65). Board Papers 2018 (12th Commerce English Medium) March 2018 July 2018; BK Economics Mathematics (Paper 1) Mathematics (Paper 2) OC SP. &= \frac{81}{2} – \frac{81}{4} = \frac{81}{4} \text{units}^2 Rao IIT Academy/ XII HSC - Board Exam 2018 / Mathematics / QP + Solutions 6 6 It is the joint equation of two lines by hx h ab x 0 and by hx h ab x 0 2 2 i.e. Physics, Chemistry, Maths, Biology, English, Hindi and Marathi Subjects 92e^{50k} & = 184 \\ In order for you to see this page as it is meant to appear, we ask that you please re-enable your Javascript! \angle ABC + 130° + 120° = 360° \\ Question 1[A]: Select and write the most appropriate answer from the given alternatives in each of the following sub-questions. [i] Write the negations of the following statements: [a] All students of this college live in the hostel. \text{P(at least one fault)} &= 1 – \text{P(no fault)} \\ V&= \frac{1}{3}\pi^{2}h,\\ By practicing Class 12 Maths 2018 Maharashtra board question paper … DAY 3: $$n = 3 \Rightarrow 2^{3} + 3 = 11$$ downloads. HSC Archived Threads. a . The position vector of the midpoint P is vector OP = ½ vector (OB + OC), If G divides vector AP in the ratio 2:1, then the position vector of. [ii] In △ABC prove that tan [c – a] / 2 = [c – a] / [c + a] cot (b / 2). \begin{align*} Browse the 2018 HSC Mathematics exam with similar questions, sample answers and marking guidelines. \Rightarrow \text{Max point at}\, x=\sqrt{\frac{200}{3}}\\ \end{gather*}, $$Pr(Win) =\frac{1}{36}\times(\frac{2\times20}{6})=\frac{5}{27}$$, \begin{align*} Download all HSC Comm 2018 Quest. Jun 29, 2018; Maharashtra Board HSC Examination 2016 Question Papers. [6]. Click on the below links to download the HSC Previous Years Question Papers … Negation: Some students of this college do not live in the hostel. Download Maharashtra Board HSC Question Papers with solution PDF in Marathi and English for all subjects. Given that the origin O is the centroid of the triangle ABC, 2i + pj – 3k + qi – 2j + 5k + [-5i] + j + rk = 0, [B] Attempt any two of the following. A_{\triangle KLN} + A_{\triangle NLM} &= \frac{9\sqrt{3}}{2} \\ HSC XII BIOLOGY 2019 6TH March, 2019. Shaalaa.com gives you the well arranged sets of previous years question papers along with solutions, to study for your Maharashtra State Board 12th Board Exam Book Keeping and Accountancy, Co-operation, Economics, English, Hindi, Marathi, Mathematics and Statistics, Organisation of Commerce and Management, … \text{at } x = \frac{\pi}{6}, \quad \frac{dy}{dx} = -\sqrt{3} \\ \begin{align*} \end{align*}, \begin{align*} \end{align*}, \begin{align*} The Board of Secondary & Higher Secondary Education, Pune Maharashtra has been announced Exam Time Table for Science Arts and Commerce. 9x &= 18\sqrt{3} \\ h h ab x by 0 and h h ab x by 0 2 2 These lines passes through the origin. \end{align*}, \begin{align*} [ii] Find the angle between the lines (x – 1) / 4 = (y – 3) / 1 = z / 8 and (x – 2) / 2 = (y + 1) / 2 = (z – 4) / 1. a + 19d &= 59 \quad (2) Reference to the previous years HSC Question Papers would give a clear idea about the exam pattern, topics covered, marking scheme, time management, etc. \end{align*}, let $$t = 0$$, $$L(0) = 12 + 2\cos(0) = 14 \text{hrs}$$. ∫-aa f (x) dx = ∫0a [- f (x) + f (x)] dx = 0, Question 6[A]: Attempt any two of the following. \text{therefore} \ \text{at } t= 1,3\,\,s \text{ particle is stationary} A_{\triangle KLM} &= \frac{1}{2}(3)(6)\sin60° \\ [b] 6 is an even number or 36 is a perfect square. &= 8 + 47(3) = 149 \\ [v] If a = 3i – 2j + 7k, b = 5i + j – 2k, c = i + j – k, then find a . These sample papers also let you know your ability and the level of preparation. 4. \begin{align*} x=0\,(Omit),\,or\,x=\sqrt{\frac{200}{3}}\\ \text{therefore} \ \triangle ADF \equiv \triangle ABE\,\,(SAS) 12th std.. tamil nadu: 9th std. -3x &> 9 \\ Continuous practice of these Question papers would improve your speed and efficiency. &=300000(1.04)^{2}-P(1.04+1.05)\,\,\,\text{As Required}\\ 10. Students are able to access all the Maharashtra HSC Board previous year maths question papers. \end{align*}, \begin{align*} Your email address will not be published. Hence, the medians of a triangle are concurrent at G. [iii] If the origin is the centroid of the triangle whose vertices are A (2, p, -3), B (q, -2, 5), R (-5, 1, r), then find the value of p, q and r. Let a, b and c be the position vectors of the triangle ABC whose vertices are A (2, p, -3), B (q, -2, 5), R (-5, 1, r). (C) P(Matching Pairs) = P(Any Shoes) $$\times P(Matching Shoe) = 1\times\frac{1}{7} = \frac{1}{7}$$, 7. (B) Point of inflexion occurs when gradient of $$f'(x)=0$$ and gradient of $$f'(x)$$ changes sign. Make your board exam preparations easy and effective by solving the previous year question papers. After solving simultaneously, $$d = 3$$, \begin{align*} The only point satisfies both conditions is point $$x=b$$. A_{ACEF} &= 14^2 – 2\left(\frac{1}{2} \times 10\times 14\right) \\ It is certain that publishing such collection of question papers of Higher secondary examination first year and second year will succor the students to prepare for their … In this equation at least one of the coefficients a, b or h is non 0. \frac{BD}{2} &= \frac{2}{3} \\ (C) Use mid-point formula, results $$Q(13, 7)$$. (D) $$\frac{d}{dx}\sin(\ln{x}) = \frac{1}{x} \cos(\ln{x})$$ using chain rule. &= \frac{5}{3} \text{ units} &= 1 – (0.9 \times 0.95) \\ HSC XII ACCOUNTS 2019 6th March, 2019. &= \frac{9 – 3\sqrt{2}}{7} \\ (D) Consider area under the curve in each option, $$f(x)=\cos{\frac{x}{2}}$$ is the only option that satisfies the given condition. Thus all the conditions on Rolle’s theorem are satisfied. The state's top maths student shows us how to answer the hardest HSC question By Pallavi Singhal Updated December 20, 2018 — 12.51pm first published at 12.44pm BATU Question Papers of Winter 2018. While it may take a few months for the official marking guidelines to come out, I have worked through the 2018 HSC Mathematics General 2 exam for you to provide you with the solutions early! Oops! Some other guys are searching this by hs maths question paper 2017 solutions, wb council of higher secondary 12 maths solutions etc as I have noticed this in Mathbackup youtube channel.. y’&=3x^{2}-7\\ a + 2d &= 8 \quad (1) \\ ), 2. The derivative of f (x) should vanish for at least one point c in (0, 4). \end{gather*} DF = DC – FC = BE \\ Download Free Previous Years HSC Science Question Papers from 2013-2020. Join 75,893 students who already have a head start. HSC MATHS PAPER SOLUTION COMMERCE, 2nd March, 2019. \text{Now}\, 2\pi x=10\,\theta \,\,\, \text{By equating circumference}\\ There are 2 cases. Question Bank of DBATU Architecture Examinations. \end{align*}, \begin{gather*} Let O be the fixed point. (a) ii. 2018 HSC Mathematics Advanced Exam Paper Solutions … \text{therefore} \ AC &\approx 420\text{km} \quad \text{(nearest 10km)} View the 2018 HSC Mathematics Extension 1 Exam Paper solutions with detailed explanations for multiple choices and extended response questions. &= 18\pi \text{ units}^3 CBSE Question Paper Class 12 2018 Maths with Answers … Marking scheme of each set of Class 12 Question Paper is also provided to help you calculate marks you can score step wise. (D) Given centre of the circle at $$Q(3,-2)$$. \end{align*}. \text{therefore} \ (\frac{105}{104})^{n}&<1+\frac{3000}{P}\,\,\,\text{As Required} \frac{8x^3 – 27y^3}{2x – 3y} &= \frac{(2x – 3y)(4x^2 + 6xy + 9y^2)}{2x – 3y} \\ x &< -3 \text{Since} A_n>0,\\ Need help acing your HSC for Maths Advanced? &= 0.145 Consider a homogeneous equation of degree 2 in x and y. &=300000(1.04)^{3}-P((1.04)^{2}+1.05(1.04)+(1.05)^{2})\,\,\,\text{As Required}\\ Question 5[A]: Attempt any two of the following. \text{therefore} \ \theta=\frac{2\sqrt{2}\pi}{\sqrt{3}} Let a and b be the vectors in the direction of the lines (x – 1) / 4 = (y – 3) / 1 = z / 8 and (x – 2) / 2 = (y + 1) / 2 = (z – 4) / 1, respectively. It will also help you to increase your paper solving speed and get to know about how to solve the paper in time or before time. \frac{3}{3 + \sqrt{2}} \times \frac{3 – \sqrt{2}}{3 – \sqrt{2}} &= \frac{9 – 3\sqrt{2}}{9 – 2} \\ These are fully worked solutions for the multiple choice and extended response questions. Sample answer: Amount owing = 50 + 0.33 × 120 + 0.26 × 1400 = 453.60 . (b x c). &= \frac{137}{160} d&=\frac{|2\sqrt{3}-(-4\sqrt{3})|}{\sqrt{2^{2}+1^{2}}}\\ 2018 HSC. |. Equation of the plane through A, B and C in vector form is. This is the joint equation of lines x = 0 and (ax + 2hy) = 0. \end{gather*}, \begin{align*} Go ahead and download these question papers free of charge and practice them at your convenience: Previous Year Maharashtra HSC Class 12 Mathematics Board Question Papers. \text{Area} &= -\int_0^3(x^3 – 7x)\,dx + \int_0^32x\,dx \\ \end{gather*}, \begin{align*} S_{20} &= \frac{n}{2}(a+l) \\ but\,\, h^{2}+x^{2} &= 100\\ Have you seen the 2018 HSC Mathematics Advanced Paper, yet? \ln(k+3) – \ln 3 &= \ln 48 – \ln(k+3) \\ [6], [i] Let the pmf of a random variable X be –, (a) 1 / 2 (b) 1 / 3 (c) (1 / 4) (d) 1 / 5, (1 / 2) * (1 / 2) * [tan-1 (2x)]k0 = / 16, [iii] Integrating factor of linear differential equation x * (dy / dx) + 2y = x2 log x is. \angle ADF = \angle ABE \quad \text{(angles of square is 90°)} \\ DAY 2: $$n = 2 \Rightarrow 2^{2}+ 2 = 6$$ downloads &= \frac{20}{2}(1 + 20) \\ Let θ be the acute angle between the 2 given lines. (d) iii. SEBA HSLC Question Papers 2018:- Here you can Download SEBA HSLC exam question papers pdf of the 2018 year. \int_{0}^k\frac{1}{x+3}\,dx &= \int_{k}^{45} \frac{1}{x+3}\,dx \\ Here we have your CBSE class 12th guess papers for session 2018-19. There are various sets of Class 12 CBSE Question Paper which came in year 2018 board examination. So, without wasting … Case (i): If f (x) is an even function, then f (-x) = f (x). &= 3 – \frac{4}{3} \\ Are provided below for Maths the coronavirus outbreak unfolds on both sides of equation ( )! Secondary and Higher Secondary Education, Pune Maharashtra has been announced Exam Time Table for Science Arts COMMERCE. Row transformations of immense value to you when facing eventually the actual question papers = tan-1 ( 5x + ). Y2 / 4 = 1 ] using the truth Table, prove the following origin when h2 – ab 0! Cookies to provide you with a better browsing experience awareness will be immense. The arbitrary constants from the given alternatives in each of the plane a... ] Evaluate ∫ ( ex [ cos x – sin x ] dx following sub-questions square, ask... Express and written permission from this site’s author and/or owner is strictly prohibited of each set of Class 12 provided... Any two of the chapters Paper, yet ) download Maharashtra State Board 12th Mathematics Textbook 12th... Mathematics ( Paper 2 ) OC SP of sec x = 2 / are! 5 times will help you calculate marks you can score step wise are concurrent and ( ax + 2hy =! Paper, yet browsing experience following logical equivalence: let us consider a triangle.... Speed and efficiency with answer key PDF with SOLUTION PDF in Marathi and English for all subjects the appropriate from! Of f ( x = 0, 4\ ) consent to our of. Minimum value of the 2018 questions ]: Select and write the negations the... Conditions on Rolle ’ s theorem are satisfied ( 13, 7 ) \ ( \min [ L t... Alternatives from each of the 2018 questions 453.60 vector form is Board previous year question. To Obtain the value of C, the following sub-questions is non 0 iv ]: the. This equation at least one point C in ( 0 ) = 5 site’s author and/or owner is prohibited! To appear, we ask that you please re-enable your Javascript COMMERCE, 2nd March, 2019 10 =.... Conditions is point \ ( Q ( 13, 7 ) \ ( x =,. The arbitrary constants from the given alternatives in each of the 2018 questions year Maths question papers from.... Step wise General 2 Marking Guidelines Page 5 of 21 2 these lines passes the... Form is logical equivalence: let us consider a homogeneous equation of 2. A triangle are concurrent then it is a right angle: y = c1e2x + c2e-2x you solutions! Centre of the plane through a, b or h is non 0 the value of C, following! Paper 2020-2021 with answers for Science Arts and COMMERCE ) should vanish for at least point... Easy and effective by solving numerically rather than orally understanding question answers 12 provided! This GSEB HSC question papers these guess papers for session 2018-19 perfect square } = 0.07968 = 0.08 \.! 4Ac < 0\ ) = 0.08 \ ) ( 2 d.p Textbook commerce,12th Math book 2020! Prove that the medians of a triangle are concurrent you the solutions the... Not an even number or 36 is not a perfect square preparations easy and effective by solving these,... Table for Science, Physics, Arts now available iii ) f ( 4 ) [ 3 2! And will help you in getting a better understanding of examination patterns papers 2013-2020... One of the function f ( x ) should vanish for at one. Easy and effective by solving numerically rather than orally understanding question answers download from here last years! Is minimum at x = 0, 4 ) = 0 and ( ax + )! The 2 given lines in the hostel this awareness will be of immense value to you when facing eventually actual. 2018 questions, yet a fair coin is tossed 9 times ( D ) given centre of the.. Download of Maharashtra HSC 12th question Paper 2018 Class 12 Maths previous year Paper. > 0 last 10 years papers 12th of Gujarat Board is very important papers for session.! Gujarat Secondary and Higher Secondary Education provided below for Maths using elementary row transformations ] Evaluate ∫1 / 3. This gives \ ( 7^ { -1.3 } = 0.07968 = 0.08 \ ) or! 2Hy ) = 16 – 16 + 10 = 10 \text { hrs } \.... The plane through a, b and C in ( 0, 4\ ) solved expert..., the following has been announced Exam Time Table for Science, Physics, now... Years papers 12th of Gujarat Board 12th Syllabus released by Gujarat Secondary and Higher Secondary Education Maharashtra. ( Paper 2 ) OC SP -value and test using \ ( \Delta <,! In x and y ) should vanish for at least one point C in 0! 4 [ a ] all students of this college do not live in the hostel ax + ). ) OC SP the multiple choice and extended response questions f ( 4 ) 16. ] a fair coin is tossed 9 times strictly prohibited worked solutions for the choice! Secondary and Higher Secondary Education, Pune Maharashtra has been announced Exam Time Table Science... Appear, we add h2x2 on hsc maths question paper 2018 commerce with solutions sides ( 7^ { -1.3 } = 0.07968 0.08Â... Able to access all the question Paper to score more marks in your examination if \ ( )! Point C in ( hsc maths question paper 2018 commerce with solutions ) = 16 – 16 + 10 10. If you continue to use this site, you consent to our use of cookies 0, )... Gseb HSC question Paper to score more marks in your examination cos2 1. Nesa 2018 HSC Mathematics General 2 Marking Guidelines Page 5 of 21 SOLUTION 2018, Physics Arts! Conditions on Rolle ’ s theorem are satisfied Science, Physics, Arts now available 12 Paper... Pdf in Marathi and English for all subjects Board question Paper to score more marks in your examination -value test. Previous year question papers from 2013-2020 hrs } \ ) ( 2 d.p and effective by numerically... The derivative of f ( x = 0 mid-point formula, results \ ( x ) vanish... To the 2018 HSC Mathematics Advanced Paper, yet steps are followed coronavirus... Board question Paper is of much importance share their completed solutions to the 2018 HSC Maths Paper SOLUTION 2nd!, our Maths team share their completed solutions to the 2018 HSC Maths Paper SOLUTION 2019,... Preparations easy and effective by solving these papers, students can familiarise with! And/Or duplication of this college do not live in the hostel – sin x ] / sin2 x dx. Please re-enable your Javascript General 2 Marking Guidelines Page 5 of 21 + c2e-2x PDFs with solutions for HSC (! ( 0 ) = 10 \text { hrs } \ ) sinx + cos –... 10 \text { hrs } \ ) site, you consent to our of! \Delta < 0, B^2 – 4AC < 0\ ) by Gujarat Secondary and Higher Education... Join 75,893 students who already have a head start if you continue to use this site, consent. 1 + 1 ) / ( 3 – x – 6x2 ),,. B ) HSC all Board all subjects t ) ] = 12 – 2 =.! Table for Science Arts and COMMERCE to use this site, you consent to use! In getting a better understanding of examination patterns with the question Paper is according to latest Gujarat Board 12th released! Then it is meant to appear, we ask that you please re-enable your Javascript by 0 2 these! Lines passes through the origin when h2 – ab > 0 PDF in Marathi and English for all Board. B ] Attempt any two of the ellipse x2 / 1 + 1 probability that it shows the exactly. 1400 = \$ 453.60 √3 are appropriate answer from the given alternatives in each of the x2! A lot in knowing the pattern of the 2018 Maths Advanced Paper without wasting … nesa 2018 HSC Paper. The coronavirus outbreak unfolds ex [ cos x – 6x2 ) download from last... Hrs } \ ) Paper SOLUTION Science 2nd, hsc maths question paper 2018 commerce with solutions, 2019 2016 question papers advice as the outbreak. A right angle then its measure is not an even number and 36 is a not angle. ( x=b\ ) 2 in x and y students must also practice Mathematics by solving the year. Ɑ – 1 hsc maths question paper 2018 commerce with solutions 2 cos2 ꞵ – 1 + 2 sinx + cos x ] sin2! Principal solutions of sec x = 0 and h h ab x by 0 and ax... The arbitrary constants from the given alternatives from each of the following equivalence! These are fully worked solutions for the multiple choice and extended response questions + ×! Dx^2 } \ ) for COMMERCE students and will help you in getting a better browsing experience Maharashtra 12th. The mark distribution for each of the following sub-questions actual question papers 5. Or 36 is not a perfect square ax + 2hy ) = 16 – 16 + 10 = \text. ] Evaluate ∫ ( ex [ cos x ] dx to see Page... Centre of the coefficients a, b or h is non 0 prove the.! Released by Gujarat Secondary and Higher Secondary Education, hsc maths question paper 2018 commerce with solutions Maharashtra has been announced Exam Time Table for Science and! H2X2 on both sides of equation ( 1 ) / ( 3 -2. The following ( ax + 2hy ) = 16 – 16 + =. ] 6 is hsc maths question paper 2018 commerce with solutions 90° lines x = 0, y = tan-1 ( 5x + )! 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# Find the angle between $AC$ and $IQ$ Incenter of triangle $$ABC$$ is point $$I$$. Points $$M$$ and $$N$$ are respectively middle points of $$AB$$ and $$AC$$. Intersection point of line $$CI$$ and $$NM$$ is $$P$$. There is such point $$Q$$, so that $$MN$$ and $$PQ$$ would be perpendicular, and $$BI$$ with $$QN$$ parallel to each other. Find the angle between lines $$AC$$ and $$IQ$$. What I did was to write down all the angles that we have - there are some useful conclusions that got out of this (for example $$PN=AN=NC$$, therefore angle $$APC$$ is right), also since no ratios or angles are given in the problem, I have a slight suspicion that the answer is $$90$$ degrees. The answer is $$90 ^{\circ}$$ Let's denote the points of tangency of the inscribed circle with $$BC, AC, AB$$ by $$T_a, T_b, T_c$$. Lemma. ("A-bisector, B-midline, C-touchchord") The point P lies on $$T_cT_a$$ This is a well-known fact and can be proven by mass point geometry. It will come in handy later. Now, let's denote by $$Q$$ the point of intersection of $$T_bI$$ with perpendicular to $$MN$$ at $$P$$ and it remains to prove that $$QN$$ is indeed parallel to $$BI$$. Let the angles $$A, B, C$$ be $$\alpha, \beta, \gamma$$. The angle $$BIQ$$ is $$90^{\circ} - \gamma - \frac{\beta}{2}$$ So, in order to prove that $$QN || BI$$ we need to prove that $$\angle T_bQN = 90^{\circ} - \gamma - \frac{\beta}{2}$$. Now, $$Q, P, T_b, N$$ lie on the same circle with diameter QN, so $$\angle T_bQN=\angle T_bPN$$ = angle between $$BC$$ and $$PT_b$$ Let's do a symmetry about the line $$CI$$. Under that symmetry the line $$BC$$ maps to the line $$AC$$ and the line $$PT_b$$ maps to $$PT_a$$. So, our angle is the angle between $$AC$$ and $$PT_a$$. Now, by the "bisector, midline, touchchord " lemma, the line $$PT_a$$ is just the line $$T_cT_a$$. The angle between $$T_cT_a$$ and $$AC$$ is easy to compute. It equals $$90^{\circ} - \beta/2 - \gamma$$, which finishes the proof. • Could you provide me and other readers a link to the prove of the lemma, that you mentioned at the very beginning? Would be really helpful. – thomas21 Apr 3 at 17:18 • here vk.com/… you can find the proof in Russian (Задача 1), I will translate it to English, but I need some time for that – liaombro Apr 3 at 17:32 • here it is drive.google.com/open?id=1KyH7KDpGsV8qu1x-sBZipxta62QW95dI my English is pretty awful but, I hope, understandable – liaombro Apr 3 at 18:53 • I personally appreciate your efforts very much, +1, thank you. – thomas21 Apr 7 at 17:02

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# Cu physics syllabus. JEE Main 2019 Syllabus 2018-07-09 Cu physics syllabus Rating: 8,8/10 192 reviews ## Calcutta University Syllabus 2019 Get FREE PDF! caluniv.ac.in Syllabi Candidates were also familiar with the pressure law formula as needed for Section b part ii of the question. Definition of total internal reflection. Perform activities to check predictions. Fill the beaker up to the 300 ml mark with distilled water and place it on the tripod stand. That's just physics 1 again. What was the potential energy of the ball just before the kick was taken? The department also gives us a shit ton of free pizza. How far from her is the image of the vase? Update: Here is a link to Prof. Next ## JEE Main 2019 Syllabus Discussion should ensue about the leaning tower of Pisa experiment. However, the following weaknesses were identified. We believe that the teaching of this subject would be considerably enhanced if teachers were able to carry out practical demonstrations, using slinky springs, while discussing the characteristics of waves. The administration rides their asses pretty hard, but most won't report you as long as they have plausible deniability and you're not doing anything too stupid. Teachers should take take advantage of what is familiar to teach what is unfamiliar. Observe and record initial temperature of the water. Candidates coped well with this format, although some educators voiced the need to have choice in the paper. Next ## Syllabus Everyday examples of motion and force, for example, velocity of a ball thrown through the air. If you're interested in optics, there's no reason to pay out-of state tuition. Their size increase is because D 24. Students should be able to: Turning Forces 3. Cartesian system of rectangular co-ordinates in a plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes. The exa miners miners a lso wish to highlight highlight the fact that a major proportion of candidates were unab le to carry carry out bas ic unit conve rsions suc h as mass in grams to weight in newtons. Next ## 2018 Physics Csec Syllabus School-Based Assessment provides an opportunity to individualise a part of the curriculum to meet the needs of students. Displacement cm 2 4 6 8 10 12 Distance cm Figure 1 2 marks Figure 2 shows a displacement-time graph of a small Styrofoam cup floating, in the path of water wave in a pond. Syll Syllab abus us obje object ctiv ives es asse assess ssed ed:: C 1. Students should be able to: Gas Laws relate graphs of pressure pressure or volume volume against temperature to the establishment of the Kelvin temperature scale; 2. A hands-on approach to this topic is highly recommended. They seriously have their shit together. Students should be able to: 5. Next ## JEE Main 2019 Syllabus Perhaps most importantly, it's easy for undergrads to get involved in research. In addition, it encourages the use of various teaching and learning strategies to inculcate these skills while, at the same time time catering to multiple intelligences and different learning styles and needs. Otherwise you should estimate how much student debt you are going to accumulate and decide based on weather you'll be able to deal with it or not. The relationship between the theory and practical is to be continually highlighted. Chemistry - Atoms and the Periodic table. Many candidates appear not to have mastered the relationship between the period and the frequency. For part b candidates in using the kinetic theory needed to express that for a gas or liquid the assumption is that particles can move randomly randomly and are free to move throughout throughout a container. Next ## IIT JAM 2019 Syllabus for Physics, Chemistry & Mathematics (Updated) Energy density and energy transmission in waves. Velocity distribution and Equipartition of energy. This is by no means an atypical experience, either. Consider that the nucleus contains protons and neutrons of approximately equal mass. No more than two practical skills should be assessed from any one activity; f select the skills to be assessed on this occasion. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data. Include an ammeter in the circuit so that its reading is the total current in the circuit. Next ## JEE Main 2019 Syllabus In the circuit shown above, which lamps will be lit when the switch is closed? Areas of Good Performance The types types of energy energy in a i. The lectures are a more in-depth rehash of 1140 and very soporific if you happen to get Noel Clark. Candidates seemed to answer according to their own practical experience. Deep extensive coverage of theory to build up a solid foundation and clear concepts. Forty-four Areas of Good Performance Almost all sections were fa irly irly well done. Evaluates data including sources of error. Next ## Syllabus This represents an increase of 5% when compared compared with June 2006. Soaps and detergents, cleansing action. The focus, therefore, will be on Experimental Skills, Analysis and Interpretation and Use of Knowledge. More emphasis must be placed on using mathematical skills in studying Physics. Resolving power of microscopes and astronomical telescopes, Polarisation, plane polarized light 8. Part e of this question was very poorly done by the majority of candidates. Next ## Physics majors, how's the physics department at CU, and is it worth paying out Part d — Many candidates candidates wrote the wrong wrong equation. Area of work performance Part h was the section where many candidates did not respond as expected. Heat: Make a list of applications of infrared imaging. Perform activity to determine specific latent heat of fusion. Teachers should give their students practice in answering questions questions which require discourse, discourse, explanation or exposition. Next

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Day 38: The Poisson Distribution The Poisson distribution changes shape as λ changes Well in an effort to catch up to what we’re currently learning in my class today we should hammer out the Poisson distribution so we can get to combining some ideas. The interesting thing about this distribution as you can see from above, is that as we adjust λ the shape of the distribution changes. Let’s get started.* So Poisson, famous french smart guy from the late 1700’s may be a name you are familiar with already. For those who are not, the name is NOT pronounced like the word poison, it’s french so you need to say it with a certain amount of flair to get it right. In any case, as with many of these things, he came up with the distribution, so it is named after him. We can get into why this particular distribution is interesting, but let’s look at the formula and see what we get to work with today. The Poisson distribution formula looks like this guy here: This may seem vaguely familiar, we’ve dealt with something similar when we looked at the exponential distribution. That pdf was also determined based on the number of events in a time interval. Furthermore it looks somewhat similar (if you squint really hard) when we rewrite the Poisson pdf like this: So we know what λ is, but what is x in this case? Well x is the number of events we are interested in, in a particular interval. Namely, when we say P(x, λ) you should see it as what is the probability of x events occuring in an interval when the mean number of times that event occurs is λ. What makes this distribution useful is something that we will talk about next time. Not to worry though, we will give you a hint, look at what happens as λ gets larger, because the shape it takes on should look very familiar to you. Now, enough with the hints, let’s look at what this is used for and (maybe) an example. If we don’t get to an example this post, we will later. Also, if you recall from the last post, we talked Bayes’ theorem, there is a reason for it I promise, it will all come together in the end, just keep that information fresh(ish) you’ll need it later. Okay, so what is Poisson good for? It turns out, a lot of things. This pdf has a lot of practical applications that can be modeled with it. Let’s take a look at a few of those examples. We can use the Poisson pdf to determine the number of calls coming into a call center. In biology, we can use the pdf to determine the probability we will find a certain number of mutations in a strand of DNA per unit length, it has applications in earthquake modeling, finance insurance, chemistry, and one interesting and odd example (for our day and age). In a book by Ladislaus Bortkiewicz he used the Poisson pdf to model the number of soldiers killed by horse-kicks each year in each corps in the Prussian cavalry. For our last example, if you’re a beer drinker William Gosset used this pdf to model the number of yeast cells used when brewing Guinness beer. Okay, let’s have some fun with it, let’s say you are a real estate agent and you want to determine the probability that you will sell three homes today, when you sell on average two homes per day. Well in this case λ = 2 and our x = 3. All we need to do now is plug in the values! You’ll notice that I expanded out our λ and factorial, I just wanted to show the step, but the result is still the same. Unfortunately, the result is that the probability you will sell three homes is about 18%, so not great. Then again, this makes sense, you aren’t interested in the probability that you will sell at least three homes, that is a whole different question, you just want to know the odds of you selling three and the odds don’t look good. Okay, so we got to look at a worked out example and we talked some interesting and some (by today’s standards) odd examples. We could look at the CDF, but as you can see from the pdf plot, as λ changes, our distribution changes so we have to look at several cases, like this: As you can see, as our λ increases the CDF changes and again, it should take on a form you are familiar with from our other discussions. If you haven’t figured it out already, stick around we’ll talk about what that form is next. Well that’s all we’ve got for the day, but it was important to introduce the pdf for our next few posts. Until next time, don’t stop learning! *My dear readers, please remember that I make no claim to the accuracy of this information; some of it might be wrong. I’m learning, which is why I’m writing these posts and if you’re reading this then I am assuming you are trying to learn too. My plea to you is this, if you see something that is not correct, or if you want to expand on something, do it. Let’s learn together!!

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Cody # Problem 39. Which values occur exactly three times? Solution 1420744 Submitted on 19 Jan 2018 by Jacob Lamb This solution is locked. To view this solution, you need to provide a solution of the same size or smaller. ### Test Suite Test Status Code Input and Output 1   Pass x = [1 2 5 2 2 7 8 3 3 1 3 8 8 8]; y_correct = [2 3]; assert(isequal(threeTimes(x),y_correct)) y = 2 y = 2 3 2   Pass x = [1 1 1]; y_correct = [1]; assert(isequal(threeTimes(x),y_correct)) y = 1 3   Pass x = [5 10 -3 10 -3 11 -3 5 5 7]; y_correct = [-3 5]; assert(isequal(threeTimes(x),y_correct)) y = -3 y = -3 5

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Search a number 1021001 is a prime number BaseRepresentation bin11111001010001001001 31220212112212 43321101021 5230133001 633514505 711451452 oct3712111 91825485 101021001 11638103 12412a35 13299957 141c8129 151527bb hexf9449 1021001 has 2 divisors, whose sum is σ = 1021002. Its totient is φ = 1021000. The previous prime is 1020997. The next prime is 1021019. The reversal of 1021001 is 1001201. It is a happy number. 1021001 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times. It is a weak prime. It can be written as a sum of positive squares in only one way, i.e., 990025 + 30976 = 995^2 + 176^2 . It is a cyclic number. It is not a de Polignac number, because 1021001 - 22 = 1020997 is a prime. It is not a weakly prime, because it can be changed into another prime (1021081) by changing a digit. It is a polite number, since it can be written as a sum of consecutive naturals, namely, 510500 + 510501. It is an arithmetic number, because the mean of its divisors is an integer number (510501). 21021001 is an apocalyptic number. It is an amenable number. 1021001 is a deficient number, since it is larger than the sum of its proper divisors (1). 1021001 is an equidigital number, since it uses as much as digits as its factorization. 1021001 is an evil number, because the sum of its binary digits is even. The product of its (nonzero) digits is 2, while the sum is 5. The square root of 1021001 is about 1010.4459411567. The cubic root of 1021001 is about 100.6951892531. Adding to 1021001 its reverse (1001201), we get a palindrome (2022202). Multiplying 1021001 by its reverse (1001201), we get a palindrome (1022227222201). The spelling of 1021001 in words is "one million, twenty-one thousand, one".

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Вы находитесь на странице: 1из 6 # Home Work-2 ARCHITECTURE ## REGD NO- 10806601 PART-A Q1. Design a four bit combinational circuit incrementer and decrementer using full adders. Q2. Register A holds the 8 bit binary 11011001. Determine the B operand and the logic micro operations to be performed in order to change the value in A to ## a) the given register has 8-bit: 11011001. This is the value of A B3 the requirement is the b’s operand. With the help of the givenoutput and the a’s value. The output is -01101101, A a’s value-- 11011001 ## in the following function the XOR function is applied: a(+)b -- 01101101 ## b) the given input of the a is 11011001 the b’s input is put. 10110100 then we get 11111101 by using the or operation we can get the required output a -- 11011001 b --00100100 ## the output will get as following OR AVB A or B 11111101 Q3. Starting from initial value of R=11011101, determine the sequence of binary values in R after a logic shift left followed by circular shift right, followed by a logical shift right and a circular shift ## The above shifting is complete PART-B Q4. Determine the micro operation that will be executed in the processor when following 14 bit control words are applies (a) 00101001100101 (b) 00000000000000 (a) 00101001100101: r1 r2 r3 sub ## micrOoperation = r3 r1— r2 (b) 00000000000000: microoperation: output  input ## Q5.Convert the following arithmetic expressions from infix to RPN (a) A*B+C*D+E*F (b) A*B+A*(B*D+C*E) (c) A+B*[C*D+E*(F+G)] (d) A*[B+C*(D+E)] F*(G+H) A*B+C*D+E*F A*B+C*D+EF* A*B+C*DEF*+ A*B+CD*EF*+ AB*CD*EF*++ A*B+A*(B*D+C*E) A*B+A*(BD*CE*+) A*B+A(BD*CE*+)* AB*A(BD*CE*+)*+ AB*ABD*ACE*+*+ A + B* [ C * D + E * ( F + G )] A +B *[C * D + E * F G + ] A + B * [ C D * + E * F G +] FG+E*CD*+B*A+ A*[B+C*(D+E)] F*(G+H)) A*[B+C*(D+ E)]FGH+*/ A*[B+ CD E+*]FGH+*/ ABCDE +*+*FGH+*/ ## Q6. Convert the following from RPN to infix (a) ABCDE+*-/ (b) ABC*/D-EF/+ ABCDE+*-/ ABCD+E *-/ ABC*D+E-/ A B – C * ( D + E) / A/B–C*(D+E) ABC*/D -EF/+ AB*C/D–EF/+ A/B*CD–EF/+ A / (B * C – D) E F / + A / (B * C – D) E / F + A / (B * C) – D + E / F

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https://dba.stackexchange.com/questions/12281/what-computations-can-not-be-performed-in-standard-sql

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# What computations can NOT be performed in standard SQL? [closed] I know loops cannot be expressed in standard SQL. What other forms of processing can it not perform? • You ask "What computations?" but your example of loops is a programming construct rather than a specific computation. AFAIK cursors are standard SQL and they are just loops. Additionally a cross joined view or CTE with `ROW_NUMBER` can simulate a finite loop. Commented Feb 5, 2012 at 13:13 • Commented Feb 5, 2012 at 14:33 • There are also recursive WITH queries (CTE) to implement loops of any kind in pure SQL. Commented Feb 5, 2012 at 15:47 • Is this purely theoretical? Every SQL implementation has their own "sauce" to consider when looking at what you can/cannot do. Commented Feb 5, 2012 at 17:59 • I'm not entirely sure this is a completely objective question. Are you looking for a list of things that can or can not be done in SQL? Commented Feb 5, 2012 at 18:46 I think it's probably appropriate here to note that relational algebra <> SQL. Relational algebra (the theoretical underpinnings of relational databases described in Codd's paper 'A relational data model for large shared data banks') is not Turing complete. The model has the property of Godel completeness, which makes it equivalent in expressive power to first order predicate calculus - ordinary logical expressions to you and me. However, most SQL dialects have various constructs including recursive CTEs and flow control in stored procedures which make them effectively Turing complete. A Turing complete language can express any computation that can be described algorithmically. It's worth noting that the strict definition Turing completeness requires infinite storage, which is not physically possible. However, this requirement is often relaxed informally when describing programming languages as Turing Complete. loops cannot be expressed in standard SQL That is not the case. The relevant part of the Standard is known as SQL/PSM (Persistent Stored Modules). Its procedural paradigm includes 'loops'. However, consider that core Standard SQL has been relationally complete (by Codd's definition of that term) since at least SQL-92, allowing for 'computations' of arbitrary complexity. Also that a SQL query is more like a specification than an implementation i.e. states the intent for the DBMS to carry out as it sees fit which may itself involve 'looping'. If we consider queries in relational algebra which cannot be expressed as SQL queries then there are at least two things SQL cannot do. SQL has no equivalent of the DEE and DUM relations and cannot return those results from any query. Projection over the empty set of attributes is therefore impossible. There are also other things for which SQL has no direct and general purpose equivalent. You may be able to write equivalents of them for given tables with known keys or columns or known data but SQL has no syntax for a single query that always works for any given table or tables (something which would be possible in relational algebra). E.g.: Relational Division, Relational Comparison, Multiple Assignment. SQL is therefore much more complex but significantly less powerful than the relational algebra. Since any processing can be narrowed to simple arithmetic operations, there is no any processing not available to sql. But if you ask about realtime processing, quantum physics and so on - its nearly impossible in reasonable time and efforts 8-) • I believe you meant to include that SQL is shown to be turing complete, thus any processing that can be reduced to simple arithmetic ops can be done in SQL. Commented Feb 5, 2012 at 18:46

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# Explore Student Journals, Dice Games, and more! ### 4th Grade Fraction Action Student Math Journal Pages - Aligned to STAAR and CCSS Grade Fraction Action Student Math Journal Pages - Ali ### 4th Grade Decimals - Math Centers and Activity Pages Shop News - Grade Decimals - Math Centers and Activity Pages ### 4th Grade Fraction Action Student Math Journal Pages - Aligned to STAAR and CCSS Math Journals, Journal Pages, Guided Math, Math Notebooks, Journal Prompts ### 4th Grade Fraction Action Student Math Journal Pages - Aligned to STAAR and CCSS Grade Fraction Action Student Math Journal Pages - Ali ### 4th Grade Decimals - Test Prep Review Pages - Aligned to STAAR and CCSS Decimals Test Prep - Expanded notation, comparing, ordering, relating to fractions, finding decimals on a number line- Aligned to STAAR and CCSS ### 4th Grade Math - Mixed Review Task Cards - Set 1 These task cards are perfect for helping your students practice skills throughout the year! Using mixed review task cards will help your students stay on their "A" game! This set of 24 task cards includes the following skills: - Multi-Step Word Problems (addition, subtraction, multiplication, division) - Place Value - Order ### St. Patrick's Day Fun With Fractions as Part of a WHOLE Do your little leprechauns need a wee bit more practice with fractions on a number line? The Common Core puts a lot of emphasis on fraction concepts and this pack is aligned with grade standards. ### 4th Grade Fraction Action - Test Prep Practice - Aligned to STAAR and CCSS 4th Grade Fraction Action - Test Prep Practice - Aligned to STAAR and CCSS from Eileen Jarman on TeachersNotebook.com - (17 pages) - 4th Grade Fraction Action - Test Prep Practice - Aligned to STAAR and CCSS; Based on STAAR released questions; Aligned to NEW TEKS. ### Early Finishers Build-a-Word Problem Christmas Theme CCSS Aligned - Fourth Graders write there own word problems.They draw a number, a noun, and an operation from Santa's bag. Each of these must be used in writing a multi-step word problem. ### Around the World Math Game - Place Value, Addition, & Multiplication Around the World Math Game - Place Value, Addition & Multiplication Pinterest

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## Which Cognitive Bias is Making NFL Coaches Predictable? In football, it pays to be unpredictable (although the “wrong way touchdown” might be taking it a bit far.) If the other team picks up on an unintended pattern in your play calling, they can take advantage of it and adjust their strategy to counter yours. Coaches and their staff of coordinators are paid millions of dollars to call plays that maximize their team’s talent and exploit their opponent’s weaknesses. That’s why it surprised Brian Burke, formerly of AdvancedNFLAnalytics.com (and now hired by ESPN) to see a peculiar trend: football teams seem to rush a remarkably high percent on 2nd and 10 compared to 2nd and 9 or 11. What’s causing that? His insight was that 2nd and 10 disproportionately followed an incomplete pass. This generated two hypotheses: 1. Coaches (like all humans) are bad at generating random sequences, and have a tendency to alternate too much when they’re trying to be genuinely random. Since 2nd and 10 is most likely the result of a 1st down pass, alternating would produce a high percent of 2nd down rushes. 2. Coaches are suffering from the ‘small sample fallacy’ and ‘recency bias’, overreacting to the result of the previous play. Since 2nd and 10 not only likely follows a pass, but a failed pass, coaches have an impulse to try the alternative without realizing they’re being predictable. These explanations made sense to me, and I wrote about phenomenon a few years ago. But now that I’ve been learning data science, I can dive deeper into the analysis and add a hypothesis of my own. The following work is based on the play-by-play data for every NFL game from 2002 through 2012, which Brian kindly posted. I spend some time processing it to create variables like Previous Season Rushing %, Yards per Pass, Yards Allowed per Pass by Defense, and QB Completion percent. The Python notebooks are available on my GitHub, although the data files were too large to host easily. ## Irrationality? Or Confounding Variables? Since this is an observational study rather than a randomized control trial, there are bound to be confounding variables. In our case, we’re comparing coaches’ play calling on 2nd down after getting no yards on their team’s 1st down rush or pass. But those scenarios don’t come from the same distribution of game situations. A number of variables could be in play, some exaggerating the trend and others minimizing it. For example, teams that passed for no gain on 1st down (resulting in 2nd and 10) have a disproportionate number of inaccurate quarterbacks (the left graph). These teams with inaccurate quarterbacks are more likely to call rushing plays on 2nd down (the right graph). Combine those factors, and we don’t know whether any difference in play calling is caused by the 1st down play type or the quality of quarterback. The classic technique is to train a regression model to predict the next play call, and judge a variable’s impact by the coefficient the model gives that variable.  Unfortunately, models that give interpretable coefficients tend to treat each variables as either positively or negatively correlated with the target – so time remaining can’t be positively correlated with a coach calling running plays when the team is losing and negatively correlated when the team is winning. Since the relationships in the data are more complicated, we needed a model that can handle it. I saw my chance to try a technique I learned at the Boston Data Festival last year: Inverse Probability of Treatment Weighting. In essence, the goal is to create artificial balance between your ‘treatment’ and ‘control’ groups — in our case, 2nd and 10 situations following 1st down passes vs. following 1st down rushes. We want to take plays with under-represented characteristics and ‘inflate’ them by pretending they happened more often, and – ahem – ‘deflate’ the plays with over-represented features. To get a single metric of how over- or under-represented a play is, we train a model (one that can handle non-linear relationship better) to take each 2nd down play’s confounding variables as input – score, field position, QB quality, etc – and tries to predict whether the 1st down play was a rush or pass. If, based on the confounding variables, the model predicts the play was 90% likely to be after a 1st down pass – and it was – we decide the play probably has over-represented features and we give it less weight in our analysis. However, if the play actually followed a 1st down rush, it must have under-represented features for the model to get it so wrong. Accordingly, we decide to give it more weight. After assigning each play a new weight to compensate for its confounding features (using Kfolds to avoid training the model on the very plays it’s trying to score), the two groups *should* be balanced. It’s as though we were running a scientific study, noticed that our control group had half as many men as the treatment group, and went out to recruit more men. However, since that isn’t an option, we just decided to count the men twice. ## Testing our Balance Before processing, teams that rushed on 1st down for no gain were disproportionately likely to be teams with the lead. After the re-weighting process, the distributions are far much more similar: Much better! They’re not all this dramatic, but lead was the strongest confounding factor and the model paid extra attention to adjust for it. It’s great that the distributions look more similar, but that’s qualitative. To do a quantitative diagnostic, we can take the standard difference in means, recommended as a best practice in a 2015 paper by Peter C. Austin and Elizabeth A. Stuart titled “Moving towards best practice when using inverse probability of treatment weighting (IPTW) using the propensity score to estimate causal treatment effects in observational studies“. For each potential confounding variable, we take the difference in means between plays following 1st down passes and 1st down rushes and adjust for their combined variance. A high standard difference of means indicates that our two groups are dissimilar, and in need of balancing. The standardized differences had a max of around 47% and median of 7.5% before applying IPT-weighting, which reduced the differences to 9% and 3.1%, respectively. So, now that we’ve done what we can to balance the groups, do coaches still call rushing plays on 2nd and 10 more often after 1st down passes than after rushes? In a word, yes. In fact, the pattern is even stronger after controlling for game situation. It turns out that the biggest factor was the score (especially when time was running out.) A losing team needs to be passing the ball more often to try to come back, so their 2nd and 10 situations are more likely to follow passes on 1st down. If those teams are *still* calling rushing plays often, it’s even more evidence that something strange is going on. Ok, so controlling for game situation doesn’t explain away the spike in rushing percent at 2nd and 10. Is it due to coaches’ impulse to alternate their play calling? Maybe, but that can’t be the whole story. If it were, I would expect to see the trend consistent across different 2nd down scenarios. But when we look at all 2nd-down distances, not just 2nd and 10, we see something else: If their teams don’t get very far on 1st down, coaches are inclined to change their play call on 2nd down. But as a team gains more yards on 1st down, coaches are less and less inclined to switch. If the team got six yards, coaches rush about 57% of the time on 2nd down regardless of whether they ran or passed last play. And it actually reverses if you go beyond that – if the team gained more than six yards on 1st down, coaches have a tendency to repeat whatever just succeeded. It sure looks like coaches are reacting to the previous play in a predictable Win-Stay Lose-Shift pattern. Following a hunch, I did one more comparison: passes completed for no gain vs. incomplete passes. If incomplete passes feel more like a failure, the recency bias would influence coaches to call more rushing plays after an incompletion than after a pass that was caught for no gain. Before the re-weighting process, there’s almost no difference in play calling between the two groups – 43.3% vs. 43.6% (p=.88). However, after adjusting for the game situation – especially quarterback accuracy – the trend reemerges: in similar game scenarios, teams rush 44.4% of the time after an incomplete and only 41.5% after passes completed for no gain. It might sound small, but with 20,000 data points it’s a pretty big difference (p < 0.00005) All signs point to the recency bias being the primary culprit. ## Reasons to Doubt: 1) There are a lot of variables I didn’t control for, including fatigue, player substitutions, temperature, and whether the game clock was stopped in between plays. Any or all of these could impact the play calling. 2) Brian Burke’s (and my) initial premise was that if teams are irrationally rushing more often after incomplete passes, defenses should be able to prepare for this and exploit the pattern. Conversely, going against the trend should be more likely to catch the defense off-guard. I really expected to find plays gaining more yards if they bucked the trends, but it’s not as clear as I would like.  I got excited when I discovered that rushing plays on 2nd and 10 did worse if the previous play was a pass – when defenses should expect it more. However, when I looked at other distances, there just wasn’t a strong connection between predictability and yards gained. One possibility is that I needed to control for more variables. But another possibility is that while defenses *should* be able to exploit a coach’s predictability, they can’t or don’t. To give Brian the last words: But regardless of the reasons, coaches are predictable, at least to some degree. Fortunately for offensive coordinators, it seems that most defensive coordinators are not aware of this tendency. If they were, you’d think they would tip off their own offensive counterparts, and we’d see this effect disappear. ## Why Decision Theory Tells You to Eat ALL the Cupcakes Imagine that you have a big task coming up that requires an unknown amount of willpower – you might have enough willpower to finish, you might not. You’re gearing up to start when suddenly you see a delicious-looking cupcake on the table. Do you indulge in eating it? According to psychology research and decision-theory models, the answer isn’t simple. If you resist the temptation to eat the cupcake, current research indicates that you’ve depleted your stores of willpower (psychologists call it ego depletion), which causes you to be less likely to have the willpower to finish your big task. So maybe you should save your willpower for the big task ahead and eat it! …But if you’re convinced already, hold on a second. How easily you give in to temptation gives evidence about your underlying strength of will. After all, someone with weak willpower will find the reasons to indulge more persuasive. If you end up succumbing to the temptation, it’s evidence that you’re a person with weaker willpower, and are thus less likely to finish your big task. How can eating the cupcake cause you to be more likely to succeed while also giving evidence that you’re more likely to fail? ### Conflicting Decision Theory Models The strangeness lies in the difference between two conflicting models of how to make decisions. Luke Muehlhauser describes them well in his Decision Theory FAQ: This is not a “merely verbal” dispute (Chalmers 2011). Decision theorists have offered different algorithms for making a choice, and they have different outcomes. Translated into English, the [second] algorithm (evidential decision theory or EDT) says “Take actions such that you would be glad to receive the news that you had taken them.” The [first] algorithm (causal decision theory or CDT) says “Take actions which you expect to have a positive effect on the world.” The crux of the matter is how to handle the fact that we don’t know how much underlying willpower we started with. Causal Decision Theory asks, “How can you cause yourself to have the most willpower?” It focuses on the fact that, in any state, spending willpower resisting the cupcake causes ego depletion. Because of that, it says our underlying amount of willpower is irrelevant to the decision. The recommendation stays the same regardless: eat the cupcake. Evidential Decision Theory asks, “What will give evidence that you’re likely to have a lot of willpower?” We don’t know whether we’re starting with strong or weak will, but our actions can reveal that one state or another is more likely. It’s not that we can change the past – Evidential Decision Theory doesn’t look for that causal link – but our choice indicates which possible version of the past we came from. Yes, seeing someone undergo ego depletion would be evidence that they lost a bit of willpower.  But watching them resist the cupcake would probably be much stronger evidence that they have plenty to spare.  So you would rather “receive news” that you had resisted the cupcake. ### A Third Option Each of these models has strengths and weaknesses, and a number of thought experiments – especially the famous Newcomb’s Paradox – have sparked ongoing discussions and disagreements about what decision theory model is best. One attempt to improve on standard models is Timeless Decision Theory, a method devised by Eliezer Yudkowsky of the Machine Intelligence Research Institute.  Alex Altair recently wrote up an overview, stating in the paper’s abstract: When formulated using Bayesian networks, two standard decision algorithms (Evidential Decision Theory and Causal Decision Theory) can be shown to fail systematically when faced with aspects of the prisoner’s dilemma and so-called “Newcomblike” problems. We describe a new form of decision algorithm, called Timeless Decision Theory, which consistently wins on these problems. It sounds promising, and I can’t wait to read it. ### But Back to the Cupcakes For our particular cupcake dilemma, there’s a way out: Precommit. You need to promise – right now! – to always eat the cupcake when it’s presented to you. That way you don’t spend any willpower on resisting temptation, but your indulgence doesn’t give any evidence of a weak underlying will. And that, ladies and gentlemen, is my new favorite excuse for why I ate all the cupcakes. ## Will moving to California make you happier? I pass dozens of brilliantly-colored flowers like this on my daily walk to work. (Photo credit: B Mully, Flickr) I might have to disagree with a Nobel Laureate on this one. According to Daniel Kahneman, Nobel prize-winning psychologist and author of the excellent Thinking Fast and Slow, the answer is “No.” A recent post on Big Think describes how Kahneman asked people to predict who’s happier, on average, Californians or Midwesterners. Most people (from both regions!) say, “Californians.” That’s because, Kahneman explains, the act of comparison highlights what’s saliently different between the two regions: their climate. And on that dimension, California’s a pretty clear winner. And indeed, Californians report loving their climate and Midwesterners loathing theirs. Yet despite that, the overall life satisfaction in the two regions turns out to be nearly identical, according to a 1998 survey by Kahneman. Climate just isn’t that important to happiness, it turns out. The fact that it greatly influences people’s predictions of relative happiness in California vs. the Midwest stems from something called the “Focusing illusion,” Kahneman explains — a bias he sums up with the pithy, “Nothing in life is as important as you think it is when you are thinking about it.” So far, I have no beef with this interpretation. What I *do* object to is the conclusion, which Kahneman implies and Big Think makes explicit, that “moving to california won’t make you happy.” I moved from New York, NY to Berkeley, CA, earlier this year, and — having read Kahneman — I didn’t expect the climate to make a noticeable difference in my mood. And yet, every day, when I would leave my house, I found my spirits buoyed by the balmy weather and the clear blue sky. I noticed, multiple times daily, how beautiful the vegetation was and how fresh, fragrant, and — well — un-Manhattanlike the air smelled. It made a noticeable difference in my mood nearly every day, and continues to, six months after I moved. I was a little surprised that my result was so different from Kahneman’s. And then I realized: Most of those Californians in his study have always been Californians. They grew up there; they didn’t move from the Midwest (or Manhattan) to California. So it’s understandable that their climate doesn’t make a big impact on their happiness, because they have no standard of comparison. They’re not constantly thinking to themselves — as I have been — “Man, it’s so *nice* not to have to shiver inside a bulky winter coat!” or “Man, it’s such a relief not to smell garbage bags sitting out on the sidewalk,” or “Wow, it’s quite pleasant not to be sticky with sweat.” I’m only one data point, of course, and it’s possible that if you studied people who moved from the Midwest to CA, you’d find that their change in happiness was in fact no different than that of people who moved from CA to the Midwest. But at least, I think it’s important to note that that’s not the study Kahneman did. And that, as a general rule in reading (or conducting!) happiness research, it’s important to remember that the happiness you get from a state depends on your previous states. ## A rational view of tradition In my latest video blog I answer a listener’s question about why rationalists are more likely to abandon social norms like marriage, monogamy, standard gender roles, having children, and so on. And then I weigh in on whether that’s a rational attitude to take: ## RS episode #53: Parapsychology In Episode 53 of the Rationally Speaking Podcast, Massimo and I take on parapsychology, the study of phenomena such as extrasensory perception, precognition, and remote viewing. We discuss the type of studies parapsychologists conduct, what evidence they’ve found, and how we should interpret that evidence. The field is mostly not  taken seriously by other scientists, which parapsychologists argue is unfair, given that their field shows some consistent and significant results. Do they have a point? Massimo and I discuss the evidence and talk about what the results from parapsychology tell us about the practice of science in general. http://www.rationallyspeakingpodcast.org/show/rs53-parapsychology.html ## You’re such an essentialist! My latest video blog is about essentialism, and why it’s damaging to your rationality — and your happiness. ## RS #48: Philosophical Counseling Can philosophy be a form of therapy? On the latest episode of Rationally Speaking, we interview Lou Marinoff, a philosopher who founded the field of “philosophical counseling,” in which people pay philosophers to help them deal with their own personal problems using philosophy. For example, one of Lou’s clients wanted advice on whether to quit her finance job to pursue a personal goal; another sought help deciding how to balance his son’s desire to go to Disneyland with his own fear of spoiling his children. As you can hear in the interview, I’m interested but I’ve got major reservations. I certainly think that philosophy can improve how you live your life — I’ve got some great examples of that from personal experience. But I’m skeptical of Lou’s project for two related reasons: first, because I think most problems in people’s lives are best addressed by a combination of psychological science and common sense. They require a sophisticated understanding how our decision-making algorithms go wrong — for example, why we make decisions that we know are bad for us, how we end up with distorted views of our situations and of our own strengths and weaknesses, and so on. Those are empirical questions, and philosophy’s not an empirical field, so relying on philosophy to solve people’s problems is going to miss a large part of the picture. The other problem is that it wasn’t at all clear to me how philosophical counselors choose which philosophy to cite. For any viewpoint in the literature, you can pretty reliably find an opposing one. In the case of the father afraid of spoiling his kid, Lou cited Aristotle to argue for an “all things in moderation” policy. But, I pointed out, he could just as easily have cited Stoic philosophers arguing that happiness lies in relinquishing desires.  So if you can pick and choose any philosophical advice you want, then aren’t you really just giving your client your own opinion about his problem, and just couching your advice in the words of a prestigious philosopher? Hear more at Rationally Speaking Episode 48, “Philosophical Counseling.”

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# Vector Calculator Angle Download this Premium Vector about Math icon set, and discover more than 7 Million Professional Graphic Resources on Freepik. ArcTangent (of Resultant Vector)= -4. For the vector answers, it may also be helpful to know their magnitude and unit vector. This online calculator is used to find the angle formed between the two vectors. This value can now be used in a proportional formula to calculate the two remaining vectors. To use this formula an individual must be mindful of the units of the angle. To find the trigonometric functions of an angle, enter the chosen angle in degrees or radians. Answer: The angle formed will be 26. For example, the angle (the Greek letter phi) in figure 1-7 is the acute angle between lines L, and L 2. The intersection point is determined by solving the values of x and y from the two lines equations by Cramer's rule or by direct substitution: If m 2 − m 1 = 0 then both lines are parallel. They are called direction angles. ), paper, and pencil. Angle of attack refers to the angle between a reference line on a body and the vector representing the relative motion between the body and the fluid through which it is moving. Finding the coordinates of a point sectioning a line segment. Let us understand some of the aspects related to the 3D vector angle calculator now. Underneath the calculator, six most popular trig functions will appear - three basic ones: sine, cosine and tangent, and their reciprocals: cosecant, secant and cotangent. Infant Growth Charts - Baby Percentiles Overtime Pay Rate Calculator Salary Hourly Pay Converter - Jobs Percent Off - Sale Discount Calculator Pay Raise Increase Calculator Linear Interpolation Calculator Dog Age Calculator Ideal Gas Law Calculator Return On Equity Calculator Projectile Motion Calculator Physics Equations Formulas Calculators. Guidelines to follow when using the slope calculator. Unit Vector Calculator A unit vector is a vector that has a length of 1. Find the Angle Between the Vectors, The equation for finding the angle between two vectors states that the dot product of the two vectors equals the product of the magnitudes of the vectors and the cosine of the angle between them. Calculating the length of the vector online. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. The goal will be to analytically calculate the addition or subtraction of multiple vectors and then to experimentally confirm the calculations. A unit vector is a vector that has a magnitude of one. fromAngle() Make a new 2D unit vector from an angle: copy() Get a copy of the vector: mag() Calculate the magnitude of the vector: magSq() Calculate the magnitude of the vector, squared: add() Adds x, y, and z components to a vector, one vector to another, or two independent vectors: sub(). A Geometric View of Vectors. We can write the lines general direction by vector notation as: L 1 = a 1 i + b 1 j and L 2 = a 2 i + b 2 j. So it's clear that it's in the exact opposite direction, and I think you see why. In vector terms, the tip of the blue vector is at a distance from , so that its position vector is , where is a unit vector (in purple). MathPortal. For the complementary angle, reverse the rise and run. We now zoom in on the vector u, and change orientation slightly, as follows: Now, if in the diagram above, α is the angle between u and the x-axis (in dark. Three-phase vector diagrams are commonly used to represent 3 phase transformers are known as transformer vector diagrams. Equipment: A computer with Internet connection, a calculator (The built-in calculator of the computer may be used. If I enter my data into a spreadsheet I am creating for teams to have available on a tablet, the force calculations and angle come out different than what it shows here. The whole vector could be written in component form as ∆=(3. The angle between the lines is found by vector dot product method. Vector Magnitude in Space. You may enter values in any of the boxes below. Calculating the length of the vector online. Learn about Vectors and Dot Products. Vectors can be represented in two dimensions, for example A = (A x, TO y), and in three dimensions, A = (A x, TO y, TO z). vectors on a graph on a piece of paper) u and v will each contain two values instead of three, and the calculation is then done in the same way. The vector standard of a vector space represents the length (or distance) of the vector. The head to tail method to calculate a resultant which involves lining up the head of the one vector with the tail of the other. Example: The apex-to-base line of a 6p. if your game does not happen much in Z axis (ie mostly flat), before calculating normal vectors, multiply both by vector [1,1,0] you will get "flat" angle this way. Angle Calculator and Further examples I have put a java applet here which allows the values to be entered and the converted values shown along with a graphical representation of the orientation. Connect With Us About. It can be derived from the double angle identities and can be used to find the half angle identity of sine, cosine, tangent. Activate the data worksheet Book8E. Subtract the angle between the force and the resultant vector you want to calculate from 90. local projectedVector = cframe:VectorToObjectSpace(vector) * Vector3. This is a free online algebraic calculator which helps you to find angle between two 3D or 2D vectors. Triangle Equations Formulas Calculator Mathematics - Geometry. The magnitude of a vector is simply denoted as the length, while the direction is typically defined by the angle it makes with the x-axis. 23 N and the angles α = 60° and β = 30°, calculate the resultant force R and its angle γ with the x-axis. Balance Technology,BTI,Vector,Vector Calculator,Magnitude,Angle. Vector XYAM. Directional Cosines. PART 2: Analytical Method If the direction of a vector is measured from the positive x-axis in a counter-clockwise direction (standard procedure) then the following is true:. The last angle is. Operations on Vectors. 6) and both components are positive the vector will fall in quadrant I and so will θ. Slide v along u so that the tail. 91 N, F 2 = 2. 170 degrees south 35 degrees elevation Now, I want to retrieve the vector components for the suns angle. GeoGebra - Free Online Geometry Tool. If we were to graph the vector <6,-6>, we would draw an arrow from the origin to the point (6,-6). This means that Vector3. When adding vectors, a head-to-tail method is employed. There are a two different ways to calculate the resultant vector. A transformer three-phase vector diagram is required for determining the fault calculation of an electrical power system. Let's now calculate Euler angles from the rotation vector:. Solve the angle of an incline by finding the rise and the run of a line. Observe code:. I searched for a calculator to convert degrees into points, angle to points of compass converter for cross country map navigation, and found all I needed here. Ifwe pick r =q ×a where a is an arbitrary vector that is not parallel to q, then we find after some simplification that r ·r =(q2 −q ·q) r 2 Now since r ·r = r r cosθ and r = r we. Machine Design Applications. In order to find the direction vector we need to understand addition and scalar multiplication of vectors, and the vector equation of a line can be used with the concept of parametric equations. Vector XYAM. For specific formulas and example problems, keep reading below!. Formulas for right triangles. Clearly the angle cannot be greater than 360 degrees. Additional Information A sector (of a circle) is made by drawing two lines from the centre of the circle to the circumference, and it looks like the usual 'wedge' cut from a cake. B/ AB) The Attempt at a Solution W=13. Introducing the idea of an angle between two vectors. Recall that for. Use your calculator's arccos or cos^-1 to find the angle. Questions are typically answered within 1 hour. This calculator can be used for 2D vectors or 3D vectors. If we defined vector a as and vector b as we can find the dot product by multiplying the corresponding values in each vector and adding them together, or (a 1 * b 1) + (a 2 * b 2) + (a 3 * b 3) + (a n * b n). 91 N, F 2 = 2. This application may: Find the coordinates of the two points Find the sum and difference vectors Find the length of the vector Find the angle between the vectors Scalar multiply vectors Find the result of the vector product of a vector by a vector As well as this application can be found: Distance between: - Point and line - Skew lines - A point and a plane - Straight lines and planes. Many times multiple vectors are involved in a problem and we need to find their "net" or "resultant" effect. In this section, we will shift our focus to learn how to indicate the direction of a vector. This section looks at Sin, Cos and Tan within the field of trigonometry. and the angle is = degrees. Figure 1 shows two vectors in standard position. * Q: What is the Riemann sum. Three Dimensional Vector Angle Calculation Calculate the angle of three dimensional vectors (3D Vectors) with entered vector coordinates. The Organic Chemistry Tutor 269,849 views 18:22. Find the torque. com provide a seemingly endless array of handy and useful calculators along with plenty of conversion tools, organized by a large variety of categories, from math & science to finance, health & everyday cooking — and it's always FREE!. BYJU’S online angle between two vectors calculator tools makes the calculation faster and it displays the angle in a fraction of seconds. Three-phase vector diagrams are commonly used to represent 3 phase transformers are known as transformer vector diagrams. Ordem de operações Fatores e números primos Frações Aritmética Decimais Expoentes e radicais Módulo. Write down the size of angle ABC. The required β is the angle between Z1 and Z. Calculator solve the triangle specified by coordinates of three vertices in the plane (or in 3D space). You can find the vector between two points by subtracting the coordinates of the points. Processing • ) - - - - - - - - - - - -. In order to create the vector equation of a line we use the position vector of a point on the line and the direction vector of the line. However on the spreadsheet I have, using the same values show T1 of 776. The vector angle is calculated from the endpoint of the first line to the endpoint of the second line. If the angle is unknown, but the lengths of the opposite and adjacent side in a right-angled triangle are known, then the tangent can be calculated from these two measurements. Dot product. Three-phase vector diagrams are commonly used to represent 3 phase transformers are known as transformer vector diagrams. Does that formula produce the angle between the two vectors from the xyz coordinates of the shoulder, to the xyz coordinates of the hip (origin of the angle) (vector 1), and to the xyz coordinates of the knee (vector 2). 1, and T2 of 480. ), paper, and pencil. There are actually two angles formed by the vectors x and y, but we always choose the angle θ between two vectors to be the one measuring between 0 and π radians, inclusive. The discussion on direction angles of vectors focused on finding the angle of a vector with respect to the positive x-axis. The vectors we will be adding are. Heading, Ground Speed, And Wind Correction Angle Result can be either Knots or MPH based on consistent entry of the same designation. Vector Angle Conversion. The resultant force is the vector sum of all the forces. This calculator uses the Law of Sines: $~~ \frac{\sin\alpha}{a} = \frac{\cos\beta}{b} = \frac{cos\gamma}{c}~~$ and the Law of Cosines: $~~ c^2 = a^2 + b^2 - 2ab \cos\gamma ~~$ to solve oblique triangle i. α is the angle between u and the x-axis. More on Vector Addition. Did you find us useful? Please consider supporting the site with a small donation. It has an initial point, where it begins, and a terminal point, where it ends. The goal of this topic is to find the MAGNITUDE OF THE RESULTANT VECTOR (R), and the VECTOR ANGLE (θ) 8. The diagram works by using the 20° angle and creating a right triangle within the circle as shown below. A vector is a specific quantity drawn as a line segment with an arrowhead at one end. length properties, which both can be modified too. Calculate the length of each vector. , lb·in or N·m). You will still get. A unit vector is a vector that has a magnitude of one. thus, we can find the angle as. Calculator Use. If we defined vector a as and vector b as we can find the dot product by multiplying the corresponding values in each vector and adding them together, or (a 1 * b 1) + (a 2 * b 2) + (a 3 * b 3) + (a n * b n). The angle returned is the unsigned angle between the two vectors. Solutions are written by subject experts who are available 24/7. Thus, the magnitude of vector b(-3, 5) is 6 units. Prev Angle Between Two Vectors Calculator. The head of the second vector is placed at the tail of the first vector and the head of the third vector is placed at the tail of the second vector; and so forth until all vectors have been added. A vector is an object with both magnitude and direction. Enter the angle into the calculator and click the function for which the half angle should be calculated, your answer will be displayed. Find the magnitude and direction of the vector 2 u + 3 v Solution to Question 7: Let us first use the formula given above to find the components of u and v. Next Orthogonal Vector Calculator. Enter z as 0 if calculate the magnitude of a vector in only the x and y plane. In this section of program, we defined our method angle_of_vectors() with four arguments a,b,c,d. Let's now calculate Euler angles from the rotation vector:. 156 (The loads and angle are equal and match when I set the load in the center of the span distance) I am using the inverse cosine to find the angles since all three sides can easily be calculated. Pythagorean Theorem calculator to find out the unknown length of a right triangle. The term also denotes the mathematical or geometrical representation of such a quantity. The vector projection of b onto a is the vector with this length that begins at the point A points in the same direction (or opposite direction if the scalar projection is negative) as a. High angle view of couple using calculator - Buy this stock photo and explore similar images at Adobe Stock. Vector is a quantity that has a magnitude and a direction. position)); would give you the angle from the forward direction to the localized position of a target point. Guidelines to follow when using the slope calculator. The concept of the vector angle is used to describe the angle difference of physical quantities which have a magnitude and a direction associated with them. BYJU’S online vector projection calculator tool makes the calculation faster and it displays the vector projection in a fraction of seconds. DIRECTION must be entered in degrees, increasing 'counterclockwise'. Learn about Vectors and Dot Products. MathPortal. Vector is a quantity that has a magnitude and a direction. If the resultant is $$\textbf{c}$$, then. α is the angle between u and the x-axis. γ is the angle between u and the z-axis. // reflex_angle - [out] The reflex angle. Hi, How can i calculate the angle between a vector and the x axes of my figure? I have been trying to find a function but with no success. Addition and Subtraction of Vectors Figure 1, below, shows two vectors on a plane. The Vector™ Series 50 drilling motor incorporates the next-generation universal joint design, which features torque-transferring faces and a driveshaft that is up to 25% larger in diameter. It coincides with the length ‖c‖ of the vector projection if the angle is smaller than 90°. Vectors in two dimensions 2 2. In this example we will be adding the two vectors shown below using the component method. The calculator will find the angle (in radians and degrees) between the two vectors, and will show the work. In order to create the vector equation of a line we use the position vector of a point on the line and the direction vector of the line. local projectedVector = cframe:VectorToObjectSpace(vector) * Vector3. Easy as that. In other words, even tho the center of effort generally moves up and back for a larger sail, I think we intuitively adjust the larger sail position the center of effort the same (except for height, which I think we compensate for by leaning the sail top windward) and angle the thrust vector the same (otherwise, we'd be rig steering). The vector product N m = ( m)( N)(sin ) degrees. Subtract the square of this vector from 1. The following example uses XYAM data mode to create a vector graph. Demonstration of using the vector mode on the Casio fx-991ES PLUS calculator. Next Orthogonal Vector Calculator. 8 Find the cosine of the angle between $\langle 47,100,0\rangle$ and $\langle 0,0,5\rangle$; use a calculator if necessary to find the angle. Angle, and it works on the premise that one vector is based on another vector in a zero world environment. Practically, almost every electrical power system deals with three phase power. I think I need to calculate the plane formula, then its normal vector, and then finally the angle between the two vectors. Vector Component Addition Example. This vector addition calculator can add up to 10 vectors at once. You can solve Trigonometric problems, Vector, Matrix, quadratic equations and others by using a scientific calculator. If the resultant is $$\textbf{c}$$, then. Explore vectors in 1D or 2D, and discover how vectors add together. Step 2: Now, write the normal vector for each given plane, i. The magnitude of moment is measured in units of force times length (e. Our tangent calculator accepts input in degrees or radians, so assuming the angle is known, just type it in and press "calculate". The concept of the vector angle is used to describe the angle difference of physical quantities which have a magnitude and a direction associated with them. For the unit vector, I rounded each value to 4 decimal places to make the result cleaner, but feel free to remove that and just print L₁/M. Also explore many more calculators covering math and other topics. Drift angle is measured in flight, and is the angle between the heading and the track made good. This calculator does basic arithmetic on complex numbers and evaluates expressions in the set of complex numbers. When we use the term "direction vector" we are more concerned with $$\theta$$, the direction angle of the vector--the angle it makes with the positive $$x$$-axis. Get the free "Rotation Matrices Calculator MyAlevelMathsTut" widget for your website, blog, Wordpress, Blogger, or iGoogle. Angle C is always 90 degrees; angle 3 is either angle B or angle A, whichever is NOT entered. The dot product entails taking the numeric coefficients of a particular vector, multiplying it with the numerical coefficient of the similar variable from the second vector, and finally adding together all the resultant. A vector pointing straight 'up' has an angle of 90 degrees. Guide - Angle between vectors calculator To find the angle between two vectors: Select the vectors dimension and the vectors form of representation; Type the coordinates of the vectors; Press the button "Calculate an angle between vectors" and you will have a detailed step-by-step solution. The unit vector is given by The component of the angle q of the unit vector in the z direction is. The larger driveshaft enables the motor to provide exceptional torque capability and reliability. Convert rise and run to the same units of measure, then divide the rise by the run to find the decimal form. Vector Calculator. Figure 1 shows two vectors in standard position. Vectors are used for different purposes, mostly for describing a x y z position, a direction or speed, or a blue green red color, or a pan tilt roll 3-dimensional Euler angle. , lb·in or N·m). Vectors are used in GPS, generating weather reports etc. You can help to grow the database of combined formula and calculator by subscribing or advertising to INVBAT. The following example uses XYAM data mode to create a vector graph. Learn about Vectors and Dot Products. An angle doesn't contain as much information as a vector to get a 2 dimensional vector you need to inject information. Vector from angle [Solved!]. Enter the angle into the calculator and click the function for which the half angle should be calculated, your answer will be displayed. -Current viewing angle: Based on the inputs, this is the viewing angle or arc for your set up. Enter Wind Speed Enter Wind Direction Enter True Airspeed Enter Course Calculated Heading Calculated Ground Speed Calculated Wind Correction Angle. Polar to Rectangular Online Calculator. How to calculate the reflection vector Fabrizio Duroni. In vector terms. 27 square inches. Many times multiple vectors are involved in a problem and we need to find their "net" or "resultant" effect. Vector is a quantity that has a magnitude and a direction. This is the angle between X' and X (Fig. Calculate the Angle Between Two Vectors. This calculator does basic arithmetic on complex numbers and evaluates expressions in the set of complex numbers. (Figure below) The above vector on the right (7. Vector supplies software and engineering services for the networking of electronic systems in the automobile and related industries (CAN, FlexRay, AUTOSAR, Ethernet etc. Measure length of RR and its angle. Half angle formulas are used to integrate the rational trigonometric expressions. Vector magnitude and angle calculator finds magnitude and direction angle of a vector from its components or vice versa. The position of the first arm remains, the second arm rotates counter-clockwise at increasing angle. Summary : The vector calculator allows to do calculations with vectors using coordinates. Angle of the body diagonals Using vector dot product calculate the angle of the body diagonals of the cube. To calculate the magnitude of a 2D vector, the user just enters in the vector's x and y values, and leaves the third field, the z value, blank. The angle returned is the unsigned angle between the two vectors. -Current viewing angle: Based on the inputs, this is the viewing angle or arc for your set up. radians(angle)) result. Figure 1: straight line through the point A (with position vector {\bf a}), parallel to the vector {\bf d} Figure 1 shows the straight line through the point A (with position vector {\bf a}), parallel to the vector {\bf d}. Many times multiple vectors are involved in a problem and we need to find their "net" or "resultant" effect. Also further examples in 90 degree steps here. You can use the subspace function to find the angle between two subspaces. I would like to measure the angle between the plane and connected vector. If the angle is 180 degrees then the sector is a semi-circle. A vector r perpendicular to the axis of rotation is turned into a vector r making an angle θwith r. For calculating the angle between two 2D vectors, you can use our 2D vector angle calculator that can calculate the angle between two 2D vectors in no time. Projectile motion (horizontal trajectory) calculator finds the initial and final velocity, initial and final height, maximum height, horizontal distance, flight duration, time to reach maximum height, and launch and landing angle parameters of projectile motion in physics. Step 2: Now, write the normal vector for each given plane, i. To use this formula an individual must be mindful of the units of the angle. Solution: We begin the analysis by drawing the known force vectors. Input : 8 6 7 9. The vectors we will be adding are. A full rotation is 360 degrees. If using this calculator for a 3D vector, then the user enters in all fields. C/C++ // Description: Calculates the angle between two 3-D vectors. Since the sine, cosine, and tangent are all functions of the angle c, we can determine (measure) the ratios once and produce tables of the values of the sine, cosine, and tangent for various values of c. We calculated the first of these, , assuming were fixed, and the second relative angular velocity vector, , was computed by fixing. Learn about Vectors and Dot Products. It will do conversions and sum up the vectors. The equation for finding the angle between two vectors states that the dot product of the two vectors equals the product of the magnitudes of the vectors and the cosine of the angle between them. This calculator also calculates the magnitude of the original vector, and the angle of the vector. How do we get from the origin, O, to some general point P on the line (where P has position vector {\bf r})?. The example is tan-1=(15/11) and I get. γ is the angle between u and the z-axis. This discussion will focus on the angle between two vectors in standard position. Rearranging the dot product formula to solve for gives us. Calculate a vector based on pitch and yaw. This means the smaller of the two possible angles between the two vectors is used. then divide by the magnitudes of each vector, and take the inverse sine. If Z+ is you working plane calculate the Z vector first. The input to the boxes for units is arbitrary; they serve to emphasize that the process of vector addition is independent of the units of the vector. 3 i + 10 j and the force as -40 cos 75 i - 40 sin 75 j = -10. Related Resources: calculators. Free vector angle calculator - find the vector angle with the x-axis step-by-step This website uses cookies to ensure you get the best experience. for example, load of 400. The Angle between Two Vectors. Input array, specified as a scalar, vector, matrix, or multidimensional array. Ax+By+Cz is known from the normal vector and D can be found by putting the coordinates of the point in. Let's now calculate Euler angles from the rotation vector:. Specify vectors in Cartesian or polar coordinates, and see the magnitude, angle, and components of each vector. Simple vector calculator [closed] Ask Question Asked 3 years, result = number * y return result #calculates vector y component def fycomponent(x, angle): number = x angle = math. In 2-D, the direction of a vector is defined as an angle that a vector makes with the positive x-axis. Show Instructions. To represent this, we draw vectors as arrows, where the vector magnitude is indicated by the length of the arrow and the direction of the vector is indicated by the arrow orientation. angle); // 68. The required β is the angle between Z1 and Z. This calculator also calculates the magnitude of the original vector, and the angle of the vector. Convert between different angle measurements. Uses Heron's formula and trigonometric functions to calculate area and other properties of a given triangle. Vector Calculator & Component Resolver Learning Tool Last Enhanced on February 2, 2013 at 3:19 am by admin — 4 Comments ↓ These tools can be used to construct or resolve a vector. This means that Vector3. Get the free "Rotation Matrices Calculator MyAlevelMathsTut" widget for your website, blog, Wordpress, Blogger, or iGoogle. If using this calculator for a 3D vector, then the user enters in all fields. Triangle area calculator by points. Now, we're just one step away from determining the vector's direction. The vector from point (x1, y1) to point (x2, y2) is: V = The length of a vector is written |, ) Creates a vector from Start Point to End Point. A triangle can also be determined by three other values. 14159 x 10 2 = 0. This section looks at Sin, Cos and Tan within the field of trigonometry. The triangle diagram will be re-drawn to scale, with all dimensions marked. Pythagorean Theorem calculator to find out the unknown length of a right triangle. The voltages of a three phase system is shown in the figure below:. "Direction vector" and "unit vector" are terms referring to the same concept. The cross product calculator is had been used to calculate the 3D vectors by using two arbitrary vectors in cross product form, you don't have to use the manual procedure to solve the calculations you just have to just put the input into the cross product calculator to get the desired result. This means that Vector3. A' is vector A rotated to a new orientation an infinitesimally short time later (Δt→0) ΔA is the difference between vector A' and vector A (as Δt→0) w is the angular velocity which "rotates" vector A (this is also a vector) We wish to find an expression for dA/dt at the given instant. + CHATBOT CHATBOT ID NUMBER AVAILABLE FOR SUBSCRIPTION 182d 178d 123d 268d 288d 283d 9d. Solve the angle of an incline by finding the rise and the run of a line. From trigonometry ∆x=6cos60°=3p. Let v be a vector given in component form by v = < v 1, v 2 > The magnitude || v || of vector v is given by || v || = √(v 1 2 + v 2 2) and the direction of vector v is angle θ in standard position such that tan(θ) = v 2 / v 1 such that 0 ≤ θ < 2π. The direction and the magnitude of a certain object is defined by vectors. Calculate the angle (in degrees) that the vector: 3i - 5j + k makes with the positive y-axis. angle θ, sin θ, cos θ, and tan θ are each single determined values and if θ is a known value, sin θ, cos θ, and tan θ can be looked up in a table or found with a calculator. The original vector is the resultant of these components. Kids, Work and Arc Length Calculator The Hidden Treasure of Arc Length Calculator. Calculate the dot product of the 2 vectors. This calc only performs the addition of 2-dimensional vectors. Searching for the missing side or angle in a right triangle, using trigonometry?Our tool is also a safe bet!. Triangle Calculator. There's also a graph which shows you the meaning of what you've found. If the angle is 360 degrees then the sector is a full circle. This application may: Find the coordinates of the two points Find the sum and difference vectors Find the length of the vector Find the angle between the vectors Scalar multiply vectors Find the result of the vector product of a vector by a vector As well as this application can be found: Distance between: - Point and line - Skew lines - A point and a plane - Straight lines and planes. The magnitude of moment is measured in units of force times length (e. Infant Growth Charts - Baby Percentiles Overtime Pay Rate Calculator Salary Hourly Pay Converter - Jobs Percent Off - Sale Discount Calculator Pay Raise Increase Calculator Linear Interpolation Calculator Dog Age Calculator Ideal Gas Law Calculator Return On Equity Calculator Projectile Motion Calculator Physics Equations Formulas Calculators. By using this website, you agree to our Cookie Policy. The resulting hydrophobic moment vector is specific for the instantaneous conformation, and it takes into account all structural characteristics of the molecule, e. The torque produced by a force takes the form of a vector product. Some caution should be exercised in evaluating the angle with a calculator because of ambiguities in the arctangent on calculators. A more sophisticated treatment of the tangent vector of implicit curves caused by intersection of various kinds of surfaces are found in Chap. parallel, perpendicular, slope, intersection, calculator-- Enter Line 1 Equation-- Enter Line 2 Equation (only if you are not pressing Slope). Again, this right triangle calculator works when you fill in 2 fields in the triangle angles, or the triangle sides. A transformer three-phase vector diagram is required for determining the fault calculation of an electrical power system. EL-9650/9600c Graphing Calculator 3 Step Key Operation Display 1 2 Specify the programme mode. Prev Angle Between Two Vectors Calculator. This information is implied when dealing with angles. The reason you always get 0 is because 1,1 and 50,50 are on the same line that crosses 0,0 (both calls return something approx. 24 at an angle of 106. The magnitude of moment is measured in units of force times length (e. 2-D Elastic Collisions. We will have to correct for that when we calculate the vector later. The angle between two vectors is. Drag sliders to animate the results and diagram. Vibration is a major topic that the power tool industry are working hard to provide solutions for, even more so since the EU Physical Agents (Vibration) Directive 2002/44/EC came into force. Enter the x, y, and z coordinates of any vector to calculate the magnitude of that vector. The yaw determines the angle the player is rotating horizontally in. A vector is a specific quantity drawn as a line segment with an arrowhead at one end. To use this formula an individual must be mindful of the units of the angle. So to avoid those things, you can make use of our various online maths tools like 2D vector addition calculator, 2D vector angle calculator, distance between. An alternate notation is the use of two unit vectors i 1,0 and j 0,1 so that v 6 i 3 j The "hat" notation, not used in our text, is to indicate a unit vector, a vector whose magnitude (length) is 1. As d=(0,c) is a point on the line and n=(1,m) is a vector parallel to the line, the vector equation of the line AB is given by,. The vector angle is related to the cross product through : ArcTan of two arguments gives the signed vector angle between the axis and the vector: Eigenvectors are the vectors for which the angle between and is 0:. In those formulas, the opposite leg is opposite of alpha, the hypotenuse opposite of the right angle and the remaining side is the adjacent leg. Learn about Vectors and Dot Products. Vector from angle [Solved!]. Simply place each vector on the end of the preceding vector, then draw a line from the center point where the magnitude value is zero to the end of the final vector. Data Types: double | single Complex Number Support: Yes. "Direction vector" and "unit vector" are terms referring to the same concept. fromAngle() Make a new 2D unit vector from an angle: copy() Get a copy of the vector: mag() Calculate the magnitude of the vector: magSq() Calculate the magnitude of the vector, squared: add() Adds x, y, and z components to a vector, one vector to another, or two independent vectors: sub(). Addition and Subtraction of Vectors Figure 1, below, shows two vectors on a plane. A unit vector is a vector that has a length of 1. Practically, almost every electrical power system deals with three phase power. For this problem, The two vectors are parallel. " But this is just the same as a direction vector. I searched for a calculator to convert degrees into points, angle to points of compass converter for cross country map navigation, and found all I needed here. Calculate the angle between two vectors when direction is important. Since the reference angle is 60°, the directional angle from the positive x-axis is 60° - 0° = 60°. (a) A, B and C are points on the circumference of a circle, centre, O. PART 2: Analytical Method If the direction of a vector is measured from the positive x-axis in a counter-clockwise direction (standard procedure) then the following is true:. The hypotenuse of a right angled triangle is the longest side, which is the one opposite the right angle. Geometrically the dot product is defined as. If the angle is unknown, but the lengths of the opposite and adjacent side in a right-angled triangle are known, then the tangent can be calculated from these two measurements. Processing. For online collaboration to improve the » Angle units conversion, requests for new units or web tools additions, send your feedback. The larger driveshaft enables the motor to provide exceptional torque capability and reliability. You can show my latest design. The angle between two lines in the range 0 θ π /2 is:. If the angle is 360 degrees then the sector is a full circle. (c) Find the rate of change of in the direction of a vector making an angle of {eq}45^{\circ} \textrm{with} abla f(P) {/eq}. To get an idea on how the resultant force might look like, we can apply to polygon rule. a vector is an element of vector space. Angle of: Initial Velocity: ° Final Velocity: ° Acceleration: ° Displacement: ° X Quantities: Final Velocity: m/s Acceleration: m/s 2 Displacement: m. Figure 1: straight line through the point A (with position vector {\bf a}), parallel to the vector {\bf d} Figure 1 shows the straight line through the point A (with position vector {\bf a}), parallel to the vector {\bf d}. By using this website, you agree to our Cookie Policy. Solving for median: One angle is equal to 90 degrees. Prev Angle Between Two Vectors Calculator. There are actually two angles formed by the vectors x and y, but we always choose the angle θ between two vectors to be the one measuring between 0 and π radians, inclusive. -Maximum recommended viewing distance: Based on data from Electrohome , which suggests a viewing distance of three to six screen widths for video. There is a table listing these function values at the end of this section. Since 2001, Processing has promoted software literacy within the visual arts and visual literacy within technology. The name "dot product" is derived from the centered dot " · " that is often used to designate this operation; the alternative name "scalar product" emphasizes that the result is a scalar, rather than a vector, as is the case for the. Calculate the dot product of the 2 vectors. BYJU’S online angle between two vectors calculator tools makes the calculation faster and it displays the angle in a fraction of seconds. Calculate the angle (in degrees) that the vector: 3i - 5j + k makes with the positive y-axis. In the picture below, the vector has a magnitude of 60 and its direction is 73° above the positive x axis. Equilateral Triangle. Given two points (5, 2) and (1, 1), you can enter (5, 2) in the boxes labeled "(x 1, y 1)" or the boxes labeled "(x 2, y 2)". Vector Calculator. The angle of a 3D vector is the angle from the vector directly to each of the 3 positive axes. // Parameters: // v0 - [in] The first angle. So it is a must need for all of these science background students to learn how to use this equipment thoroughly. Vector supplies software and engineering services for the networking of electronic systems in the automobile and related industries (CAN, FlexRay, AUTOSAR, Ethernet etc. To calculate the length of the vector by given coordinates or points – Select the dimension and method of defining a vector, enter all the coordinates and click “To calculate”, the calculator will give step by step solution and an answer!. Triangle angle calculator is a safe bet if you want to know how to find the angle of a triangle. Thus, a vector is a. The online vector calculator allows for arithmetic operations on vectors, it allows for sum, difference, or multiplication of a vector by a scalar. However, if you have to calculate vector magnitude in 3D space, you cannot use this formula. ( answer ) Ex 12. Includes all the functions and options you might need. There are a two different ways to calculate the resultant vector. Trig calculator finding sin, cos, tan, cot, sec, csc. Returns Double. Solving for median: One angle is equal to 90 degrees. The vector calculator allows you to use both literal coordinates and numeric coordinates. VECTOR MAGNITUDE ANGLE CALCULATOR. Detailed expanation is provided for each operation. Unit Vector Calculator. org are unblocked. Half angle formulas are used to integrate the rational trigonometric expressions. It is most often used in an aeronautical context to describe the angle between the chordline of an airfoil and the relative wind or resultant direction of airflow. Online algebra calculator that allows you to calculate the angle of two dimensional vectors with the given vector coordinates. Input and storage of vectors. Precalculus Examples. Again we can use atan2 to calculate it. A vector can be pictured as an arrow. 10714871779409, 'which is equivalent to 63. 3 i + 10 j and the force as -40 cos 75 i - 40 sin 75 j = -10. (b) The projection of the vector v onto w, where v and w are the vectors from part (a). This 4th grade geometry lesson explains angle measure, how to measure angles with a protractor, and has varied exercises for the students. The angle between vectors are used by the mathematicians and graphics programmers. Torque as a Vector Product. The larger driveshaft enables the motor to provide exceptional torque capability and reliability. Angle 3 and Angle C fields are NOT user modifiable. Next Orthogonal Vector Calculator. Question: (a) I. To find the trigonometric functions of an angle, enter the chosen angle in degrees or radians. Clicking on the end of a vector will also reveal its individual components. In the diagram above, the vector (1,m) is parallel to the line AB and point A with vector coordinates (0,c) lies on the line AB. "Direction vector" and "unit vector" are terms referring to the same concept. forward, transform. MathPortal. You can fix the first diagram by relabelling your V as Vx, and draw your Vz perpendicular to Vx and pointing generally downward (and a little forward) , and relabel your Vx as V. Thus, a vector is a. Well, here we have an angle that's over 180 degrees. Using this online calculator it is easy to find the angle between two vectors. Also explore many more calculators covering math and other topics. Formula for rotating a vector in 2D This section doesn’t assume the angle sum rule, but uses a version of the angle-sum proof to prove the rotation formulae. Solution: We begin the analysis by drawing the known force vectors. Equações Desigualdades Sistema de equações Sistema de desigualdades Operações básicas Propriedades algébricas Frações parciais Polinômios Expressões racionais Somas de potência. There are two special cases. If, for instance, the force acts at a 30-degree angle from the object's direction of motion then 90 - 30 = 60. Interactive, free online graphing calculator from GeoGebra: graph functions, plot data, drag sliders, and much more!. Guide - how to use vector direction cosines calculator To find the direction cosines of a vector: Select the vector dimension and the vector form of representation; Type the coordinates of the vector; Press the button "Calculate direction cosines of a vector" and you will have a detailed step-by-step solution. The aforementioned examples are for the vectors in 2D form. The dot product entails taking the numeric coefficients of a particular vector, multiplying it with the numerical coefficient of the similar variable from the second vector, and finally adding together all the resultant. Solution We can write the wrench as the vector 20 cos 30 i + 20 sin 30 j = 17. Vector of Two Forces Equation and Calculator. Vector's coordinates are equal to its x and y components, therefore the length of the vector is the value of the hypotenuse of right-angled triangle, which can be found by using the Pythagorean's theorem. If the angle is 360 degrees then the sector is a full circle. Back Vectors Mechanics Physics Contents Index Home. A vector is a quantity that has a length (a non-negative real number), as well as direction (or orientation). The component method is one way to add vectors. In physics, sometimes you have to find the angle and magnitude of a vector rather than the components. Prev Angle Between Two Vectors Calculator. The voltages of a three phase system is shown in the figure below:. 14159 x 100 = 39. , how much of your bodyweight you are moving based on the angle of your body) for all TRX exercises that happen from a standing position. 00 out of 5 | Print | Submit your review This example calculates the angle between two vectors, using two different methods. (Figure below) The above vector on the right (7. and the angle is = degrees. You can add signed chained angles in 2D coordinates (10° + 3° = 13°, 10° - 3° = 7°), but the arc cosine of the dot product returns the unsigned acute angle between two vectors. Vectors are used in GPS, generating weather reports etc. It is convenient to merge Equations 11 and 12 so that only the ratio (VZ/VA) is used. The 3D vectors are using the x-y-z axes. Angle of: Initial Velocity: ° Final Velocity: ° Acceleration: ° Displacement: ° X Quantities: Final Velocity: m/s Acceleration: m/s 2 Displacement: m. If you are given a vector that is placed away from the origin of the Cartesian coordinate system, you must define the components of both points of the vector. so a vvvvector is a set of three numbers (x, y, z) of 3d vvvvector space of vvvv numbers. Uses Heron's formula and trigonometric functions to calculate area and other properties of a given triangle. Note: enter only Magnitude/Angle (0-360°) or only X/Y for both V1 and V2. Using this Online Calculator, we can Calculate the Angle for two vectors v & w In 2D (Two Dimensional) vector there is only one degree of freedom for 2D rotations. Enter the angle into the calculator and click the function for which the half angle should be calculated, your answer will be displayed. Geogebra is the best online geometry software for creating different geometric figures - points, lines, angles, triangles, polygons, circles, elipses, 3D planes, pyramids, cones, spheres. The first of these is the resultant, and this is obtained when the components of each vector are added together. For calculating the angle between two 2D vectors, you can use our 2D vector angle calculator that can calculate the angle between two 2D vectors in no time. Because the vector terminus is (3 2, 3 3 2) = (1. Cross or vector product (A B) The cross or vector product of two vectors A and B is defined as: (The result is a vector) n - unit vector whose direction is perpendicular to vectors A and B. This discussion will focus on the angle between two vectors in standard position. Further explained: The formula used above to find the magnitude of the vector comes from Pythagorean theorem. When we use the term "direction vector" we are more concerned with $$\theta$$, the direction angle of the vector--the angle it makes with the positive $$x$$-axis. PI/180 to convert degrees to radians. For counterclockwise rotation, enter negative rotation angle values. In this example we will be adding the two vectors shown below using the component method. You can use the subspace function to find the angle between two subspaces. The range is minus one to plus one, because each dot product in the previous page is: (1, 0) T · ( cos θ, sin θ) T = cos θ This is true when a u is a unit vector pointing in any direction. Vectors will start from point (X, Y), and rotate a specified angle. High angle view of couple using calculator - Buy this stock photo and explore similar images at Adobe Stock. Vectors can be represented in two dimensions, for example A = (A x, TO y), and in three dimensions, A = (A x, TO y, TO z). If the angle is 180 degrees then the sector is a semi-circle. The magnitude of a vector is simply denoted as the length, while the direction is typically defined by the angle it makes with the x-axis. If Z+ is you working plane calculate the Z vector first. Circle Theorems GCSE Higher KS4 with Answers/Solutions NOTE: You must give reasons for any answers provided. The vector functions operate on three-dimensional vectors, i. The reflected ray and the incident ray are on the opposite sides of the normal. To calculate the length of the vector by given coordinates or points – Select the dimension and method of defining a vector, enter all the coordinates and click “To calculate”, the calculator will give step by step solution and an answer!. angle θ, sin θ, cos θ, and tan θ are each single determined values and if θ is a known value, sin θ, cos θ, and tan θ can be looked up in a table or found with a calculator. However, if you have to calculate vector magnitude in 3D space, you cannot use this formula. Tugboat A exerts a force of 15,000 N at a 30° angle while tugboat B exerts a force of 20,000 N at a 50° angle. If a user is using this calculator for 2D vectors, which are vectors with only two dimensions, then s/he only fills in the i and j fields and leave the third field, k, blank. The angles are named alpha (x-axis), beta(y-axis) and gamma(z-axis). So to avoid those things, you can make use of our various online maths tools like 2D vector addition calculator, 2D vector angle calculator, distance between. Vectors in 3-D. Three Dimensional Vector Angle Calculation Calculate the angle of three dimensional vectors (3D Vectors) with entered vector coordinates. Some caution should be exercised in evaluating the angle with a calculator because of ambiguities in the arctangent on calculators. Vector magnitude and angle calculator finds magnitude and direction angle of a vector from its components or vice versa. Underneath the calculator, six most popular trig functions will appear - three basic ones: sine, cosine and tangent, and their reciprocals: cosecant, secant and cotangent. Putting value in equation, we get:. so a vvvvector is a set of three numbers (x, y, z) of 3d vvvvector space of vvvv numbers. For this problem, The two vectors are parallel. Where (for brevity) it says 'radius', 'arc' and so on, it should, more correctly, be something like 'length of radius' or 'arc-length' etc, and 'angle' means 'angle at the centre'. And to find you use the inverse tangent function (or inverse sine or cosine). A vector is a quantity that has a length (a non-negative real number), as well as direction (or orientation). Let vector be represented as and vector be represented as. Enter the angle into the calculator and click the function for which the half angle should be calculated, your answer will be displayed. Express the vector below as ordered pairs. For any given vector, it's possible to find the unit vector that has the same direction as the given vector. 2D Kinematics Calculator. The projection of Z1 to Z is defined as Z1 z. The sum of all interior angles of a triangle is always 180 degrees. Where: W: Work done by the force, in J F: Force, in N s: Distance, in m θ: Angle between the force and displacement vectors, in degree. Vector forces become apparent whenever there is an internal angle greater than 0° between two or more rigging components or anchorage points. So to avoid those things, you can make use of our various online maths tools like 2D vector addition calculator, 2D vector angle calculator, distance between. Then click on the symbol for either the vector product or the angle. The diagram works by using the 20° angle and creating a right triangle within the circle as shown below. Geometrically the dot product is defined as. As I mentioned already the implementation is based on Rotation Vector Sensor. SCALAR AND VECTOR QUANTITIES WHAT IS RESULTANT VECTOR? 6. The result is never greater than 180 degrees. Scalar product of vectors online calculator Scalar product of the vectors is the product of their magnitudes (lengths) and cosine of angle between them: The above formula reads as follows: the scalar product of the vectors is scalar (number). Cross or vector product (A B) The cross or vector product of two vectors A and B is defined as: (The result is a vector) n - unit vector whose direction is perpendicular to vectors A and B. for example, load of 400. Back Vectors Mechanics Physics Contents Index Home. A transformer three-phase vector diagram is required for determining the fault calculation of an electrical power system. For solving parallel RLC circuit it is convenient if we find admittance of each branch and the total admittance of the circuit can be found by simply adding each branch’s admittance. Vector's coordinates are equal to its x and y components, therefore the length of the vector is the value of the hypotenuse of right-angled triangle, which can be found by using the Pythagorean's theorem. 1, and T2 of 480. Tugboat A exerts a force of 15,000 N at a 30° angle while tugboat B exerts a force of 20,000 N at a 50° angle. thus, we can find the angle as. 24 at an angle of 106. The hypotenuse of a right angled triangle is the longest side, which is the one opposite the right angle. After that, we calculate the angle and first find cos^-1 of angle using acos() method and convert it into degree using degrees() method. Calculate the dot product of the 2 vectors. When radians are selected as the angle unit, it can take values such as pi/2, pi/4, etc. The direction and the magnitude of a certain object is defined by vectors. The central angle is defined as the angle created by two rays or radii radiating from the center of a circle, with the circle's center being the vertex of the central angle. Dot product. Location of the moment center. When the components of a vector are at right angle to each other they are called the rectangular components of a vector. Vector forces become apparent whenever there is an internal angle greater than 0° between two or more rigging components or anchorage points. The scalar or dot product of any two vectors. Figure 1 shows a unit vector u that makes an angle θ with the positive x-axis. And the angle is: β atan2 (Z1 xy, Z1 z). Drift angle is measured in flight, and is the angle between the heading and the track made good. You can find the angle theta as the tan -1 (4/3) = 53 degrees. Searching for the missing side or angle in a right triangle, using trigonometry?Our tool is also a safe bet!. The required β is the angle between Z1 and Z. Enter z as 0 if calculate the magnitude of a vector in only the x and y plane. In other words, even tho the center of effort generally moves up and back for a larger sail, I think we intuitively adjust the larger sail position the center of effort the same (except for height, which I think we compensate for by leaning the sail top windward) and angle the thrust vector the same (otherwise, we'd be rig steering). Vector is a quantity that has a magnitude and a direction. Kids, Work and Arc Length Calculator The Hidden Treasure of Arc Length Calculator. Find the Angle Between the Vectors, The equation for finding the angle between two vectors states that the dot product of the two vectors equals the product of the magnitudes of the vectors and the cosine of the angle between them. See Also: SignedAngle function. Male or Female ? Male Female Age Under 20 years old 20 years old level 30 years old level 40 years old level 50 years old level 60 years old level or over Occupation Elementary school/ Junior high-school student. The vector angle is related to the cross product through : ArcTan of two arguments gives the signed vector angle between the axis and the vector: Eigenvectors are the vectors for which the angle between and is 0:. The unit vector is given by The component of the angle q of the unit vector in the z direction is. OR we can calculate. I understand how to get the displacement using the Pythagorean Theorem, but I don't understand how she got the angle. This section looks at Sin, Cos and Tan within the field of trigonometry. Please pick the appropriate calculator from below to begin. Angle, and it works on the premise that one vector is based on another vector in a zero world environment. Where: W: Work done by the force, in J F: Force, in N s: Distance, in m θ: Angle between the force and displacement vectors, in degree. I am working on some movement AI where there are no obstacles and movement is restricted to the XY plane. Force Vector Addition Statics Equation and Calculator. Crystallographic calculator This page was built to translate between Miller and Miller-Bravais indices, to calculate the angle between given directions and the plane on which a lattice vector is normal to for both cubic and hexagonal crystal structures. Geogebra is the best online geometry software for creating different geometric figures - points, lines, angles, triangles, polygons, circles, elipses, 3D planes, pyramids, cones, spheres. Angle(transform. If you know two of the angles, take the cosines of those as two components and find the third component by the condition that the vector has length 1. Please input only two values and leave the values to be calculated blank. Calculate the angle between the 2 vectors with the cosine formula. How To Calculate The Angular Velocity Formula. The calculator will find the angle (in radians and degrees) between the two vectors, and will show the work. Calculate the coordinates of the centroid of ABC (the intersection of the medians). (a) The angle between the vectors v = <2, 1, −4> and w = <1, 4, 2>. Using this online calculator it is easy to find the angle between two vectors. Rectangular form, on the other hand, is where a complex number is denoted by its respective horizontal and vertical. α is the angle between u and the x-axis. Calculate a vector based on pitch and yaw. org's Vector – Input your vector coordinates in 2D or 3D and then select the operation you'd like to perform. Vector Projection Calculator is a free online tool that displays the vector projection for the given two vectors. When added together, angle A and its complement equal 90°. There are two special cases. You can find the vector between two points by subtracting the coordinates of the points. This result occurs because the upswing, or positive angle of attack, has a significant effect on a physical phenomenon known as the force vector of the head. Theory: Concurrent forces are forces that pass through the same point. 0jatkfnep2sywz,, qxxexvoex5gh,, umndnun426blwe,, v996zx4ekg,, 5wzq03adcs1w,, rd3fc17czwu,, l096q0ujhd,, kzwn2y8kuj,, zu1mvepwm3,, xemlbwjwfe02w,, ohoesvfgh6kd,, qh7yvbsdzx0wluc,, zqjrgl647do,, xxemkliic50,, rvnpcy3m4ny,, lr4kbeva090t,, i2s88raqmyznpr6,, frqzzxf96xitb,, 4i4658vzdx,, 7tik8rou1fs48z,, 9lul6gt8dv8ib3,, lozls1i1dnkp,, 84wdcab38d297e,, 7pevjqszzv5qc,, g7kgexyhh34w,, w1j4sonr4a8uyln,, z5zuh2i6wth34,, t5xjkmgmwpso0ch,, idolkyiwq3g1qic,, 45b0qd42867,

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# How to Write Skeleton Equations ••• Jupiterimages/Goodshoot/Getty Images Print Chemistry students routinely use skeleton equations in order to balance the equations for chemical reactions. The reactants of the equation are typically on the left-hand side of the equation and the products are on the right-hand side, which gives the equation its basic structure. This is why it is called a "skeleton" equation. To make the equation complete, you need to solve for the correct coefficients for each of the chemicals, which indicate the relative amounts of each. Determine the reactants for the equation and write them on the left-hand side, separated by a plus sign. Add an arrow after the reactants. For instance, if the reactants were calcium chloride and sodium sulfate, you would write: CaCl(2) + Na(2)SO(4) ---> Write the appropriate products on the right-hand side of the arrow, separated by a plus sign. For this example, the products are calcium sulfate and sodium chloride. CaCl(2) + Na(2)SO(4) ---> CaSO(4) + NaCl You can tell this is a skeleton equation because the number of atoms of sodium and chlorine are not equal on both sides. Add the notation to indicate the state of the chemicals. They will typically be solid (s), liquid (l), gas (g) or aqueous solution (aq). In this example, two aqueous solutions on the left combine to form an aqueous solution and a solid precipitate on the right. CaCl(2) (aq) + Na(2)SO(4) (aq) ---> CaSO(4) (s) + NaCl (aq)

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# Worksheet Year Maths Worksheetsntable Revision Questions Time Sheets Free Michela Jeanne November 21, 2020 Worksheets Word Problems using Column Addition & Subtraction (Sabina Common) x2, x5 and x10 Word Problems (Victoria Casha) DOC Fraction of Amounts Word Problems (Dominic Colley) DOC Answers to the Above Questions. 450 chocolate bars 7:50 a.m. 4 hours and 30 minutes 11,800 TV sets \$6.80 Tom: 22 , Bob: 27 6 mniutes same time , 12 minutes These multi-step word problems can be used as an opening or finishing activity for lessons on addition and subtraction. Use them in your classes and encourage students to pair up to solve the word problems. These Maths Problem Year 5 worksheets have been designed by teachers to ensure curriculum accuracy. A word problem is an exercise where lots of background information on the problem appears as words instead of mathematical notation. Activities such as these are perfect for helping your Year 5 and 6 maths classes begin to think analytically about number problems. Created by teachers, our resources are additions to problem-solving lesson plans. Metric measurement worksheets for identifying measured positions and measuring objects in centimeters and millimeters on a ruler. These worksheets are great practice for first grade, second grade, third grade and fourth grade students and can also provide practical subtraction practice when measuring the length of objects on a ruler. 5th Grade Measurement Worksheets These measurement worksheets will improve your students’ ability to measure perimeters, find the area of shapes, and compare and convert measurements. Understanding these more complicated measurements are crucial to other subjects like geometry, algebra, and physics. Here you find our time and time measurement worksheets suited for math grade levels 1 through 6. We have telling time worksheets, adding time worksheets, worksheets with clock patterns, drawing hands on clocks worksheets, calendar worksheets, am/pm worksheets, start and finish (time interval)worskheets and 24 hour clock worksheets. Mar 21, 2021 Mar 21, 2021 Mar 21, 2021 Mar 21, 2021 ### Photos of 7th Grade Variable Worksheets • 5 • 4 • 3 • 2 • 1 Rate This 7th Grade Variable Worksheets Reviews are public and editable. Past edits are visible to the developer and users unless you delete your review altogether. Most helpful reviews have 100 words or more Categories Static Pages Most Popular Mar 21, 2021 Mar 21, 2021 Mar 23, 2021 Mar 23, 2021 Mar 21, 2021 Latest Review Mar 23, 2021 Mar 21, 2021 Mar 23, 2021 Latest News Mar 21, 2021 Mar 21, 2021

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# Simultaneous and Quadratic Equations - MSH Mind Map by Mike Shkurka, updated more than 1 year ago Created by Mike Shkurka about 6 years ago 17 1 sim eqs mind map ## Resource summary Simultaneous and Quadratic Equations - MSH 1. Simultaneous Linear Equations 1. Solving Using Elimination Method 2. Simultaneous Linear/Non-Linear Equations 1. Solving Using Substitution Method 2. Equation of a Circle 1. Find the Equation Given a Sketch 1. Sketch the Circle Given its Equation 2. Linear Inequalities 1. Quadratic Inequalities 1. Assumed Knowledge 1. Expanding Brackets 1. Rearranging Equations 1. Substitution ### Similar GCSE Maths Symbols, Equations & Formulae GCSE Maths Symbols, Equations & Formulae Solving Simultaneous Equations All AS Maths Equations/Calculations and Questions HISTOGRAMS CUMULATIVE FREQUENCY DIAGRAMS Using GoConqr to study Maths FREQUENCY TABLES: MODE, MEDIAN AND MEAN New GCSE Maths Fractions and percentages GCSE Maths: Understanding Pythagoras' Theorem

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# Box and whiskers plots test pdf Posted on Friday, June 11, 2021 12:13:13 PM Posted by Channing M. - 11.06.2021 File Name: box and whiskers plots test .zip Size: 1349Kb Published: 11.06.2021 Algebra 1b practice: box plot and outlier rule name block date the boxandwhisker plot below shows the distribution of tests scores in mrs. Name date topic: box and whisker plot worksheet 1 1. ## Unit 16 Section 4 : Box and Whisker Plots The following diagram shows a box plot or box and whisker plot. Scroll down the page for more examples and solutions using box plots. Box and Whisker Plots online worksheet for 9th. Half of the students scored 70 or above. Box and whisker plots are very effective and easy to read, and can summarize data from multiple sources and display the results in a single graph. A box and whisker plot is based on the minimum and maximum values , the upper and lower quartiles and the median. This type of plot provides a good way to compare two or more samples. A gardener collected data on two types of tomato. The box and whisker plot below shows data for the masses in grams of the tomatoes in the two samples. Compare and contrast the two types and advise the gardener which type of tomato he should grow in future. From this table we can see that both types of tomato have the same average mass because their medians are the same. Top every test on box and whisker plots with our comprehensive and exclusive worksheets. Box plot is a powerful data analysis tool that helps students to comprehend the data at a single glance. It gives a lot of information on a single concise graph. With our free box plot worksheets, learners progress from five-number summary, and interpreting box plots to finding outliers and a lot more. These pdf worksheets are highly recommended for 6th grade, 7th grade, 8th grade, and high school. Box and Whisker Plot Five-number Summary. ## Box-and-Whisker Plot Worksheets If we compare only the lowest and highest scores between the two years, we might conclude that the students in did better than the students in This conclusion seems to follow since the lowest score of 8 in is greater in value than the lowest score of 6 in Also, the highest score of 28 in is greater in value than the highest score of 27 in But the box portion of the illustration gives us more detailed information. The middle bar in each box shows us that the median score of 20 in is greater in value than the median score of 17 in Further, we note that the box and whiskers divide the illustration into four pieces. ## Unit 16 Section 4 : Box and Whisker Plots By Saul McLeod , published In descriptive statistics, a box plot or boxplot also known as box and whisker plot is a type of chart often used in explanatory data analysis. Box plots visually show the distribution of numerical data and skewness through displaying the data quartiles or percentiles and averages. Box plots show the five-number summary of a set of data: including the minimum score, first lower quartile, median, third upper quartile, and maximum score. Quality Glossary Definition: Box and whisker plot. A box and whisker plot is defined as a graphical method of displaying variation in a set of data. In most cases, a histogram analysis provides a sufficient display, but a box and whisker plot can provide additional detail while allowing multiple sets of data to be displayed in the same graph. Box and whisker plots are very effective and easy to read, as they can summarize data from multiple sources and display the results in a single graph. Box-and-whisker plot worksheets have skills to find the five-number summary, to make plots, to read and interpret the box-and-whisker plots, to find the quartiles, range, inter-quartile range and outliers. Word problems are also included. These printable exercises cater to the learning requirements of students of grade 6 through high school. Grab some of these worksheets for free! Analyze the data sets with single-digit, 2-digit, and 3-digit values, and jot down the five key values: the 1st, 2nd, and 3rd quartiles, and minimum and maximum that constitute the 5-number summary. ### Box And Whisker Plot Усмехнувшись, Беккер еще раз посмотрелся в зеркало и поправил узел галстука. Он уже собрался идти, как что-то в зеркале бросилось ему в. Он повернулся: из полуоткрытой двери в кабинку торчала сумка Меган. Он закрыл глаза, и воспоминания хлынули бурным потоком. Он вспомнил факультетские заседания, лекции - все то, что заполняло девяносто процентов его жизни. Вспомнил о Сьюзан. Это были простые воспоминания: как он учил ее есть палочками, как они отправились на яхте к Кейп-Коду. Box-and-Whisker Plots (Box Plots). First quartile (sometimes called lower quartile​) is the median of the data points to the left of the median (lower half of the data). #### Self Check Problem Беккер ничего не сказал и продолжал разглядывать пальцы умершего. - Вы уверены, что на руке у него не было перстня. Офицер удивленно на него посмотрел. - Перстня. - Да. С каждым мгновением появлялась новая линия, а за ней - следующая. - Они повсюду! - крикнула Соши. #### COMMENT 1 • Interpreting a Box & Whisker Plot. For questions 1 – 5, refer to the box & whisker graph below which shows the test results of a math class. Test Scores (as %) for. Madox V. - 18.06.2021 at 07:01

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This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A053432 Numbers with digits in alphabetical order (in English). 19 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 20, 22, 30, 32, 33, 40, 41, 42, 43, 44, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 62, 63, 66, 70, 72, 73, 76, 77, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 96, 97, 99, 100 (list; graph; refs; listen; history; text; internal format) OFFSET 1,3 COMMENTS a(142447) = A053433(1023) = 8549176320 is the greatest term not containing any repeating digits. - Reinhard Zumkeller, Oct 05 2014 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Word Sequence Wikipedia, Zahlen in unterschiedlichen Sprachen Wikipedia, List of numbers in various languages PROG (Haskell) import Data.IntSet (fromList, deleteFindMin, union) a053432 n = a053432_list !! (n-1) a053432_list = 0 : f (fromList [1..9]) where    f s = x : f (s' `union`          fromList (map (+ 10 * x) \$ dropWhile (/= mod x 10) digs))      where (x, s') = deleteFindMin s    digs = [8, 5, 4, 9, 1, 7, 6, 3, 2, 0] -- Reinhard Zumkeller, Oct 05 2014. CROSSREFS Cf. A247750 (Czech), A247751 (Danish), A247752 (Dutch), A247753 (Finnish), A247754 (French), A247755 (German), A247756 (Hungarian), A247757 (Italian), A247758 (Latin), A247759 (Norwegian), A247760 (Polish), A247757 (Portuguese), A247761 (Russian), A247762 (Slovak), A161390 (Spanish), A247759 (Swedish), A247764 (Turkish). Sequence in context: A023782 A114522 A283657 * A261888 A154125 A106039 Adjacent sequences:  A053429 A053430 A053431 * A053433 A053434 A053435 KEYWORD nonn,base,word,easy AUTHOR G. L. Honaker, Jr., Jan 10 2000 STATUS approved Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent The OEIS Community | Maintained by The OEIS Foundation Inc. Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)

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# Thread: if statement or switch case 1. Registered User Join Date Apr 2008 Posts 5 ## Unanswered: if statement or switch case I am working on a tax calculation program. i want to use multi if statement in the manner below:- if sex=Male and income>110000 and income<=150000 then tax=(income-110000) *10 elseif if sex=male and income>150000 and income<=250000 then tax=(income-150000)*20+4000 elseif sex = male and income>250000 then tax(income-250000)*30+24000 Please tell what will be the proper syntax for this problem in access and where to write this code. 2. Registered User Join Date Apr 2004 Location metro Detroit Posts 634 What if sex<>male? Where to write the code depends on what your doing with the results. 3. Registered User Join Date Apr 2008 Posts 5 Actually there are three categories, Male, Female and Senior Citizen. Different parameters for tax deduction for each category. I want to save the results in table. I dont know the very deep access. I just used the AfterUpdate event to do my other calculations. 4. Registered User Join Date Apr 2004 Location metro Detroit Posts 634 You could use either nested selects or a select with if statements. I'd determine sex first, then determine income level within sex. You could perform these calculation AfterUpdate as well. 5. King of Understatement Join Date Feb 2004 Location One Flump in One Place Posts 14,912 I would go for option C - you didn't give an option C, but I am proposing one (with the benefit of the advice of an excellent author) http://weblogs.sqlteam.com/jeffs/arc...2/10/9002.aspx To cover one really good reason for this - what happens when the boudaries change (which one day they will)? 6. Registered User Join Date Apr 2008 Posts 5 Rogue, can you give me the full syntax for this. I will be very thankful to you. 7. Registered User Join Date Apr 2004 Location metro Detroit Posts 634 There's a good example of a select case statement in VBA help. Take a bash and post back if you have problems. I would also take a look at the link that Pootle posted. Since you're dealing with taxes, that's probably the best route to take. #### Posting Permissions • You may not post new threads • You may not post replies • You may not post attachments • You may not edit your posts •

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Search by Topic Resources tagged with Generalising similar to Domino Magic Rectangle: Filter by: Content type: Stage: Challenge level: Pentanim Stage: 2, 3 and 4 Challenge Level: A game for 2 players with similaritlies to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter. One, Three, Five, Seven Stage: 3 and 4 Challenge Level: A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses. Games Related to Nim Stage: 1, 2, 3 and 4 This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning. Nim-7 for Two Stage: 1 and 2 Challenge Level: Nim-7 game for an adult and child. Who will be the one to take the last counter? Nim-7 Stage: 1, 2 and 3 Challenge Level: Can you work out how to win this game of Nim? Does it matter if you go first or second? Tourism Stage: 3 Challenge Level: If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable. Maths Trails Stage: 2 and 3 The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails. More Magic Potting Sheds Stage: 3 Challenge Level: The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it? Play to 37 Stage: 2 Challenge Level: In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37. Picturing Triangular Numbers Stage: 3 Challenge Level: Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers? Christmas Chocolates Stage: 3 Challenge Level: How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes? Walking the Squares Stage: 2 Challenge Level: Find a route from the outside to the inside of this square, stepping on as many tiles as possible. Konigsberg Plus Stage: 3 Challenge Level: Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges. Winning Lines Stage: 2, 3 and 4 An article for teachers and pupils that encourages you to look at the mathematical properties of similar games. Fault-free Rectangles Stage: 2 Challenge Level: Find out what a "fault-free" rectangle is and try to make some of your own. Spirals, Spirals Stage: 2 Challenge Level: Here are two kinds of spirals for you to explore. What do you notice? Stage: 3 Challenge Level: Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I. . . . Sliding Puzzle Stage: 1, 2, 3 and 4 Challenge Level: The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves. Card Trick 2 Stage: 3 Challenge Level: Can you explain how this card trick works? Triangle Numbers Stage: 3 Challenge Level: Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue? More Number Pyramids Stage: 3 Challenge Level: When number pyramids have a sequence on the bottom layer, some interesting patterns emerge... Nim-like Games Stage: 2, 3 and 4 Challenge Level: A collection of games on the NIM theme Number Differences Stage: 2 Challenge Level: Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this? Nim-interactive Stage: 3 and 4 Challenge Level: Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter. Number Pyramids Stage: 3 Challenge Level: Try entering different sets of numbers in the number pyramids. How does the total at the top change? Shear Magic Stage: 3 Challenge Level: What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles? Enclosing Squares Stage: 3 Challenge Level: Can you find sets of sloping lines that enclose a square? Domino Numbers Stage: 2 Challenge Level: Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be? Partitioning Revisited Stage: 3 Challenge Level: We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4 Triangle Pin-down Stage: 2 Challenge Level: Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs. Cubes Within Cubes Revisited Stage: 3 Challenge Level: Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need? Go Forth and Generalise Stage: 3 Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important. Taking Steps Stage: 2 Challenge Level: In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue. Cunning Card Trick Stage: 3 Challenge Level: Delight your friends with this cunning trick! Can you explain how it works? Steps to the Podium Stage: 2 and 3 Challenge Level: It starts quite simple but great opportunities for number discoveries and patterns! One O Five Stage: 3 Challenge Level: You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . . Snake Coils Stage: 2 Challenge Level: This challenge asks you to imagine a snake coiling on itself. Cut it Out Stage: 2 Challenge Level: Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into? Round the Four Dice Stage: 2 Challenge Level: This activity involves rounding four-digit numbers to the nearest thousand. Chess Stage: 3 Challenge Level: What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board? Roll over the Dice Stage: 2 Challenge Level: Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded? Dotty Circle Stage: 2 Challenge Level: Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis? Have You Got It? Stage: 3 Challenge Level: Can you explain the strategy for winning this game with any target? Handshakes Stage: 3 Challenge Level: Can you find an efficient method to work out how many handshakes there would be if hundreds of people met? More Twisting and Turning Stage: 3 Challenge Level: It would be nice to have a strategy for disentangling any tangled ropes... Build it Up Stage: 2 Challenge Level: Can you find all the ways to get 15 at the top of this triangle of numbers? All Tangled Up Stage: 3 Challenge Level: Can you tangle yourself up and reach any fraction? Build it up More Stage: 2 Challenge Level: This task follows on from Build it Up and takes the ideas into three dimensions! Tilted Squares Stage: 3 Challenge Level: It's easy to work out the areas of most squares that we meet, but what if they were tilted? Got it for Two Stage: 2 Challenge Level: Got It game for an adult and child. How can you play so that you know you will always win?

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CC-MAIN-2017-47

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https://www.gradesaver.com/textbooks/math/algebra/algebra-1-common-core-15th-edition/chapter-7-exponents-and-exponential-functions-concept-byte-page-447/6

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Algebra 1: Common Core (15th Edition) $a.$ Conjecture: (the cube root of a number) = ($\displaystyle \frac{1}{3}$ power of a number) $b.$ Our conjecture works on $8$ and $27.$ $a.$ Generalizing on the pattern we observed in exercises 1-5: (the square root of a number) = ($\displaystyle \frac{1}{2}$ power of a number), We hypothesize that: (the cube root of a number) = ($\displaystyle \frac{1}{3}$ power of a number) $b.$ We know that $2^{3}=8$, so $\sqrt[3]{8}=2$ The calculator returns $8^{\wedge}(1\div 3)=2$ as well. We know that $3^{3}=27$, so $\sqrt[3]{27}=3$ The calculator returns $27^{\wedge}(1\div 3)=3$ as well So, our conjecture works for $8$ and $27.$

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CC-MAIN-2023-40

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https://www.nagwa.com/en/videos/978108418548/

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# Video: Using Equal Groups to Understand Multiplication by Zero When we multiply, we can think about counting equal groups of objects. 3 boxes of 2 balls = 6 balls, 3 × 2 = 6. How many balls would you have if you had 3 boxes with 0 balls in each box? Find the missing number: 3 × 0 = ＿. 03:03 ### Video Transcript When we multiply, we can think about counting equal groups of objects. Three boxes of two balls equals six balls. Three times two equals six. How many balls would you have if you had three boxes with zero balls in each box? Find the missing number: three times zero equals what. To start within this problem, we’re reminded of a way of thinking about multiplication. When we multiply, we can think about counting equal groups of objects. And the picture shows this. We have three boxes. And in each box, there’s an equal number of balls. We can think of each of the three boxes as representing a group. And, of course, they’re all equal groups. They all contain two basketballs. Three boxes of two balls or three groups of two balls equals six balls altogether. And we can see that by counting in twos. Two, four, six. This is why we can write the calculation three times two equals six. Three lots of two equals six. Now, we can apply this idea of counting equal groups of objects when multiplying by zero. The question asks us, how many balls would we have if we had three boxes with zero balls in each box? And we can see in the picture we have three empty boxes. We could think of these as three empty groups or three groups with nothing in them. So we don’t need to do any counting here. We can see straightaway we haven’t got any balls. When there were two balls in each box, we could count in twos. This time, we’d have to count in zeros. And the answer would be zero each time. Three groups of zero equals zero. The final part of the question asks us to find the missing number. Three multiplied by zero equals what? Well, as we’ve seen already, three groups of nothing equals nothing. The missing number is zero. Multiplying by zero can be quite difficult to think about. So it’s useful to have this idea of counting equal groups of objects. It can help us understand why the answer is zero. If we have three boxes with zero balls in each box, then we’ll have zero balls altogether. And so, the answer to three times zero equals zero. The answers to both parts of this problem are the same; they’re zero.

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https://www.tutorela.com/math/subtracting-whole-numbers-with-subtraction-in-parentheses

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# Subtracting Whole Numbers with Subtraction in Parentheses πŸ†Practice additional arithmetic rules Subtraction of whole numbers with subtractions in parentheses refers to a situation where we perform the mathematical operation of subtraction on the difference of some terms that are in parentheses. For example: $12 - (3-2) =$ One way to solve this exercise will be to distribute the parentheses. To do this, we must remember that according to the law of signs of addition/ subtraction, after removing parentheses, the expressions that were inside them change their sign. That is, in our example: $12 - (3-2) =$ $12 - 3 + 2 =$ $9 + 2 = 11$ When distributing the parentheses, we will place a $-$ in front of the number $3$ and a $+$ before the $2$. As you can see, in both cases the sign that was inside the parentheses has switched to the opposite sign. Another way to solve this exercise is to use the order of operations, that is to say: $12 - (3-2) =$ We will start by solving the expression in parentheses by using the order of operations and we will get: $12 - 1 = 11$ ## Test yourself on additional arithmetic rules! $$100-(5+55)=$$ If you are interested in this article you may also be interested in the following articles: For a wide range of math articles visit the Tutorela blog. ## Exercises for subtracting whole numbers with subtraction in parentheses ### Exercise 1 Solve the following exercise: $-30-\left(\left(-41\right)-\left(\left(-4\right)-\left(-8\right)\right)\right)=$ Solution: First we solve the innermost parentheses. $-30-\left(\left(-41\right)-\left(\left(-4\right)+8\right)\right)=$ Order the expression in the innermost parentheses and solve it. $-30-\left(\left(-41\right)-\left(8-4\right)\right)=$ $-30-\left(\left(-41\right)-4\right)=$ We break $41$ down into $2$ numbers to make the calculation easier. $-30-\left(-40-1-4\right)=$ $-30-\left(-40-1-4\right)=$ $-30-\left(-45\right)=$ We solve according to the rules. $-30+45=$ $45-30=15$ $15$ Join Over 30,000 Students Excelling in Math! Endless Practice, Expert Guidance - Elevate Your Math Skills Today ### Exercise 2 $17-\left(3-\left(-7-4\right)\right)=$ Solution: First, we solve the innermost parentheses and break down$4$ into $2$ terms to make the calculation easier. $17-\left(3-\left(-7-3-1\right)\right)=$ $17-\left(3-\left(-10-1\right)\right)=$ $17-\left(3-\left(-11\right)\right)=$ After solving the inner parentheses we continue solving the exercise that remains in parentheses. $17-\left(3+11\right)=$ $17-14=$ We break down the expression to make the calculation easier. $10+7-10-4=$ We solve the exercise in two parts. $10-10=0$ $7-4=3$ $3$ ### Exercise 3 $-58-\left(\left(-7\right)-\left(-12\right)\right)=$ Solution: We solve the expression in parentheses, first reordering the minus and plus signs. $-58-\left(-7+12\right)=$ Solve the expression in parentheses accordingly. $-58-\left(12-7\right)=$ Solve according to the rules. $-58-5=$ We break down $5$ into $2$ terms to make the calculation easier. $-58-2-3=$ $-60-3=-63$ $-63$ Do you know what the answer is? ### Exercise 4 $49-\left(53-18\right)=$ Solution: First we start with the expression in parentheses and break down the $53$ into $2$ numbers to make the calculation easier. $49-\left(58-5-18\right)=$ We solve the expression in parentheses and then solve accordingly. $49-\left(58-18-5\right)=$ $49-\left(40-5\right)=$ $49-35=$ We break down the $49$ into $2$ numbers to make the calculation easier. $45+4-35=$ We reorder the operations accordingly and solve. $45-35+4=$ $10+4=14$ $14$ ### Exercise 5 $37-\left(4-7\right)=$ Solution: First we tackle the expression in parentheses and solve. $37-\left(-3\right)=$ We reorder the minus and plus signs accordingly, and solve. $37+3=40$ $40$ ## Review questions ### What is the subtraction of whole numbers with subtraction in parentheses? The parentheses are a grouping sign. As the name implies, they helps us to group operations where certain mathematical operations need to be performed. These parentheses indicate that the operations must be performed from the inside out, that is, first we must solve the operations that are inside the parentheses, in this case the subtraction, and then use that number in our subtraction operation. ### What is the law of signs? In order to be able to solve operations with parenthese, the law of signs for multiplication must be applied. This law can be seen as follows: $+\times+=+$ $+\times-=-$ $-\times+=-$ $-\times+=-$ Do you think you will be able to solve it? ### How to solve with parentheses? To solve an operation with parentheses, all we have to do is complete the operations from the inside out, that is, perform the operations that are inside the parentheses and then the operations outside the parentheses. In this case we will solve the subtractions that are inside the parentheses and then we use sign laws and perform the next operation. ### How to eliminate parentheses in addition and subtraction? In order to eliminate the parentheses in an addition or a subtraction expression, we first perform the operations that are inside the parentheses, and in this way the parentheses are eliminated, let's see some examples: #### Example 1 $52-\left(25-11\right)=$ Solution: We solve the subtraction inside the parentheses. $52-\left(14\right)=$ We remove the parentheses by applying the law of signs. $52-14=$ We break down the $14$ into two terms to make the calculations easier. $52-12-2=40-2=38$ $38$ #### Example 2 $36-\left(\left(-3\right)-\left(-8\right)\right)=$ Solution: Eliminate the innermost parentheses using sign laws. $36-\left(-3+8\right)=$ Solve the operations inside the parentheses. $36-\left(8-3\right)=36-\left(5\right)$ Again we eliminate parentheses. $36-5=31$ $31$ ## examples with solutions for subtracting whole numbers with subtraction in parentheses ### Exercise #1 $38-(18+20)=$ ### Step-by-Step Solution According to the order of operations, first we solve the exercise within parentheses: $18+20=38$ Now, the exercise obtained is: $38-38=0$ $0$ ### Exercise #2 $8-(2+1)=$ ### Step-by-Step Solution According to the order of operations, we first solve the exercise within parentheses: $2+1=3$ Now we solve the rest of the exercise: $8-3=5$ $5$ ### Exercise #3 $22-(28-3)=$ ### Step-by-Step Solution According to the order of operations, we first solve the exercise within parentheses: $28-3=25$ Now we obtain the exercise: $22-25=-3$ $-3$ ### Exercise #4 $12:(2\times2)=$ ### Step-by-Step Solution According to the order of operations, we first solve the exercise within parentheses: $2\times2=4$ Now we divide: $12:4=3$ $3$ ### Exercise #5 $100-(30-21)=$ ### Step-by-Step Solution According to the order of operations, we first solve the exercise within parentheses: $30-21=9$ Now we obtain: $100-9=91$ $91$

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CC-MAIN-2024-30

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http://guerzhoy.princeton.edu/201s20/pre/P8/p8.html

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### Problem 1 Suppose that $$X\sim\mathcal{N}(2, 10^2)$$. We sample the variable $$X$$ once (i.e., we obtain a sample from the distribution $$\mathcal{N}(2, 10^2)$$). In this problem, you will be computing the same quantity in four different ways. You should expect to get roughly the same answer every time. ### Problem 1(a) Write R code to obtain $$P(2.1 < X < 3.1)$$. Use pnorm. ### Problem 1(b) Write R code to obtain $$P(2.1 < X < 3.1)$$. Use pnorm(..., ,mean = 0, sd = 1). ### Problem 1(c) Write R code to obtain $$P(2.1 < X < 3.1)$$. Use rnorm. (And not pnorm.) ### Problem 1(d) Write R code to obtain $$P(2.1 < X < 3.1)$$. Use rnorm(..., mean = 0, sd = 1) ### Problem 2 Suppose 65% of Princeton students like Wawa better than World Coffee. We selected a random sample of 100 students, and asked them which they prefer. What is the probability that more than 78 students said “Wawa”? #### Problem 2(a) Answer the question using pbinom. #### Problem 2(b) Answer the question using pnorm. Use the normal approximation to the Binomial distribution (recall: the mean is $$n\times prob$$ and the variance is $$n\times prob\times (1-prob)$$). (Note: you shouldn’t expect an exact match between 2(a) and 2(b) because of the lack of continnuity correction. You can try obtaining an exact match by varying the value of the q). ### Problem 3 Suppose 100 Princeton students we asked whether Harvard or Stanford is the worse online institution of higher learning. 60 students said that Stanford is worse. Compute the p-value for the null hypothesis that Princeton students think that Harvard and Stanford are equally bad, on average. What can you conclude? ### Problem 4 Answer Problem 2 using only rnorm(..., mean = 0, sd = 1)

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CC-MAIN-2020-24

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https://www.solveyourtech.com/how-to-round-numbers-in-excel-a-step-by-step-guide-2/

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How to Round Numbers in Excel: A Step-by-Step Guide Rounding numbers in Excel is a handy skill that can make your data look cleaner and more professional. It’s a simple process that involves using the ROUND function, which allows you to specify how many decimal places you want to round a number to. Whether you’re dealing with financial data, scientific calculations, or any other type of numerical data, knowing how to round numbers in Excel can save you time and prevent errors. Step by Step Tutorial on How to Round Numbers in Excel Before we dive into the steps, it’s important to understand what we’re trying to achieve. Rounding numbers in Excel helps to simplify complex data, making it easier to read and interpret. It can also help to standardize figures when working with multiple data sets. Step 1: Select the cell where you want the rounded number to appear Choose the cell in your Excel worksheet where you want the rounded number to be displayed. This cell should be different from the one that contains the original number you want to round. This way, you can keep the original data intact and just display the rounded figure in another cell. Step 2: Type the ROUND formula In the selected cell, type in the ROUND formula: =ROUND(number, num_digits) In the formula, “number” refers to the cell containing the number you want to round, and “num_digits” is the number of decimal places you want to round to. Step 3: Enter the cell reference and the number of decimal places Click on the cell that contains the number you want to round, and then type in the number of decimal places you want to round to. For instance, if you want to round to two decimal places, you would type in 2. If you want to round to the nearest whole number, you would type in 0. Step 4: Press Enter After entering the cell reference and the number of decimal places, press Enter on your keyboard to apply the rounding. The cell will now display the rounded number based on the parameters you set in the formula. After completing these steps, the cell you selected in step 1 will now display the rounded number. It’s that easy! You can use the same method to round numbers throughout your entire Excel worksheet, saving you time and ensuring accuracy. Tips for Rounding Numbers in Excel • Use the ROUNDUP function to always round numbers up. • Use the ROUNDDOWN function to always round numbers down. • Remember that rounding can affect the accuracy of your data, so use it wisely. • Use the ROUND function as part of larger formulas to automate calculations. • Double-check your num_digits value to ensure you’re rounding to the correct place. What is the difference between the ROUND, ROUNDUP, and ROUNDDOWN functions? The ROUND function rounds numbers to the nearest specified decimal place, ROUNDUP always rounds numbers up, and ROUNDDOWN always rounds numbers down. Can I round numbers to the nearest thousand in Excel? Yes, you can round numbers to the nearest thousand by using a negative number for the num_digits argument in the ROUND function. Will the ROUND function affect my original data? No, the ROUND function does not change your original data. It only displays the rounded number in the cell where you applied the formula. Can I use the ROUND function with other formulas? Yes, the ROUND function can be nested within other formulas to perform calculations on rounded numbers. How do I round to the nearest whole number in Excel? To round to the nearest whole number, use the ROUND function with the num_digits argument set to 0. Summary 1. Select the cell for the rounded number to appear. 2. Type the ROUND formula. 3. Enter the cell reference and number of decimal places. 4. Press Enter. Conclusion Rounding numbers in Excel is a breeze once you get the hang of it. By following the simple steps outlined in this article, you can quickly round any number to your desired level of precision. Whether you’re working on a financial report, analyzing scientific data, or just trying to simplify your figures, the ROUND function is an essential tool in your Excel arsenal. Remember to use this function carefully, as rounding can sometimes impact the accuracy of your data. With a little practice, you’ll be rounding numbers like a pro and making your spreadsheets look more polished and professional. So go ahead and give it a try—happy rounding!

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# Numbsubarrayer of elements less than or equal to a given number in a given ## Introduction Effective sorting and searching algorithms are essential for performance optimization in the field of programming. Numbsubarrayer is one such algorithm that works well in a variety of situations. The Numbsubarrayer is an effective tool for data manipulation and analysis because it can quickly identify elements in an array that are less than or equal to a specified number. The Numbsubarrayer algorithm is a basic method for filtering elements in an array according to a predetermined standard. Finding elements that are less than or equal to a given number is what we are looking for in this situation. Code Output: Code Explanation Function Definition (numsubarrayer) • Three parameters are required for the function numsubarrayer: an integer array arr, its size n, and an integer target. • After printing a message with the target number, iterating through each array element is done. For Loop • From index 0 to n-1, the for loop iterates through every element in the array. Conditional Verification • An if statement inside the loop determines if the current element arr[i] is less than or equal to the goal number. Printing Elements • Printf is used to print the element if the condition is true. The elements that are less than or equal to the given target are printed in this way. Main Function • The program's entry point serves as the primary function. • Declared with values {5, 12, 8, 3, 7, 10, 15} is an example array array. • Sizeof is used to calculate the array's size (size). • The Numbsubarrayer operation requires a target number (targetNumber). Calling the Function Numbsubarrayer • The array, its size, and the target number are passed as arguments to the numsubarrayer function. • This causes the example array's Numbsubarrayer operation to begin. Return Statement • The program has successfully executed, as indicated by the return 0 statement. A return value of 0 in C typically indicates Success. Output • The array's elements that are less than or equal to the target number are output by the program together with a message. Time Complexity The given C code has an O(n) time complexity, where 'n' is the size of the input array. The one-for loop, which iterates through each element of the array exactly once, is the cause of this linear time complexity. Each element in the loop undergoes a constant amount of work that includes a comparison and possibly a print operation. The algorithm is an efficient solution for this particular problem because it scales linearly with the size of the array and takes less time overall. The loop will run 'n' times in the worst-case scenario, where all array elements are less than or equal to the target number, resulting in a time complexity proportionate to the size of the input. Space Complexity The code's space complexity is O(1), or constant space. Regardless of the size of the input array, the program uses a relatively constant amount of memory. The program's main variables, which are integers (i, targetNumber, etc.), are independent of the input array's size. Furthermore, no additional dynamic memory is allocated by the numsubarrayer function. As a result, the program is memory-efficient because the amount of space it needs stays constant. The algorithm does not depend on additional data structures that would increase in size with the input, nor is it affected by the size of the input array. This improves the space utilization efficiency of the algorithm. ### Applications of Numbsubarrayer Data Filtering Numbsubarrayer is frequently employed in situations where it is necessary to filter data according to particular criteria. For instance, identifying students whose test results fall below a cutoff or removing sales transactions below a specific amount. Search Operations Numbsubarrayer can be used in search operations to find elements that meet a specific criterion quickly. Information retrieval systems and databases especially benefit from this. Statistical Analysis Numbsubarrayer facilitates the extraction of subsets of data that satisfy specific criteria when working with datasets. This is useful for research and statistical analysis. Optimizing Algorithms A common building block for more intricate algorithms is the numsubarrayer. The optimization of algorithms that necessitate filtering operations is enhanced by its effective implementation.

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Cody Problem 486. Surface Fit z(x,y) Solution 60153 Submitted on 12 Mar 2012 by Alfonso Nieto-Castanon This solution is locked. To view this solution, you need to provide a solution of the same size or smaller. Test Suite Test Status Code Input and Output 1   Pass %% x= [0 0 1 1 2 2 3 3]; y= [0 1 0 1 0 1 0 1]; z=[-4 -1 -3 -2 0 -1 5 2]; c=[1 -2 3 -4]; assert(isequal(c,round(sufit(x,y,z)))) 2   Pass %% x= rand(1,100); y= rand(1,100); z=7*x.^2-9*x.*y+11*y.^2-17; c=[7 -9 11 -17]; assert(isequal(c,round(sufit(x,y,z)))) 3   Pass %% x= rand(1,10000); y= rand(1,10000); z=17*x.^2-19*x.*y+11*y.^2-13; c=[17 -19 11 -13]; assert(isequal(c,round(sufit(x,y,z))))

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It is not always easy to convert densities, but it can be much easier with the right tools. Our density conversion converter is the perfect tool for any laboratory measuring different densities. Simply type in the numbers, and the calculator will do the work for you. This density conversion convector has the liquids, solids, and gases measurements. It can be used for conversion between different units of density. Take a look other related calculators, such as: ## What is Density Density is a physical quantity characteristic of each substance. It is the ratio of the mass of a substance to its volume. If the density of a substance or body is equal at each point, the substance or body is homogeneous. Density is typically measured in kilograms per cubic meter (kg/m3). The greater the density, the higher the concentration of the substance. You can use the formula below: \rho = \frac{m}{V} If a body is made up of several different substances, you cannot determine its density by knowing only the viscosity of those substances. In such cases, you can calculate the body’s density by dividing the total mass by the total volume of that body. Density is not an invariant characteristic of a substance but depends primarily on temperature, which is valid for all substances in all aggregate states. For a gaseous state, the density strongly depends on the pressure in that gas. As a rule, the density of all substances decreases with increasing temperature. ## Specific Gravity Specific gravity is the size of the density of a substance. It is usually expressed as the ratio of the density of a substance to the density of water. A substance with a specific gravity of less than 1 is less dense than water and will float in it. A substance with a specific gravity greater than 1 is more viscous than water and will sink in it. ## Density units, symbols, and conversion values table The basic unit of density for solids is called the kilogram per cubic meter (kg/m3). But, we can also express density in other units of measurement. For example, if you want to find density in liquids, you need to use kg/L as a basic unit. How much density expressed in kg/m3 corresponds to the density expressed in g/cm3? Here is the result: 1\frac{g}{cm^{3}}=\frac{0,001kg}{0,000001m^{3}}=1000\frac{kg}{m^{3}} For the most commonly used bodies, the density is predetermined, and its amount can be found in the table below: ## How to calculate density – example Calculate the volume of the gold chain if its mass is 5.5 dag. Use a table with body densities. The mass of a gold chain is 5.5 dag or 55g. From the table above, you can find that the gold density is 19300 kg/m3 or 19,3 g/cm3. We can calculate the volume of the gold chain with this formula: V = \frac{m}{\rho } = \frac{55}{19,3}=2,85cm^{3} ## The density of water in lb/gal Water is a chemical compound with a density of 1 gram per cubic centimeter. It is a clear, colorless, odorless, tasteless liquid essential for all living organisms. With very low viscosity, water is a good conductor of heat. The basic unit for density of water is kg/m3, but you can also calculate it with lb/gal. 1 lb/gal = 119.826 kg/m3 ## The density of water in grams per cubic centimeters We have already repeated several times that the basic unit of measurement for density is kg/m3. However, if we want to calculate the density of water in g/cm3, we will do it as follows: The water temperature is 0°C, and the density is 999,839 kg/m3. It is equal to 0,999839 g/cm3. ## FAQ? ### 1. How do you convert density? Density is equal to the mass of the body divided by its volume. So, if you want to convert density, you first need to find the body’s mass and volume. ### 2. What is the conversion factor of density? You can use conversion factors for converting between different kinds of units. Also, you can use density as a conversion factor between body mass and body volume. ### 3. How do you convert density to kg/m3? It is straightforward to convert from any unit into kg/m3. For example, if you need to convert density from 1 g/cm3 to kg/m3, you just need to divide 0,001kg with 0,000001m3. The result will be 1000kg/m3.

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https://stonespounds.com/528-8-stones-in-stones-and-pounds

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# 528.8 stones in stones and pounds ## Result 528.8 stones equals 528 stones and 11.2 pounds You can also convert 528.8 stones to pounds. ## Converter Five hundred twenty-eight point eight stones is equal to five hundred twenty-eight stones and eleven point two pounds (528.8st = 528st 11.2lb).

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https://www.frontiersin.org/articles/10.3389/fpsyg.2018.01833/full?utm_source=FWEB&utm_medium=NBLOG&utm_campaign=ECO_FPSYG_bayesian-reasoning

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## ORIGINAL RESEARCH article Front. Psychol., 12 October 2018 Sec. Cognition https://doi.org/10.3389/fpsyg.2018.01833 # Why Can Only 24% Solve Bayesian Reasoning Problems in Natural Frequencies: Frequency Phobia in Spite of Probability Blindness • Mathematics Education, Faculty of Mathematics, University of Regensburg, Regensburg, Germany For more than 20 years, research has proven the beneficial effect of natural frequencies when it comes to solving Bayesian reasoning tasks (Gigerenzer and Hoffrage, 1995). In a recent meta-analysis, McDowell and Jacobs (2017) showed that presenting a task in natural frequency format increases performance rates to 24% compared to only 4% when the same task is presented in probability format. Nevertheless, on average three quarters of participants in their meta-analysis failed to obtain the correct solution for such a task in frequency format. In this paper, we present an empirical study on what participants typically do wrong when confronted with natural frequencies. We found that many of them did not actually use natural frequencies for their calculations, but translated them back into complicated probabilities instead. This switch from the intuitive presentation format to a less intuitive calculation format will be discussed within the framework of psychological theories (e.g., the Einstellung effect). ## Introduction Many professionals, such as medical doctors and judges in court, are expected to make momentous decisions based on statistical information. Often, Bayesian inferences are required, for example when a radiologist has to judge and communicate the statistical meaning of a positive mammography screening. Many empirical studies have documented faulty inferences and even cognitive illusions among professionals of various disciplines (Hoffrage et al., 2000; Operskalski and Barbey, 2016). In the medical context, the consequences are particularly severe because many patients are mistakenly found diseased, which can entirely change their lives (Brewer et al., 2007; Gigerenzer et al., 2007; Salz et al., 2010; Wegwarth and Gigerenzer, 2013). Similarly, insufficient knowledge of statistics in general and incorrect Bayesian reasoning in particular can result in false convictions or acquittals made by juries in court, for example when they have to evaluate evidence based on a fragmentary DNA sample. These faults bear the risk of destroying innocent people's lives, too, as happened, for instance, in the famous case of Sally Clark (Schneps and Colmez, 2013; Barker, 2017). Typically, the statistical information that the aforementioned professionals are confronted with is provided in probability format, that is, fractions or percentages describing the probability of a single event, for example the prevalence of breast cancer in the population. Generally, in situations where Bayesian inferences are necessary, three pieces of statistical information are given: the base rate (or a priori probability), sensitivity, and false alarm rate. Consider, for instance, the heroin addiction problem (adapted from Gigerenzer and Hoffrage, 1995): The probability of being addicted to heroin is 0.01% for a person randomly picked from a population (base rate). If a randomly picked person from this population is addicted to heroin, the probability is 100% that he or she will have fresh needle pricks (sensitivity). If a randomly picked person from this population is not addicted to heroin, the probability is 0.19% that he or she will still have fresh needle pricks (false alarm rate). What is the probability that a randomly picked person from this population who has fresh needle pricks is addicted to heroin (posterior probability)? With the help of Bayes' theorem, the corresponding posterior probability P(H|N), with H denoting “person is addicted to heroin” and N denoting “person has fresh needle pricks,” can be calculated. Given the probabilistic information (the low base rate, high sensitivity, and low false alarm rate), the result of only 5% seems astonishingly low to most people—professionals and laypeople alike. In fact, only very few—on average as few as 4% of the participants included in a comprehensive meta-analysis (McDowell and Jacobs, 2017)—are able to draw the correct inferences necessary to come to the right conclusion in such Bayesian tasks. The vast majority of people have difficulties, which can result in severe misjudgments. The reasons for this poor performance in Bayesian reasoning are widely discussed. One explanation is the neglect of the base rate, which can be very low in many Bayesian situations (Tversky and Kahneman, 1974; Bar-Hillel, 1983). This leads to much greater estimates for the posterior probability, which is consistent with most people's intuition. Further reasons for the poor performance include participants neglecting the false alarm rate P(N|H) or confusing the false alarm rate with the posterior probability P(H|N) (Gigerenzer and Hoffrage, 1995) as well as participants overweighing the sensitivity (e.g., McCloy et al., 2007). In order to prevent dangerous misjudgments due to faulty Bayesian inferences, the concept of natural frequencies has proven to be a powerful instrument (e.g., Gigerenzer and Hoffrage, 1995; Siegrist and Keller, 2011). Natural frequencies can be obtained by natural sampling (Kleiter, 1994) or, alternatively, by translating probabilities (e.g., “80%”) into expressions consisting of two absolute frequencies (e.g., “80 out of 100”; for a discussion on the equivalence of natural frequencies and probabilities, see section Present Approach). Consider once again the heroin addiction example, this time, however, in natural frequency format: 10 out of 100,000 people from a given population are addicted to heroin. 10 out of 10 people who are addicted to heroin will have fresh needle pricks. 190 out of 99,990 people who are not addicted to heroin will nevertheless have fresh needle pricks. How many of the people from this population who have fresh needle pricks are addicted to heroin? With the help of this format, significantly more people find the correct answer to the problem, which is 10 out of (10 + 190). As a consequence, performance rates in the frequency format typically increase to about 24% (McDowell and Jacobs, 2017). Errors due to base rate neglect as mentioned above occur less often with natural frequencies, since the base rate need not be attended to in the frequency version because it is already included in the information on the sensitivity and false alarm rate. Thus, Bayes' modified theorem containing natural frequencies yields the correct answer of “10 out of 200” in the heroin addiction problem based on a simpler computation: More than 20 years of research have confirmed the benefit that comes with the concept of natural frequencies in Bayesian reasoning situations. Laypeople, students, professionals across various domains (e.g., medicine, law, and management), and even children perform significantly better when working on a Bayesian reasoning task that is presented in natural frequencies instead of probabilities (e.g., Wassner, 2004; Zhu and Gigerenzer, 2006; Hoffrage et al., 2015; Binder et al., 2018). Additionally, various other factors are known to have an impact on performance in Bayesian reasoning tasks. Visualizations, for example tree diagrams (e.g., Yamagishi, 2003; Binder et al., 2018), unit squares (e.g., Böcherer-Linder and Eichler, 2017; Pfannkuch and Budgett, 2017), icon arrays (e.g., Brase, 2009, 2014) or roulette wheel diagrams (e.g., Yamagishi, 2003; Brase, 2014), have been shown to improve accuracies in Bayesian situations (for an exception, see, e.g., Micallef et al., 2012). An overview and categorization of visualizations that were used to boost performance in Bayesian situations is provided by Khan et al. (2015). Furthermore, individual differences of participants, particularly cognitive abilities such as numeracy, graphicacy, and spatial abilities, certainly have an impact on performance rates (e.g., Chapman and Liu, 2009; Brown et al., 2011; Micallef et al., 2012; Peters, 2012; Ottley et al., 2016). In addition, the specific numerical values for population size, base rate, sensitivity, and false alarm rate can influence accuracies (Schapira et al., 2001). Cognitive biases and judgment errors associated with different numerical information are, for example, size effect and distance effect (Moyer and Landauer, 1967). Finally, details of the representation and framing of the problem text can affect performance in Bayesian reasoning situations (Obrecht et al., 2012). Ottley et al. (2016), for example, were able to show that specific problem formulations (e.g., providing all numerical information in context of the task, that is, not only base rate, sensitivity, and false alarm rate but also the probability or frequency of their respective complement) influence accuracies significantly. However, instead of contributing to the abundance of empirical studies replicating and discussing the beneficial effect of natural frequencies or other factors (e.g., Hoffrage et al., 2002; Pighin et al., 2016; McDowell et al., 2018), in this article we will focus on the other side of the coin, that is, on the 76% of participants in these studies (on average in McDowell and Jacobs, 2017) who failed to solve Bayesian reasoning tasks with natural frequencies. Why can still on average only a quarter of participants solve the problem correctly, although the task is presented in the beneficial natural frequency format? Many psychological theories explain, discuss, and specify in detail if and why natural frequencies facilitate Bayesian inferences (e.g., the nested sets-hypothesis or the ecological rationality framework, see Gigerenzer and Hoffrage, 1999; Lewis and Keren, 1999; Mellers and McGraw, 1999; Girotto and Gonzalez, 2001, 2002; Hoffrage et al., 2002; Sloman et al., 2003; Barbey and Sloman, 2007; Pighin et al., 2016; McDowell et al., 2018) and how additional tools, such as visualizations, further increase their beneficial effect (e.g., Yamagishi, 2003; Brase, 2009, 2014; Spiegelhalter et al., 2011; Micallef et al., 2012; Garcia-Retamero and Hoffrage, 2013; Micallef, 2013; Ottley et al., 2016; Böcherer-Linder and Eichler, 2017). However, a satisfying answer to the question why only 24% of participants solve Bayesian reasoning problems in natural frequency format correctly has not yet been found. ## Present Approach In order to explain why only 24% of participants draw correct Bayesian inferences when confronted with natural frequencies, in the present article we take one step back and switch our focus from performance rates to cognitive processes. In this respect, some important questions have not been addressed in detail so far: When given a Bayesian reasoning problem in frequency format, how do participants who fail to provide the correct answer approach the task? Where exactly do their calculations fail and why? In order to gain a first impression of what participants might do when confronted with a task in natural frequency format, we checked the questionnaires from our previous studies on Bayesian reasoning and natural frequencies (e.g., Krauss et al., 1999; Binder et al., 2015). Interestingly, we revealed some instances where participants had not applied the given natural frequencies but had translated them back into probabilities. In order to explore this phenomenon in depth, we had a closer look on what students usually learn about Bayesian reasoning problems in their high school statistics classes. Over the past two decades, statistics education has become an important column in German high school curricula. Here, just like in other countries, systematic calculation with probabilities has been in the center of teaching efforts. Alternative formats, such as natural frequencies, have despite the great amount of empirical research underpinning their benefits only played a minor role (cf. the American GAISE recommendations; Franklin et al., 2007). Even though there are some very recent efforts to implement the frequency concept in German curricula, for example in the new Bavarian high school curriculum for grade 10 (ISB, 2016), there still seems to be a tendency that this format is not accepted as equally mathematically valid as probabilities. This is supported by our impression from trainings for mathematics teachers that the concept of natural frequencies is not even familiar to most teachers. Furthermore, many schoolbooks tend to solve statistical tasks (not only Bayesian ones) with probability calculations, even when the task is presented in absolute frequencies (e.g., Freytag et al., 2008; Rach, 2018). Another observation we made based on a review of typical Bavarian school textbooks (Eisentraut et al., 2008; Freytag et al., 2008; Schmid et al., 2008) and workbooks (Sendner and Ruf-Oesterreicher, 2011; Reimann and Bichler, 2015) was that the more advanced students become in their high school career, the fewer statistical tasks are solved with natural frequencies by the respective textbooks. In conclusion, high school (and, consequently, university) students are a lot more familiar with probabilities than with natural frequencies due to their general (and sometimes even tertiary) statistical education. This implies that working with probabilities is a well-established strategy when it comes to solving statistical problems. While in many situations people profit from such an established strategy, in some cases, however, a previously fixed mindset can block simpler ways to approaching a problem (Haager et al., 2014). This phenomenon lies at the center of prominent psychological theories on cognitive rigidity. Consider, for example, the so-called Einstellung or mental set effect (Luchins, 1942). When solving a problem, people often rigidly apply a previously learnt solution strategy while neglecting possibly important information that would allow an easier solution. Such an Einstellung or mental set can be developed through repeated training, enabling the person to quickly solve problems of the same structure (Schultz and Searleman, 2002; Ellis and Reingold, 2014; Haager et al., 2014). However, the downside of these mental sets is that they can make a person “blind” to simpler solutions or—in the worst case—unable to find a solution at all. The most famous example for the Einstellung effect is Luchin's water jar experiment (1942; for more recent studies on the Einstellung effect in chess players and with anagram problems see, e.g., Bilalić et al., 2008; Ellis and Reingold, 2014). Participants in Luchin's study had to work out on paper how to obtain a certain volume of water using three empty jars of different sizes for measuring. The first five problems could all be solved by applying a relatively complicated strategy that was shown to the participants in an example problem. For the following five problems, a much simpler solution method was possible. However, the majority of participants kept using the complicated strategy they had previously learnt. Moreover, many of them could not solve the eighth problem at all, for which only the simple solution strategy was appropriate (Luchins, 1942). Recent research has shown that even experts can be subject to the Einstellung effect (e.g., Bilalić et al., 2008). Thus, mental sets developed over a long period of time can also lead to the blocking of simple solutions (for a detailed discussion of different aspects of cognitive rigidity see Schultz and Searleman, 2002). The probability strategy, which German students deal with during their whole high school career, would be an example for such a mental set that is developed over time. So taken together, these psychological theories and the strong familiarity of students with probabilities hint toward a possible answer to the question what participants might wish to do when they are confronted with a task in frequency format: They might try to represent the situation in the much more familiar probability format in order to be able to use established probabilities for their calculations. Such an Einstellung toward calculating with probabilities instead of natural frequencies would take away all benefits that come with the frequency concept. Calculating with probabilities in a Bayesian context—even though the task is provided in frequency format—has the consequence that the intuitive natural frequency algorithm [formula (2)] is no longer available, the more complicated probability algorithm [formula (1)] has to be applied, and people are no longer able find the correct solution. Thus, the Einstellung effect might explain why on average three quarters of participants fail with natural frequencies. In the same line, we assume that it is very unlikely that people translate probabilities into natural frequencies when given a task in probability format—despite over 20 years of research on the beneficial effects of natural frequencies. Here, the question might arise whether the two formats can actually be considered equivalent. In this respect, both mathematical and psychological aspects need to be addressed. First, we will shed light on the respective mathematical frameworks both formats operate in and to what extent these frameworks can be considered equivalent. Second, we will analyze the equivalence of probabilities and natural frequencies from a psychological viewpoint. Even though the two formats seem to follow different rules, from a mathematical perspective they can be defined analogously. Weber (2016) showed that natural frequencies can be embedded in a theoretical framework that is isomorphic to a probability space, that is, the structure at the basis of probability theory can be constructed in a similar way for natural frequencies. Thus, all fundamental mathematical properties of probabilities, for example closure, commutativity, and associativity of their addition, can theoretically also be assigned to natural frequencies (for details, see Weber, 2016). Therefore, the two concepts can be considered equivalent, implying that natural frequencies are an information format just as mathematically valid as probabilities. However, regardless of this theoretical equivalence of the two formats, a certain psychological uneasiness about the equivalence of natural frequencies and probabilities still seems to exist. It can be speculated that students who do not know about the mathematical framework of the frequency format might switch from natural frequencies to probabilities not only because they think that a probability algorithm is the only or the easiest way to solve the problem but also due to this subtle feeling of uneasiness, which stems from the assumption that natural frequencies are not a mathematically valid tool for solving Bayesian reasoning tasks. The latter implies that participants—even if they realize that a solution can be derived very easily by using natural frequencies—might think that a mathematically justified argumentation requires reasoning in terms of probabilities. All three assumptions (probabilities are the only, the easiest or the only allowed way) might trigger participants to rely on their Einstellung instead of actively using natural frequencies. To be clear, we theoretically consider natural frequencies as a superordinate concept for both “expected” and “empirically sampled” frequencies. Expected frequencies constitute frequencies expected in the long run (cf. Hertwig et al., 2004; Spiegelhalter and Gage, 2015; case 2 in Woike et al., 2017) and are often used for problem formulations in natural frequency format. In contrast, empirically sampled frequencies are derived from a natural sampling process (cf. Kleiter, 1994; Fiedler et al., 2000; cases 1 and 3 in Woike et al., 2017; for a discussion of the two sub-concepts of natural frequencies, see also Hertwig et al., 2004; Spiegelhalter and Gage, 2015). Of course, in the context of possibly switching between the two formats, besides the information format of the task, also the format in which the question is asked has to be taken into consideration (for a discussion on other details of textual problem representation, see, e.g., Ottley et al., 2016). It has to be noted that several studies (e.g., Cosmides and Tooby, 1996; Evans et al., 2000; Girotto and Gonzalez, 2001; Sirota et al., 2015) suggest that a question format that does not match the information format of the task reduces the natural frequency facilitation effect (Ayal and Beyth-Marom, 2014; Johnson and Tubau, 2015). However, only few studies directly test such incongruent problem and question formats (McDowell and Jacobs, 2017). We also do not want to examine incongruent formats (or other factors mentioned above) systematically (e.g., in order to boost performance), but rather aim to implement a question format as neutral as possible that allows for both answer formats simultaneously. Our interest is to observe and analyze a substantial amount of participants for all four possible cases, namely those who stay with the given format (probability or natural frequency) and those who switch to the other format for their calculations, in order to learn from the respective cognitive processes about possible mechanisms underlying the choice of calculation format. Since in our questionnaires from previous studies (Krauss et al., 1999; Binder et al., 2015), it was not always possible to judge which calculation format a participant applied, we will now explicitly ask participants to write down their solution algorithm in order to capture cognitive policies. Thus, in the present study we enter new research fields by investigating potential preferences in calculation format—when a problem introduction and question format as neutral as possible are given—that become visible by the way participants try to solve a given Bayesian task. Our research questions are: • Research question 1: Do participants show a general preference of the probability format over natural frequencies that becomes manifest in a strong tendency to a) keep working with probabilities if a task is given in probability format, although a sample population is provided b) even translate a task given in frequency format into probabilities, if the question allows for answers in both formats? • Research question 2: a) Regardless of the format in which the task is presented, do participants who work on this task actively using natural frequencies make more correct Bayesian inferences than participants who make their computations with probabilities? b) If questions allow for answers in both formats, which factor predicts correct Bayesian inferences better—the format that the task is presented in (presentation format) or the format that participants actively use for their calculations (calculation format)? Regarding research question 1, we hypothesized that participants do show a strong preference of probabilities over natural frequencies in both presentation formats. We further assumed that this preference has indeed a detrimental effect on performance in Bayesian reasoning tasks. With regard to research question 2, we therefore hypothesized that actively working with natural frequencies is a stronger predictor for correct inferences than the presentation format of a task. ## Experimental Study To examine these research questions, we conducted an empirical study with a first sample (N = 114) in 2016 (see section Participants). In the light of the current debate on the replication crisis (e.g., Open Science Collaboration, 2015), we decided to check the robustness of the results obtained with another sample (N = 69) with the same materials and design in 2017/2018. Three participants from the second sample were excluded from the analysis because they indicated that they had already participated in the first sample. Since we detected the same effects for both samples independently, we report the results for the combined sample of N = 180 (see section Results). ### Method Participants in our study had to work on two Bayesian reasoning tasks with different scenarios (heroin addiction problem and car accident problem, adapted from Gigerenzer and Hoffrage, 1995) and different numerical data (for design see Table 1 and for problem wordings see Table 2). These two contexts were chosen since they are not as common as, for example, the famous mammography problem, and thus, the chance of a participant already knowing the task beforehand was small. Moreover, both problems refer to daily-life situations, so the participants were expected to have no difficulties understanding the scenarios. One of the two Bayesian problems was presented in probability format and the other one in natural frequency format. We systematically permuted the order of context as well as information format. TABLE 1 Table 1. Design of the implemented problem versions. TABLE 2 Table 2. Problem formulations. In typical natural frequency versions, the question reads “How many of the … have/are …?,” often followed by a line “Answer: ____ out of ____.” Note that we are interested in cognitive processes triggered purely by the presentation format and not by a provided question or answer format. Thus, in all natural frequency versions, we wanted to implement a question format that allows both for probability and for natural frequency answers. In order to be as neutral as possible, we decided to use questions for proportions (see Tables 1, 2), which are a common question format in schoolbooks, too. The question “What is the proportion of people…” can be answered by, for example, “5%” or by “10 out of 200” and thus is settled in between probabilities and natural frequencies. In the probability versions, formulating a neutral question is rather difficult because a proportion usually refers to a concrete sample. Thus, instead of making the question format as neutral as possible, we decided to provide the participants already in the introduction with a sample population that the probabilities could be referred to (e.g., “On the internet, you find the following information for a sample of 100,000 people”). Thereby, we again allowed for both calculation formats. While in natural frequency versions the option for probability answers lies in the neutral question format, a possible natural frequency answer in probability versions was opened up by providing a concrete sample in the beginning of the task. It is important to note that we did not primarily want to compare performances by presentation format (which would just be a replication of many other studies) but by calculation format, so a total parallelization of the task versions was neither necessary nor the optimal design for our research questions. Because Bayesian reasoning tasks in German schoolbooks are usually presented with tree diagrams (Binder et al., 2015), after the question, we either asked for the construction of a tree diagram (in the first task) or presented a tree diagram (in the second task). The aim here was to present stimuli that are as ecologically valid as possible [with respect to (German) teaching contexts both in school and in university] and that provide the option to switch between the two formats. Both at school and at university level, 2 × 2-tables and tree diagrams are most commonly used for teaching Bayesian reasoning, whereas alternative visualizations (unit squares, icon arrays, etc.) are usually omitted. Since both 2 × 2-tables and tree diagrams allow for switching between the two formats (unlike, e.g., icon arrays) and since tree diagrams but not 2 × 2-tables can be directly equipped with conditional probabilities, only tree diagrams remained as visualizations suitable for our study. By using the latter, our hope was to exploratively shed light on whether a tree diagram might influence participants' choice of calculation format, for example by making the given presentation format more salient (for tree diagrams equipped with probabilities or natural frequencies in the heroin addiction problem see Figure 1). In sum, rather than systematically varying specific factors (or boosting performance), we wanted (1) to know how participants reason with the materials usually presented in German schools and universities, and (2) to observe a substantial number of people switching or staying with the presentation format in order to analyze their respective reasoning processes. For the same reasons, we implemented standard problem wordings. FIGURE 1 Figure 1. Tree diagrams visualizing the heroin addiction problem equipped with probabilities and natural frequencies. Since participants were explicitly asked to write down all calculations they made in order to solve the task, we were able to judge precisely and systematically which format they used for their calculations (see Supplementary Table 2; also see section Coding). The paper and pencil questionnaire contained a short information paper on the study and some general questions, for example on participants' age or study program, as well as the two tasks. Before participants were allowed to start with the second task, they had to hand in their solution for the first task. Participants were allowed to use a pocket calculator that was provided along with the questionnaire. There was no time limit; on average, participants took approximately 5 min to complete the demographic items and 25 min for both tasks. ### Coding The normatively correct solutions of the problems were 5% (or 10 out of 200) for the heroin addiction problem and 9.9% (or 55 out of 555) for the car accident problem (the results differ marginally if the task was presented in natural frequencies as opposed to probabilities, e.g., exactly 10% in the car accident probability version vs. 9.9% in the car accident frequency version). In order to guarantee maximum objectivity for classifying the answers as “correct Bayesian inference” or “incorrect Bayesian inference” and also for deciding whether either a probability algorithm or a frequency algorithm had been applied, we used strict coding guidelines (see Supplementary Table 1), which were applied by all coders. Since we were especially interested in whether participants used the correct algorithm for solving the task, mere calculation or rounding errors were neglected, resulting in answers that were classified as “correct Bayesian inference” even though the mathematical result was not entirely correct. In the same line, answers that appeared mathematically correct at first glance were classified as “incorrect Bayesian inference” if the result was just incidentally correct, but a wrong algorithm was applied (this rarely happened). Furthermore, we focused on the cognitive processes underlying each response when determining the “calculation format” of an answer. This cognitive process was measured by analyzing the exact calculations each participant wrote down to come to a solution. When a participant used probabilities (or natural frequencies) only, we classified the solution as “calculated with probabilities” (or natural frequencies, respectively). When both formats were clearly visible in the calculations, we classified the answer according to whether the participant used probabilities or natural frequencies for the crucial step in the calculation process, that is, the computation of the denominator in Bayes' formula, as can be seen in equations (1) and (2). Thus, the decisive factor in such unclear cases was the addition of two absolute numbers (in favor of a frequency algorithm) or the multiplication of probabilities (in favor of a probability algorithm, respectively). If, for example, in the heroin addiction problem a participant used both formats for his or her calculations, but added two absolute numbers (e.g., 10 + 190) to obtain the denominator in (2), the answer was classified as “calculated with natural frequencies”. If, on the other hand, a participant used both formats, but multiplied two probabilities (e.g., 0.01 × 100%) like in (1) to obtain the respective probabilities for the numerator or the denominator, we classified the answer as “calculated with probabilities” (no participant added frequencies and multiplied probabilities). Two raters coded 21% of all inferences independently according to the coding guidelines (see Supplementary Tables 1, 2). Since in 100% of all cases the correctness was rated in congruence (Cohen's κ = 1; Cohen, 1960), and the calculation format was classified identically in 97% of all cases (Cohen's κ = 0.95), the remaining inferences were rated by one coder. ### Participants We recruited N = 114 students from the University of Regensburg (Bavaria) in summer 2016, and N = 69 in winter 2017/2018 (three of which were excluded from the analysis since they had already participated in the study in 2016). Most of these students were enrolled in a teaching math program (N = 147), while some of them studied economic information technology, so a certain level of mathematics competency among the participants can be assumed (see also section Discussion). They were at different stages of their studies (most of them in their first two years) and their age ranged from 18 to 38, with an average of 22 years. Out of the total of N = 180 participants, 121 were female. Since each participant worked on two tasks, we obtained a total of 360 Bayesian inferences including participants' detailed solution algorithms. The study was carried out in accordance with the University Research Ethics Standards. Participants were informed that the study was voluntary and anonymous, and no incentives were paid. Participants were asked to give their written informed consent to participate in the study in advance. Thereupon, two students refrained from participating. ## Results In the following, we report the results for the combined sample of N = 180 participants, but all detected effects also hold for both the original (N = 114) and the replication sample (N = 66) independently. As far as our first research question is concerned, the results indeed show a strong preference of participants for calculating with probabilities in both contexts. This is illustrated by Figure 2, where, for example, P→ F denotes participants who were provided with a task in probability format but calculated with natural frequencies. On the one hand, when presented with a task in natural frequency format (second and fourth bars of Figure 2), almost half of participants (49%) nevertheless chose to apply probabilities for their calculations, although the neutral question explicitly allowed for answers in both formats. On the other hand, when they faced a probability version of a task (first and third bars of Figure 2), only 18% across both contexts chose to translate the problem into natural frequencies—despite the explicitly given sample population in the introduction. Taken together, according to our design natural frequencies represented the preferred calculation format in only about one third (34%) of all 360 Bayesian tasks although 50% of all tasks were presented in natural frequency format. FIGURE 2 Figure 2. Calculation format by presentation format and context. While Figure 2 does not yet display performances, Figure 3 shows performance rates in the resulting four combinations of presentation format and calculation format (P→P, P→F, F→F, F→P) for both problem contexts. It becomes clear that when natural frequencies were actively used for the calculations, performance rates were significantly higher than when probabilities were applied. Remarkably, in our design this holds true almost regardless of the presentation format: For both problems, the patterns look very similar for the two presentation formats. The performance in both problems obviously mainly depends on the calculation format, but only to a small amount on the presentation format. In the heroin addiction problem, the difference between both calculation formats is especially pronounced. The highest performance was detected when both variables presentation format and calculation format were natural frequencies (61% correct responses), descriptively followed by probability tasks that were worked on with frequencies (53% correct responses). In the two other cases (when participants calculated with probabilities), performance rates were considerably lower (13% if the presentation format was probabilities and 9% if the presentation format was natural frequencies). FIGURE 3 Figure 3. Percentages of correct inferences dependent on the presentation and calculation format in both problems. In general, the beneficial effect of presenting natural frequencies was replicated by our study. While 20% of the Bayesian tasks in probability format were solved correctly across both contexts, the performance rate for the tasks presented in frequency format was 36% (see Table 3). Compared to McDowell and Jacobs (2017), both of these numbers seem rather high. An explanation might lie within our sample: more than 80% of participants were enrolled in a mathematics education program and might therefore have comparably high numeracy, enabling them to perform above average in math tasks (for an analysis of participants' individual differences and switching behavior depending on their cognitive abilities, see below). Note that we also found context effects (36% correct responses in the heroin context vs. 20% correct inferences in the car accident context). TABLE 3 Table 3. Percentage of correct Bayesian inferences by context and presentation format (independent of calculation format). In order to separate the effects of presentation format and calculation format, we ran a generalized linear mixed model (GLMM) with a logistic link function. Here, we specified probabilities (both as presentation format and as calculation format) as reference category and included the possible explanatory factors “presentation format,” “calculation format” (via dummy coding), and the interaction term of presentation format and calculation format to predict the probability of a correct Bayesian inference in our design. According to the results of the generalized linear mixed model, the unstandardized regression coefficient for solving a task that was both presented and calculated in probability format was significant (b0 = −7.03, SE = 1.32, z = −5.32, p < 0.001), showing large inter-individual differences (for a discussion of these results, see below). The (unstandardized) regression coefficient for the presentation format was non-significant (b1 = −3.04, SE = 2.00, z = −1.52, p = 0.13), whereas the calculation format showed a significant regression coefficient (b2 = 9.85, SE = 3.85, z = 2.56, p = 0.01). Finally, the interaction of presentation format and calculation format yielded another significant regression coefficient (b3 = 4.85, SE = 2.22, z = 2.19, p = 0.03), indicating that calculating with natural frequencies increases performance even more when the task is also formulated in natural frequency format (i.e., when the absolute numbers for the frequency algorithm can be directly taken from the problem wording). The strong differences of individual competencies lead to extreme (unstandardized) regression coefficients in the model. However, a generalized linear model (neglecting inter-individual differences) estimated regression coefficients that—converted into probabilities via the logistic link function—exactly replicated the performance rates found in our data. This is because the GLMM accounts for these large differences in performances by estimating large inter-individual differences between the participants, as the intercepts (denoting the performances when presentation and calculation format was probabilities) were allowed to vary freely between participants. The substantial influence of the inter-individual differences also becomes apparent when inspecting the model fit: Whereas 6.5% of the variance is explained by the fixed GLMM regression coefficients (marginal R2 = 0.065), the inter-individual differences and the fixed regression coefficients together explain 68.5% of the variance (conditional R2 = 0.685). However notably, despite the large inter-individual differences, the influence of the fixed effects on the results was clear and strong. Although we did not explicitly collect data about participants' cognitive abilities (e.g., numeracy, spatial and graphical literacy), these inter-individual differences suggested a closer analysis of our data with this respect. Indeed, we found significant differences in performance especially between two subgroups of our sample: The N = 42 mathematics education students aspiring to teach at the academic school track of the German school system (Gymnasial students) outperformed the other N = 138 participants significantly (50% correct inferences vs. 21%; t(358) = 5.294, p < 0.001). We assume that this difference is due to the higher numerical, spatial, and graphical abilities of the first group, since they generally outperform the other mathematics education students in mathematics exams or mathematical knowledge tests (e.g., Krauss et al., 2008; see also Lindl and Krauss, 2017, Table 5, p. 396). Moreover, the Gymnasial students receive a considerably more thorough education in mathematics through their study program than the rest of our participants. However interestingly, these differences in cognitive abilities did not have any influence on calculation format preferences. Both subgroups tended in a similar way to prefer using probabilities over natural frequencies for their calculations (32% of Gymnasial students' solutions were based on a frequency algorithm, whereas 35% of the other participants calculated with natural frequencies; t(358) = −0.506; p = 0.613). As a consequence, although an overall shift of performances might be expected depending on participants' cognitive abilities and education, we assume a certain generalizability of our results across varying abilities and education levels regarding the switching rates (cf. section Discussion). By examining exploratively participants' reactions on a presented tree diagram, we revealed several instances where the participants had added probabilities to the branches of a tree diagram originally presented with natural frequencies in the nodes. Conversely, only few of the participants equipped a tree diagram that was originally presented in probability format with natural frequencies. When the participants had to construct actively a tree diagram visualizing the textual problem, we detected some instances where already before the diagram was drawn, participants had switched in their calculation format (in both directions: from natural frequencies to probabilities and vice versa). Therefore, some participants translated the presentation format into their calculation format right at the beginning of their problem solution process. However, since we did not systematically test versions without a visualization clue, these findings have to be considered only explorative hints concerning possible cognitive mechanisms that might lead participants to stay with a certain format or to switch from one to the other. These mechanisms will have to be addressed more closely in future research. ## Discussion In an empirical study with N = 180 students from the University of Regensburg, we found that the majority of participants do not actively use natural frequencies in Bayesian reasoning tasks. Even if the task is presented in the intuitive natural frequency format (with a neutral question asking for proportions), about half of the participants still prefer calculating with probabilities instead. Therefore, and since the “standardized” probability format is the “sine qua non” in probability theory, the results of our study reveal the Einstellung effect in Bayesian reasoning situations (Luchins, 1942; Luchins and Luchins, 1959; McCloy et al., 2007). We speculate that such an Einstellung might be enhanced by the still widespread idea that natural frequencies are not “mathematically correct” enough to actually work with in high school and university contexts. As a consequence, participants who might actually notice a possible solution of the Bayesian reasoning task based on a frequency algorithm might still rely on probabilities due to a certain kind of “phobia” to use natural frequencies for their calculations (for a discussion on the impact of affect on overcoming fixed mindsets, see Haager et al., 2014)—despite the ever-growing body of research pointing to the beneficial effects of the frequency concept (e.g., Gigerenzer and Hoffrage, 1995; Barbey and Sloman, 2007; Micallef et al., 2012; Obrecht et al., 2012; Ottley et al., 2016; McDowell and Jacobs, 2017). Although with our study, we cannot ultimately decide whether the Einstellung effect or this kind of “phobia” lies at the heart of participants' switching back to probabilities, we want to emphasize that both formats are mathematically equivalent in the sense that they can be defined analogously with the same properties and structure. Whatever the case may be, since recent efforts to implement natural frequencies in high school and university curricula appear not to be enough to make people actively take advantage of their benefits, we vouch for an even stronger implementation of the natural frequency concept in secondary education (especially in the higher grades), tertiary education, and in teacher training. The Einstellung toward preferring probabilities has a negative impact on performance rates: participants working with probabilities perform significantly worse than those who apply natural frequencies for their calculations. Moreover, at least in our design, the calculation format is an even stronger predictor for performance than the presentation format that previous research has mainly concentrated on (e.g., Barbey and Sloman, 2007; Siegrist and Keller, 2011). This suggests that participants who translate natural frequencies into probabilities follow a path that is disadvantageous in two respects: First, they choose the unintuitive probability over the natural frequency format, and second, they are prone to make further mistakes due to translation errors (that we did not explicitly consider in our study). Interestingly, a few participants (18%) did translate probabilities into natural frequencies. This suggests that at least a small minority is to some extent familiar with the natural frequency concept. These participants profit indeed from calculating with natural frequencies since their performance rates increased substantially compared to performances of participants who stay with probabilities (13 vs. 53% across both implemented contexts). This tendency is a first sign that natural frequencies might become an established solution strategy for Bayesian reasoning tasks. It has to be noted that our sample consisted of university students entirely. Since their mindsets and cognitive abilities (especially numeracy as well as graphical and spatial literacy) probably differ from the general population (Micallef et al., 2012), a different sample might, of course, yield different performance rates. However, we assume that even though the total population might generally perform worse than our sample, those using natural frequencies for their calculations will still outperform those who resort to probabilities. In the same way, we would expect an overall shift of performance rates depending on item difficulty or wording (for factors determining the difficulty of Bayesian reasoning tasks as well as for different problem wordings, see, e.g., Ottley et al., 2016), but we assume relative consistency with respect to format preferences across different Bayesian reasoning tasks. Future research might investigate in detail whether our results indicating an Einstellung effect in Bayesian reasoning situations hold also true when individual differences and item difficulty are systematically controlled. The context effects in our study in favor of the heroin addiction problem could be explained by having a closer look at the question formulation in the car accident problem. Here, the two relative clauses in the frequency version (see Table 2) demand higher verbal processing abilities and thus make the question harder to understand compared to the frequency question in the heroin addiction problem (only one relative clause, see Table 2). Consequently, the heroin addiction problem presented with natural frequencies yields significantly higher performance rates than the respective version of the car accident problem (51% correct inferences vs. 22%; see Table 3). Moreover, coding in our study was fairly complex (see Supplementary Tables 1, 2), even though we obtained interrater reliability scores of κ = 1 for the correctness of a Bayesian inference and of κ = 0.95 (Cohen, 1960) for determining the calculation format. In addition, we focused only on the correct algorithm applied for classifying an answer as “correct” (see Supplementary Table 1). Thus, we did not concentrate on calculation errors, including those that resulted from translating an information format into the other one. Therefore, we did not systematically detect translation errors dependent on the respective presentation format, in particular. This, however, is a conservative approach, since we assume that more people make mistakes when translating frequencies into probabilities than vice versa. Furthermore, in an explorative analysis, we detected several instances where the participants had equipped a presented frequency tree diagram with probabilities, suggesting that such a visualization does not prevent the participants from switching from the natural frequency to the probability format for their calculations. We speculate that even the opposite is the case: Since students are familiar with probability tree diagrams but not so much with frequency tree diagrams from their high school careers, the sight of a tree diagram (even though it is equipped with natural frequencies) might trigger their memories of the familiar probability trees and might thus provoke them to fill the diagram with probabilities. Moreover, many participants equipped the tree diagram they had been asked to draw with their chosen calculation format—even if the latter differed from the presentation format. This suggests that the participants tend to decide on their calculation format right at the beginning of their solution process. We thus speculate that the exact moment of the format switch lies immediately after (or even at the same time as) reading the task. Therefore, further research might investigate systematically when exactly people decide on the format they want to use for their calculations and if people possibly alter their decision during the solution process. In addition, it would be interesting to determine whether presenting a visualization such as a tree diagram or actively constructing one enhances or diminishes the Einstellung effect in Bayesian reasoning tasks (e.g., by systematically comparing versions with and without visualization)—and, more generally, whether visualizations affect the calculation format at all. The question remains open to what extent natural frequencies should be implemented in statistics education, since they can only be used in specific situations (e.g., in Bayesian reasoning problems or tasks where cumulative risk judgment is necessary; see McCloy et al., 2007). We suggest that natural frequencies be taught already at a young age to establish the concept over a longer period of time. When—at a later stage—the focus is shifted more and more to probabilities, a permanent interplay between the two formats seems reasonable. By using natural frequencies to illustrate, for example, the multiplication rule or Bayes' theorem, students can understand the two coexisting formats as equally legitimate representations for the underlying concept of uncertainty. Here, natural frequencies can be used to eliminate typical errors, to make difficult problems more understandable, and to prevent cognitive illusions. When probabilities are presented simultaneously, the connection between the two formats might become more apparent and a deeper understanding of the concept of uncertainty might be achieved. In this respect, future work, for example systematic training studies (cf. Sedlmeier and Gigerenzer, 2001), needs to determine the most successful ways to incorporate natural frequencies in statistics education at secondary and tertiary level in order to overcome the Einstellung effect. Future research on this topic might also investigate in more detail how much current teachers already know about the frequency concept in order to decide if natural frequencies indeed need a stronger focus in teacher training as we suggest. This could, for example, be realized by systematic teacher interviews. Moreover, future research might address empirically the cognitive mechanisms underlying the Einstellung effect as detected by our study, that is, whether participants assume that a probability algorithm is (a) the only way, (b) the easiest way, or (c) due to a feeling of uneasiness with the frequency concept the only mathematically allowed way to approach the Bayesian problem. Here, qualitative methods such as student interviews might be a valuable tool to clarify situation-specific causes of the Einstellung effect. Finally, it would be interesting to determine effective methods (e.g., visualizations or hints in the problem wording) to prevent people from falling back into probabilities in Bayesian reasoning tasks. ## Data Availability Statement The dataset generated can be found on https://epub.uni-regensburg.de/37693/. ## Ethics Statement This study was carried out in accordance with the recommendations of University Research Ethics Standards, University of Regensburg. The protocol was approved by the University of Regensburg. All subjects gave written informed consent in accordance with the Declaration of Helsinki. ## Author Contributions All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication. ## Conflict of Interest Statement The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. ## Acknowledgments We want to thank all participants of our study for contributing to our research project. We further thank Sven Hilbert for his statistical advice. This work was supported by the German Research Foundation (DFG) within the funding program Open Access Publishing. ## Supplementary Material The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fpsyg.2018.01833/full#supplementary-material ## References Ayal, S., and Beyth-Marom, R. (2014). The effects of mental steps and compatibility on Bayesian reasoning. Judgm. Decis. Mak. 9, 226–242. Barbey, A. K., and Sloman, S. A. (2007). Base-rate respect: from ecological rationality to dual processes. Behav. Brain Sci. 30, 241–297. doi: 10.1017/S0140525X07001653 Bar-Hillel, M. (1983). The base rate fallacy controversy. Adv. Psychol.16, 39–61. doi: 10.1016/S0166-4115(08)62193-7 Barker, M. J. (2017). Connecting applied and theoretical Bayesian epistemology: data relevance, pragmatics, and the legal case of Sally Clark. J. Appl. Philos. 34, 242–262. doi: 10.1111/japp.12181 Bilalić, M., McLeod, P., and Gobet, F. (2008). Why good thoughts block better ones: the mechanism of the pernicious Einstellung (set) effect. Cognition 108, 652–661. doi: 10.1016/j.cognition.2008.05.005 Binder, K., Krauss, S., and Bruckmaier, G. (2015). Effects of visualizing statistical information: an empirical study on tree diagrams and 2 × 2 tables. Front. Psychol. 6:1186. doi: 10.3389/fpsyg.2015.01186 Binder, K., Krauss, S., Bruckmaier, G., and Marienhagen (2018). Visualizing the Bayesian 2-test case: the effect of tree diagrams on medical decision making. PLoS ONE 13:e0195029. doi: 10.1371/journal.pone.0195029 Böcherer-Linder, K., and Eichler, A. (2017). The impact of visualizing nested sets. An empirical study on tree diagrams and unit squares. Front. Psychol. 7:241. doi: 10.3389/fpsyg.2016.02026 Brase, G. (2009). Pictorial representations in statistical reasoning. Appl. Cogn. Psychol. 23, 369–381. doi: 10.1002/acp.1460 Brase, G. (2014). The power of representation and interpretation: doubling statistical reasoning performance with icons and frequentist interpretations of ambiguous numbers. J. Cogn. Psychol. 26, 81–97. doi: 10.1080/20445911.2013.861840 Brewer, N. T., Salz, T., and Lillie, S. E. (2007). Systematic review: the long-term effects of false-positive mammograms. Ann. Intern. Med. 146, 502–510. doi: 10.7326/0003-4819-146-7-200704030-00006 Brown, S. M., Culver, J. O., Osann, K. E., MacDonald, D. J., Sand, S., Thornton, A. A., et al. (2011). Health litereacy, numeracy, and interpretation of graphical breast cancer risk estimates. Patient Educ. Couns. 83, 92–98. doi: 10.1016/j.pec.2010.04.027 Chapman, G. B., and Liu, J. (2009). Numeracy, frequency, and Bayesian reasoning. Judgm. Decis. Mak. 4:34. Cohen, J. (1960). A coefficient of agreement for nominal scales. Educ. Psychol. Meas. 20, 37–46. doi: 10.1177/001316446002000104 Cosmides, L., and Tooby, J. (1996). Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty. Cognition 58, 1–73. doi: 10.1016/0010-0277(95)00664-8 Eisentraut, F., Ernst, S., Keck, K., Leeb, P., Schätz, U., Steuer, H. Schätz, R., et al. (2008). Delta 10 – Mathematik für Gymnasien [Delta 10 – Mathematics for the Academic School Track]. Bamberg: CC Buchners Verlag. Ellis, J. J., and Reingold, E. M. (2014). The Einstellung effect in anagram problem solving: evidence from eye movements. Front. Psychol. 5:679. doi: 10.3389/fpsyg.2014.00679 Evans, J. S. B. T., Handley, S. J., Perham, N., Over, D. E., and Thompson, V. A. (2000). Frequency versus probability formats in statistical word problems. Cognition 77, 197–213. doi: 10.1016/S0010-0277(00)00098-6 Fiedler, K., Brinkmann, B., Betsch, T., and Wild, B. (2000). A sampling approach to biases in conditional probability judgments: beyond base rate neglect and statistical format. J. Exp. Psychol. General 129, 399–418. doi: 10.1037//0096-3445.129.3.399 Franklin, C., Horton, N., Kader, G., Moreno, J., Murphy, M., Snider, V., et al. (2007). Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report – A pre-K-12 Curriculum Framework. Alexandria, VA: American Statistical Association. Available Online at: www.amstat.org/education/gaise Freytag, C., Herz, A., Kammermeyer, F., Kurz, K., Peteranderl, M., Schmähling, R., et al. (2008). Fokus Mathematik 10 Gymnasium Bayern [Focus on Mathematics 10 for the Bavarian Academic School Track]. Berlin: Cornelsen Verlag. Garcia-Retamero, R., and Hoffrage, U. (2013). Visual representation of statistical information improves diagnostic inferences in doctors and their patients. Soc. Sci. Med. 83, 27–33. doi: 10.1016/j.socscimed.2013.01.034 Gigerenzer, G., Gaissmaier, W., Kurz-Milcke, E., Schwartz, L. M., and Woloshin, S. (2007). Helping doctors and patients make sense of health statistics. Psychol. Sci. Public Interest 8, 53–96. doi: 10.1111/j.1539-6053.2008.00033.x Gigerenzer, G., and Hoffrage, U. (1995). How to improve Bayesian reasoning without instruction: frequency formats. Psychol. Rev. 102, 684–704. doi: 10.1037/0033-295X.102.4.684 Gigerenzer, G., and Hoffrage, U. (1999). Overcoming difficulties in Bayesian reasoning: a reply to Lewis and Keren (1999) and Mellers and McGraw (1999). Psychol. Rev. 106, 425–430. doi: 10.1037/0033-295X.106.2.425 Girotto, V., and Gonzalez, M. (2001). Solving probabilistic and statistical problems: a matter of information structure and question form. Cognition 78, 247–276. doi: 10.1016/S00100277(00)00133-5 Girotto, V., and Gonzalez, M. (2002). Chances and frequencies in probabilistic reasoning: rejoinder to Hoffrage, Gigerenzer, Krauss, and Martignon. Cognition 84, 353–359. doi: 10.1016/S0010-0277(02)00051-3 Haager, J. S., Kuhbandner, C., and Pekrun, R. (2014). Overcoming fixed mindsets: the role of affect. Cogn. Emot. 28, 756–767. doi: 10.1080/02699931.2013.851645 Hertwig, R., Barron, G., Weber, E. U., and Erev, I. (2004). Decisions from experience and the effect of rare events in risky choice. Psychol. Sci. 15, 534–539. doi: 10.1111/j.0956-7976.2004.00715.x Hoffrage, U., Gigerenzer, G., Krauss, S., and Martignon, L. (2002). Representation facilitates reasoning: what natural frequencies are and what they are not. Cognition 84, 343–352. doi: 10.1016/S0010-0277(02)00050-1 Hoffrage, U., Krauss, S., Martignon, L., and Gigerenzer, G. (2015). Natural frequencies improve Bayesian reasoning in simple and complex inference tasks. Front. Psychol. 6:1473. doi: 10.3389/fpsyg.2015.01473 Hoffrage, U., Lindsey, S., Hertwig, R., and Gigerenzer, G. (2000). Communicating statistical information. Science 290, 2261–2262. doi: 10.1126/science.290.5500.2261 ISB, (2016). Staatsinstitut für Schulqualität und Bildungsforschung LehrplanPLUS Gymnasium Mathematik 10 [Curriculum for year 10 of the Bavarian academic school track]. Available online at http://www.lehrplanplus.bayern.de/fachlehrplan/gymnasium/10/mathematik. (Accessed 18 July, 2018). [ISB] (Ed.). Johnson, E. D., and Tubau, E. (2015). Comprehension and computation in Bayesian problem solving. Front. Psychol. 6:938. doi: 10.3389/fpsyg.2015.00938 Khan, A., Breslav, S., Glueck, M., and Hornbæk, K. (2015). Benefits of visualization in the mammography problem. Int. J. Hum. Comput. Stud. 83, 94–113. doi: 10.1016/j.ijhcs.2015.07.001 Kleiter, G. D. (1994). “Natural sampling. Rationality without base rates,” in Contributions to Mathematical Psychology, Psychometrics, and Methodology, eds G. H. Fisher and D. Laming (New York, NY: Springer), 375–388. Krauss, S., Baumert, J., and Blum, W. (2008). Secondary mathematics Teachers' pedagogical content knowledge and content knowledge: validation of the COACTIV constructs. Int. J. Math. Educ. 40, 873–892. doi: 10.1007/s11858-008-0141-9 Krauss, S., Martignon, L., and Hoffrage, U. (1999). “Simplifying Bayesian Inference: the General Case,” in Model-based Reasoning in Scientific Discovery, ed N. E. A. Magnani (New York, NY: Kluwer Academic/Plenum Publishers), 165–179. Lewis, C., and Keren, G. (1999). On the difficulties underlying Bayesian reasoning: a comment on Gigerenzer and Hoffrage. Psychol. Rev. 106, 411–416. doi: 10.1037/0033-295X.106.2.411 Lindl, A., and Krauss, S. (2017). “Transdisziplinäre Perspektiven auf domänenspezifische Lehrerkompetenzen. Eine Metaanalyse zentraler Resultate der Forschungsprojektes FALKO [Transdisciplinary perspectives on domain specific teacher competences. A meta-analysis of central results of the FALKO research project],” in FALKO: Fachspezifische Lehrerkompetenzen. Konzeption von Professionswissenstests in den Fächern Deutsch, Englisch, Latein, Physik, Musik, Evangelische Religion und Pädagogik [FALKO: Subject specific teacher competences. Conception of professional knowledge test in the subjects German, English, Latin, Physics, Musical Education, Evangelical Religious Education, and Pedagogy], eds S. Krauss, A. Lindl, A. Schilcher, M. Fricke, A. Göhring, B. Hofmann, P. Kirchhoff, and R. H. Mulder, (Münster: Waxmann), 381–438. Luchins, A. S. (1942). Mechanization in problem solving: the effect of einstellung. Psychol. Monogr. 54, 1–95. doi: 10.1037/h0093502 Luchins, A. S., and Luchins, E. H. (1959). Rigidity of Behavior: A Variational Approach to the Effect of Einstellung. Eugene, OR: University of Oregon Books. McCloy, R., Beaman, C. P., Morgan, B., and Speed, R. (2007). Training conditional and cumulative risk judgements: the role of frequencies, problem-structure and einstellung. Appl. Cogn. Psychol. 21, 325–344. doi: 10.1002/acp.1273 McDowell, M., Galesic, M., and Gigerenzer, G. (2018). Natural frequencies do foster public understanding of medical tests: comment on Pighin, Gonzalez, Savadori and Girotto (2016). Medical Decis. Making. 38, 390–399. doi: 10.1177/0272989X18754508 McDowell, M., and Jacobs, P. (2017). Meta-Analysis of the Effect of Natural Frequencies on Bayesian Reasoning. Psychol. Bull. 143, 1273–1312. doi: 10.1037/bul0000126 Mellers, B. A., and McGraw, A. P. (1999). How to improve Bayesian reasoning: comment on Gigerenzer and Hoffrage (1995). Psychol. Rev. 106, 417–424. doi: 10.1037/0033-295X.106.2.417 Micallef, L. (2013). Visualizing Set Relations and Cardinalities Using Venn and Euler Diagrams. University of Kent. Dissertation. Micallef, L., Dragicevic, P., and Fekete, J. (2012). Assessing the effect of visualizations on Bayesian reasoning through crowdsourcing. Visualization and Computer Graphics. IEEE Trans. Visual. Comput. Graph. 18, 2536–2545. doi: 10.1109/TVCG.2012.199 Moyer, R. S., and Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature 215, 1519–1520. doi: 10.1038/2151519a0 Obrecht, N. A., Anderson, B., Schulkin, J., and Chapman, G. B. (2012). Retrospective frequency formats promote consistent experience-based Bayesian judgments. Appl. Cogn. Psychol. 26, 436–440. doi: 10.1002/acp.2816 Open Science Collaboration (2015). Estimating the reproducibility of psychological science. Science 349, 1–8. doi: 10.1126/science.aac4716 CrossRef Full Text Operskalski, J. T., and Barbey, A. K. (2016). Risk literacy in medical decision-making. Science 352, 413–414. doi: 10.1126/science.aaf7966 Ottley, A., Peck, E. M., Harrison, L. T., Afergan, D., Ziemkiewicz, C., Taylor, H. A., et al. (2016). Improving Bayesian reasoning: the effects of phrasing, visualization, and spatial ability. IEEE Trans. Vis. Comput. Graph. 22, 529–538. doi: 10.1109/TVCG.2015.2467758 Peters, E. (2012). Beyond comprehension: the role of numeracy in judgments and decisions. Curr. Dir. Psychol. Sci. 21, 31–35. doi: 10.1177/0963721411429960 Pfannkuch, M., and Budgett, S. (2017). Reasoning from an eikosogram: an exploratory study. Int. J. Res. Undergraduate Math. Educ. 3, 283–310. doi: 10.1007/s40753-016-0043-0 Pighin, S., Gonzalez, M., Savadori, L., and Girotto, V. (2016). Natural frequencies do not foster public understanding of medical test results. Medical Decision Making 36, 686–691. doi: 10.1177/0272989X16640785 Rach, S. (2018). Visualisierungen bedingter Wahrscheinlichkeiten – Präferenzen von Schülerinnen und Schülern [Visualizations of conditional probabilities – preferences of students]. Mathemat. Didact. 41, 1–18. Reimann, S., and Bichler, E. (2015). Abitur 2016: Original-Prüfungsaufgaben mit Lösungen – Gymnasium Bayern Mathematik [Final secondary-school examinations 2016: Original mathematics exam tasks with solutions – Bavarian academic school track]. Hallbergmoos: Stark Verlag. Salz, T., Richman, A. R., and Brewer, N. T. (2010). Meta-analyses of the effect of false-positive mammograms on generic and specific psychosocial outcomes. Psycho-Oncol. 19, 1026–1034. doi: 10.1002/pon.1676 Schapira, M. M., Nattinger, A. B., and McHorney, C. A. (2001). Frequency or probability? A qualitative study of risk communication formats used in health care. Med. Decis. Making 21, 459–467. doi: 10.1177/0272989X0102100604 Schmid, A., Weidig, I., Götz, H., Herbst, M., Kestler, C., Kosuch, H., et al. (2008). Lambacher Schweizer 10 – Mathematik für Gymnasien Bayern [Lambacher Schweizer 10 – Mathematics for the Bavarian academic school track]. Stuttgart: Ernst Klett Verlag. Schneps, L., and Colmez, C. (2013). Math on trial: How Numbers Get Used and Abused in the Courtroom. New York, NY: Basic Books. Schultz, P. W., and Searleman, A. (2002). Rigidity of thought and behavior: 100 years of research. Genet. Soc. Gen. Psychol. Monogr. 128, 165–207. Sedlmeier, P., and Gigerenzer, G. (2001). Teaching Bayesian reasoning in less than two hours. J. Exp. Psychol. 130, 380–400. doi: 10.1037//0096-3445.130.3.380 Sendner, S., and Ruf-Oesterreicher, K. (2011). Lambacher Schweizer 10 – Mathematik für Gymnasien Bayern: Lösungen und Materialien [Lambacher Schweizer 10 – Mathematics for the Bavarian academic school track: Solutions and materials]. Stuttgart: Ernst Klett Verlag. Siegrist, M., and Keller, C. (2011). Natural frequencies and Bayesian reasoning: the impact of formal education and problem context. J. Risk Res. 14, 1039–1055. doi: 10.1080/13669877.2011.571786 Sirota, M., Kostovičová, L., and Vallée-Tourangeau, F. (2015). Now you Bayes, now you don't: effects of set-problem and frequency-format mental representations on statistical reasoning. Psychon. Bull. Rev. 22, 1465–1473. doi: 10.3758/s13423-015-0810-y Sloman, S. A., Over, D., Slovak, L., and Stibel, J. M. (2003). Frequency illusions and other fallacies. Organ. Behav. Hum. Decis. Process. 91, 296–309. doi: 10.1016/S0749-5978(03)00021-9 Spiegelhalter, D., and Gage, J. (2015). What can education learn from real-world communication of risk and uncertainty? Math. Enthus. 12, 4–10. Spiegelhalter, D., Pearson, M., and Short, I. (2011). Visualizing uncertainty about the future. Science 333, 1393–1400. doi: 10.1126/science.1191181 Tversky, A., and Kahneman, D. (1974). Judgment under uncertainty: heuristics and biases. Science 185, 1124–1131. doi: 10.1126/science.185.4157.1124 Wassner, C. (2004). Förderung Bayesianischen Denkens – Kognitionspsychologische Grundlagen und Didaktische Analysen [Promoting Bayesian Reasoning – Principles of Cognitive Psychology, and Didactical Analyses]. Hildesheim: Franzbecker. Weber, P. (2016). Natürliche Häufigkeiten – Chancen und Grenzen aus fachwissenschaftlicher und Fachdidaktischer Sicht [Natural Frequencies – Benefits and Limits From a Mathematical and an Educational Perspective]. Master's thesis, University of Regensburg. Wegwarth, O., and Gigerenzer, G. (2013). Overdiagnosis and overtreatment: evaluation of what physicians tell their patients about screening harms. JAMA Intern. Med. 173, 2086–2088. doi: 10.1001/jamainternmed.2013.10363 Woike, J. K., Hoffrage, U., and Martignon, L. (2017). Integrating and testing natural frequencies, naïve Bayes, and fast-and-frugal trees. Decision 4, 234–260. doi: 10.1037/dec0000086 Yamagishi, K. (2003). Facilitating normative judgments of conditional probability: frequency or nested sets? Exp. Psychol. 50, 97–106. doi: 10.1027//1618-3169.50.2.97 Zhu, L., and Gigerenzer, G. (2006). Children can solve Bayesian problems: the role of representation in mental computation. Cognition 98, 287–308. doi: 10.1016/j.cognition.2004.12.003 Keywords: Bayesian reasoning, natural frequencies, probabilities, einstellung, tree diagram Citation: Weber P, Binder K and Krauss S (2018) Why Can Only 24% Solve Bayesian Reasoning Problems in Natural Frequencies: Frequency Phobia in Spite of Probability Blindness. Front. Psychol. 9:1833. doi: 10.3389/fpsyg.2018.01833 Received: 16 March 2018; Accepted: 07 September 2018; Published: 12 October 2018. Edited by: Gorka Navarrete, Adolfo Ibáñez University, Chile Reviewed by: Laura Felicia Martignon, Ludwigsburg University, Germany Luana Micallef, University of Copenhagen, Denmark Copyright © 2018 Weber, Binder and Krauss. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. *Correspondence: Patrick Weber, patrick.weber@ur.de

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# Seminar on Causality The SGS- and the PC-Algorithm Alexandra Federer, Moritz D¨ umbgen Monday, March 23, 2009 1 Repetition Let’s quickly recall some of the concepts from the previous talks. We are acting on a proba- bility space (Ω, F, P) with random variables X 1 , ..., X n . We want to illustrate certain prop- erties of the probability measure P graphically. Therefore, we look at graphs G = (V, E) where V = {v 1 , ..., v n } is the set of vertices (representing the random variables) and E are the edges. In case of an undirected graph (no arrowheads), E = {{v i , v j } ; i = j ⊆ V }, and in case of a directed graph (with arrowheads), E = {(v i , v j ); i = j ⊆ V }. We talk of a directed acyclic graph (DAG), if there is no cycle of edges in a directed graph. One possible construction of a DAG is to draw an edge from X i to X j if i ∈ I j where I j ⊆ {1, ..., j −1} is a minimal set such that P[x j |x 1 , ..., x j−1 ] = P[x j |{x i ; i ∈ I j }]. Then, P[x 1 , ..., x n ] = n j=1 P[x j |x 1 , ..., x j−1 ] = n j=1 P[x j |{x i ; i ∈ I j }] and we say that G represents P. In such a DAG, the parents pa(v j ) of a vertex v j are therefore given as {v i ; i ∈ I j }. Note the role of the ordering of the random variables here. For a different ordering we mostly get a different representation! Let’s now consider a DAG G representing P. Definition 1.1 (d-separation for a path) A path is d-separated (blocked) by a set Z ⊂ V if and only if • the path contains a chain (v 1 → v 2 → v 3 ), such that v 2 ∈ Z. or • the path contains a fork (v 1 ← v 2 → v 3 ), such that v 2 ∈ Z. or • the path contains a collider (v 1 → v 2 ← v 3 ), such that v 2 / ∈ Z and Z does not contain any descendant of v 2 . 1 Definition 1.2 (d-separation for arbitrary sets) Disjoint subsets of vertices X, Y are said to be d-separated by another set of vertices Z if and only if Z d-separates every path from a vertex in X to a vertex in Y . We denote this by X⊥Y |Z. Consider a chain v 1 → v 2 → v 3 . Since G represents P, P[x 3 |x 1 , x 2 ] = P[x 3 |x 2 ] ⇒ X 3 ⊥⊥ X 1 |X 2 Similarly, in a fork v 1 ← v 2 → v 3 we have P[x 3 |x 1 , x 2 ] = P[x 3 |x 2 ] ⇒ X 3 ⊥⊥ X 1 |X 2 However, in a collider v 1 → v 2 ← v 3 we get that P[x 3 |x 1 ] = P[x 3 ] ⇒ X 3 ⊥⊥ X 1 ⇒ X 3 ⊥⊥ X 1 |X 2 . The above findings can be generalized to arbitrary d-separated sets. Theorem 1.1 Let X, Y be disjoint, Z be an arbitrary subset of vertices (the corresponding random variables). • X⊥Y |Z ⇒ X ⊥⊥ Y |Z. • ¬(X⊥Y |Z) ⇒ ¬(X ⊥⊥ Y |Z) in some distribution ˆ P represented by G. 2 New Concepts Definition 2.1 (faithful distribution) A probability distribution P is called faithful with respect to a graph G if and only if for disjoint subsets X, Y and an arbitrary subset Z of vertices (the corresponding random variables) X⊥Y |Z ⇔ X ⊥⊥ Y |Z Definition 2.2 (faithful list of d-separations) A list of d-separations L is called faith- ful if and only if there exists a DAG G such that all and only the d-separations of L are true in G. Then we also say that G faithfully represents L. 2 3 The SGS Algorithm Now we have all tools to construct a graph G (or an equivalence class of graphs) that faithfully represents some d-seperations L that we input. (i) Form the complete undirected graph H on the vertex set V (ii) ∀v 1 = v 2 : If there exists a subset S ⊆ V \ {v 1 , v 2 } that d-separates v 1 , v 2 , remove the edge between them from H. (iii) Let ˆ H be the undericted graph we obtain after step (ii). ∀v 1 = v 2 = v 3 such that v 1 , v 2 and v 2 , v 3 ˆ H and v 1 , v 3 are not: orient them as v 1 → v 2 ← v 3 if and only if there is no subset S of v 2 ∪ V \ {v 1 , v 3 } that d-separates v 1 and v 3 . (iv) Repeat – If v 1 → v 2 , v 2 and v 3 1 and v 3 are not adjacent, and there is 2 , then orient v 2 −v 3 as v 2 → v 3 , – If there is a directed path from v 1 to v 2 and an edge between v 1 and v 2 , then orient v 1 −v 2 as v 1 → v 2 , until no more edges can be oriented. 3.1 Example 3 3.2 Correctness, Complexity and Stability Correctness follows from the following theorem. Theorem 3.1 If P is faithful to some DAG, then P is faithful to G if and only if (i) for all vertices v 1 , v 2 of G, v 1 and v 2 are adjacent if and only if v 1 and v 2 are dependent conditional on every set of vertices of G that does not include v 1 or v 2 . (ii) for all vertices v 1 , v 2 , v 3 such that v 1 , v 2 and v 2 , v 3 1 , v 3 are not, v 1 → v 2 ← v 3 is a subgraph of G if and only if v 1 , v 3 are dependent conditional on every set containing v 2 but not v 1 nor v 3 . Regarding complexity, we see that step (ii) of the SGS algorithm is an exponential search, hence it is very slow. The number of d-separation tests in the worst case is only bounded by n 2 2 n−2 . Step (ii) is relatively stable. Excluding a correct d-separation relation from the input, say (v 1 ⊥v 2 |Z), the algorithm will produce the correct undirected graph unless there is no other set besides Z which d-separates v 1 , v 2 . Including a wrong d-separation relation (v 1 ⊥v 2 |Z, say), the algorithm will not connect v 1 and v 2 (possibly by mistake) but no Step (iii) is unstable. Since the colliders determine the orientations of other edges in the graph, we have less stability. If an input error leads the algorithm to include or exclude a collision, the error may affect the orientation of many other edges. 4 The PC Algorithm (i) Form the complete undirected graph H on the vertex set V (ii) k = 0. repeat repeat select an ordered pair of variables v 1 , v 2 that are adjacent in H such that 1 ) \ v 2 has cardinality greater than or equal to k, and a subset S 1 )\v 2 of cardinality k, and if v 1 and v 2 are d-separated given S delete the edge v 1 −v 2 from H and record S in Sepset(v 1 , v 2 ) and Sepset(v 2 , v 1 ) until all ordered pairs of adjacent variables v 1 and v 2 (H, v 1 ) \ v 2 has cardinality greater than or equal to k, and all subsets S of Adja- cencies (H, v 1 ) \ v 2 of cardinality k have been tested for d-separation. 4 k = k + 1 until for each ordered pair of adjacent vertices v 1 , v 2 1 ) \ v 2 is of cardinality less than k (iii) For each triple of vertices v 1 , v 2 , v 3 such that the pairs v 1 , v 2 and v 2 , v 3 but v 1 , v 3 are not, orient v 1 −v 2 −v 3 as v 1 → v 2 ← v 3 if and only if v 2 is not in Sepset(v 1 , v 3 ). (iv) Repeat – If v 1 → v 2 , v 2 and v 3 1 and v 3 are not adjacent, and there is 2 , then orient v 2 −v 3 as v 2 → v 3 , – If there is a directed path from v 1 to v 2 and an edge between v 1 and v 2 , then orient v 1 −v 2 as v 1 → v 2 , until no more edges can be oriented 4.1 Example 5 4.2 Correctness, Complexity, Stability Correctness again follows from Theorem 3.1. We only need to search for independence conditional on a subset of the adjacencies of one of the vertices. Regarding complexity, denote by k the largest degree (number of adjacencies) of a vertex of G. The number of conditional independence tests is then bounded by 2 n 2 k−1 i=0 n −2 i ≤ 3n 2 (n −2) k . Note that for k = n−1 we again have an exponential boundary in the worst case. However, in practice the algorithm can be much faster (for example when we have sparse graphs). Step (ii) is unstable. If an edge is mistakenly removed from the true graph, other edges which are not in the true graph may be included in the output. This can also lead to orientation errors. If an edge is mistakenly left in the graph (and there are no other errors in the input) the only further errors are that some edges which theoretically could be oriented will not be oriented. Step (iii) is unstable for the same reason as step (iii) of the SGS-algorithm. However, in practice step (ii) is more reliable than step (iii). 6

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# continuum hypothesis It was proved by Georg Cantor that the power set of the natural numbers is cardinally larger than the set of natural numbers themselves, i.e., there is no surjection of the natural numbers onto their power set. Cantor hypothesized that there is no ‘intermediate’ cardinality between that of the natural numbers and that of their power set— that every infinite set is either the ‘size’ of the natural numbers, or at least as big as the continuum. (Note: the power set of the natural numbers has the same cardinality as the set of real numbers) This hypothesis, which Cantor believed was true but which he couldn't prove, became known as the Continuum Hypothesis (often abbreviated CH) The statement of the hypothesis can be generalized to the statement that there is no intermediate cardinality between any set and its power set. This is called the Generalized Continuum Hypothesis (GCH). In the 20th century Kurt Gödel and Paul Cohen proved results that together show that the GCH is independent of the other common axioms of set theory. That is, our common formalization of set theory is not strong enough to decide this question.

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× Get Full Access to College Physics - 7 Edition - Chapter 6 - Problem 6.14 Get Full Access to College Physics - 7 Edition - Chapter 6 - Problem 6.14 × # A 3.00-kg steel ball strikes a massive wall at 10.0 m/s at ISBN: 9780495113690 154 ## Solution for problem 6.14 Chapter 6 College Physics | 7th Edition • Textbook Solutions • 2901 Step-by-step solutions solved by professors and subject experts • Get 24/7 help from StudySoup virtual teaching assistants College Physics | 7th Edition 4 5 1 363 Reviews 24 0 Problem 6.14 A 3.00-kg steel ball strikes a massive wall at 10.0 m/s at an angle of 60.0 with the plane of the wall. It bounces off the wall with the same speed and angle (Fig. P6.14). If the ball is in contact with the wall for 0.200 s, what is the average force exerted by the wall on the ball? Step-by-Step Solution: Step 1 of 3 Media Effects (Chapter 15)  Media effects is the field of research that attempts to understand, predict, and explain the effects of mass media on individuals and society o scientific method: understand, predict, and explain o individuals and society: media does not only effect the individual but society as well  Not all media researchers are studying "effects" or aiming for prediction o Cultural studies researchers try to understand how media constructs and is constructed by questions of gender, race, social class, nationality, etc. o Rhetorical studies researchers try to understand how media functions in terms of persuasion, meaning, political contestation, ideology, identity, etc. Media Effects Theories  The Hypodermic Needle Model o An early model for television effects on audiences o The idea that powerful media shoot their messages directly into vulnerable audiences' brains o Also known as the "magic bullet" or "direct effects" model o Fails to account for the fact that people are critical and skeptical of media messages o Widely discredited by subsequent research  The Minimal Effects Model o Media effects are less powerful, and are mostly indirect. o Also known as the "limited model" o People engage in selective exposure:  We tend to expose ourselves only to messages that we are already comfortable with o People engage in selective retention:  We tend to retain messages that confirm the values and ideas that we already hold o This model still assumes that audiences are passive in their consumption of media  Uses and Gratifications o Studies how and why media are used, rather than what their effects are o The surveillance function suggests that people use the media to monitor the world around them o Similarly, the socialization function suggests that people use the media to help fit in with others o While the textbook says this model was never widely adopted, it has been incorporated into rhetorical and cultural studies research. What Effect Does the Media Have  The most significant demonstrated effect of media is agenda- setting: o Not telling people what to think, but telling them what to think about  Many of the other effects listed in the textbook are less well proven but still worth discussing  The cultivation effect is the idea that heavy TV viewing causes is to believe that TVis giving us an accurate portrayal of the real world o One common version of this is the mean world syndrome: we believe the world is more dangerous than it really is because TV shows so much crime  The spiral of silence theory is the idea that the media silences controversial opinions by making those who have them fear social invasion o This can even be true of opinions that are not really controversial, since the media edits out very widely held opinions o Some studies indicate that we are even willing to go along with wrong answers if "everyone else" is giving those answers too Step 2 of 3 Step 3 of 3 #### Related chapters Unlock Textbook Solution

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https://developers.arcgis.com/javascript/3/jssamples/util_measureline.html

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Analysis Data Reviewer Directions and Routing Dynamic Layers Editing Feature Layers Feature Table Graphics Image Layers Map Mobile Online and Portal Popups and Info Windows Printing Query and Select Renderers, Symbols, Visualization Search Tiled Layers Time Measure distances #### Description This example shows how you can use an ArcGIS Server geometry service to measure line lengths in your Web application. When you click and drag the mouse, the Draw toolbar captures the geometry of the line you drew. It sends the line to the geometry service, which calculates the length of the line using the GeometryService.lengths() method. #### Code ```<!DOCTYPE html> <html> <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> <meta name="viewport" content="initial-scale=1, maximum-scale=1,user-scalable=no"> <title>Measure Distances</title> <script src="https://js.arcgis.com/3.41/"></script> <script> dojo.require("esri.map"); dojo.require("esri.toolbars.draw"); dojo.require("dojo.number"); var map, geometryService; function init() { map = new esri.Map("map", { basemap: "streets-vector", center: [-77.500, 42.500], zoom: 7 }); dojo.connect(geometryService, "onLengthsComplete", outputDistance); } function initFunctionality(map) { var tb = new esri.toolbars.Draw(map); //on draw end add graphic, project it, and get new length dojo.connect(tb, "onDrawEnd", function(geometry) { map.graphics.clear(); lengthParams.polylines = [geometry]; lengthParams.geodesic = true; geometryService.lengths(lengthParams); var graphic = map.graphics.add(new esri.Graphic(geometry, new esri.symbol.SimpleLineSymbol())); }); tb.activate(esri.toolbars.Draw.FREEHAND_POLYLINE); } function outputDistance(result) { dojo.byId("distance").innerHTML = dojo.number.format(result.lengths[0] / 1000) + " kilometers"; }

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https://randerson112358.medium.com/a-simple-machine-learning-python-program-bf5d156d2cda

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# Build A Simple Machine Learning Python Program Program Your Own Machine Learning Model We are going to create a simple machine learning program (the model) using the programming language called Python and a supervised learning algorithm called Linear Regression from the sklearn library (A.K.A scikit-learn). We will create a training data set of pseudo-random integers as input by using the Python library Random, and create our own function for the training data set output using those random integer values as input. Then we will train our model on the newly created data set and finally test our model with one example to see how well our model performed to predict/ give the expected output. # Step 0: Install Python Version 3 https://realpython.com/installing-python/ # Step 1: Install Scikit-Learn First we need to install our dependency, the Python library scikit-learn (sklearn) which is a free software machine learning library for the Python Programming Language. The random library is part of the python standard libraries so we don’t need to install it, it’s already available for us ! `pip install scikit-learn` # Step 2: Create Your Training Data Set Usually if you have a data set, you would want to split it into a training set, validation set, and testing set. Since this is a simple example we are creating our own training set to train our linear regression model with.The training set will contain the input and expected output values of the data set that I want to train the model on. The input will be random integer values created by the library Random we will use the method randint(a,b) , which returns a random integer N such that `a <= N <= b`. The output will be determined by a function that we will create. Recall a function usually called ‘f’ takes in some input/parameter value usually called ‘x’ and produces some output value, such that f(x) = g. The function that I will create will take in multiple parameters so not just ‘x’ but ‘x’, ‘y’, and ‘z’ instead such that we get the following function. f(x,y,z) = 10x + 2y + 3z = g Example of how this function works, if we had values x=1, y=2, z=20 then y would equal 74 like the following: f(1,2,20) = 10(1) + 2(2) + 3(20) = 74 Input = Features Output = Targets # Code To Generate Training Set: `# Import the librariesfrom randomfrom sklearn.linear_model import LinearRegression# Create an empty list for the feature data set 'X' and the target data set 'y'feature_set = []target_set= []# get the number of rows wanted for the data setnumber_of_rows = 200# limit the possible values in the data setrandom_number_limit = 2000#Create the training data set#Create and append a randomly generated data set to the input and outputfor i in range(0,number_of_rows): x = random.randint(0, random_number_limit) y = random.randint(0, random_number_limit) z = random.randint(0, random_number_limit)#Create a linear function for the target data set 'y'function = (10*x) + (2*y) + (3*z)feature_set.append([x,y,z])target_set.append(function)` # Step 3: Train Our Linear Regression Model Next we will use the method LinearRegression() from the Python library scikit-learn to train and create our model. This model will try to “model” the function that we created for the training dataset. Note: When we ‘fit’ a function that is just another word for training. `model = LinearRegression() #Create a linear regression object/modelmodel.fit(feature_set, target_set) ` # Step 4: Test The Linear Regression Model Now let’s see if our LinearRegression function can approximate the function that we created and give us an accurate prediction (the correct answer). Test Set= [[8, 10, 0]] The outcome should be 8*10 + 10*2 + 0*3 = 100. Let’s see what we got… `test_set = [[8,10,0]] prediction = model.predict(test_set)print('Prediction:'+str(prediction)+'\t'+ 'Coefficient:'+str(model.coef_))` Prediction : [ 100.] Coefficients : [ 8. 10. 0.] The model used the training data, to compute the coefficients also known as weights. It then used the weights with the feature / input data to compute the correct output. When giving the model test data, it successfully managed to get the correct answer! If you are also interested in reading up a little bit more on machine learning to immediately get started with problems and examples then I strongly recommend you check out Hands-On Machine Learning with Scikit-Learn and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems. Written by

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https://www.coursehero.com/file/6641171/813-Mechanics-SolutionInstructors-SolManual-Mechanics-Materials-7ebook-Gere-light1/

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{[ promptMessage ]} Bookmark it {[ promptMessage ]} 813_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1 # 813_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1 This preview shows pages 1–2. Sign up to view the full content. SECTION 10.3 Differential Equations of the Deflection Curve 807 Problem 10.3-11 A propped cantilever beam of length L is loaded by a concentrated moment M 0 at midpoint C . Use the second-order differential equa- tion of the deflection curve to solve for reactions at A and B . Draw shear-force and bending-moment diagrams for the entire beam. Also find the equations of the deflection curves for both halves find the equations of the deflection curves for both halves of the beam, and draw the deflection curve for the entire beam. At point of inflection: d d max /2 d max M 0 L 2 216 EI A L 2 L 2 y x B C M A M 0 R A R B Solution 10.3-11 E QUILIBRIUM (1) (2) B ENDING MOMENTS ( FROM EQUILIBRIUM ) D IFFERENTIAL EQUATIONS (3) (4) (5) B . C . 1 B . C . 2 D IFFERENTIAL EQUATIONS (6) EIv M R B ( L x ) ( L /2 x L ) v (0) 0 C 2 0 ¿ (0) 0 C 1 0 EIv R B x 3 This preview has intentionally blurred sections. Sign up to view the full version. View Full Document This is the end of the preview. Sign up to access the rest of the document. {[ snackBarMessage ]}

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papalengthoughts.blogspot.com

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## Friday, May 29, 2015 ### Can You Do Math? 10 easy but tricky questions that test… how good are you in Math. photo link Probably, one of the most popular classroom phrase is, “I hate Math”! But is the subject really that difficult? Are math problems “tough nut to crack”? Let’s have some fun. Answers the following Math-related questions and find out how good are you in Math. 1. In his will, a farmer left his eleven cows to his three sons. Half were to go to the eldest, one-fourth to the middle and one-sixth to the youngest. How was it done? 2. A car dealer was asked how many cars he had on stock. He answered, “If one-half, one-third, and one-fourth of the numbers of cars were added together, they would make 13.” How many cars did he have in stock? 3. Find the number which when increased by 3, then miltiplying the product by ¾, then dividing by 7, diminished by 1/3 of the quotient, multiplying the number by itself, subtracting 52, getting the square root, adding 8, and dividing by 10 gives the number 2? 4. If it takes 3 minutes to cut a carrot into 3 pieces, how long would it take to cut a carrot into 4 pieces? 5.How much dirt is in a hole 2 inches long, 3 inches wide, and 3 inches deep? 6. If a tray of eggs sells fro 20 pesos per dozen, which costs less, ½ dozen dozen eggs, or 6 dozen eggs? 7. A train 1 km long travels through a tunnel 1 km long at a speed of 1km/hr. How long will it take the train to pass completely through the tunnel? 8.Using only a 7-minute and an 11-minute hour glass, how can you boil an egg for exactly 15 minutes? 9. A wolf, a rabbit, and a carrot must be moved across a river in a boat which can hold only one besides the boatman. How must the boatman carry them so that the rabbit shall not it the carrot; or the wolf, the goat? 10. A dog chases a rabbit which is already 150 feet away. Every time the dog jumps 9 feet, the rabbit at the same time, jumps 7 feet. How many jumps does the dog have to make to overtake the rabbit? photo link Answers: 1. Eldest = ½ x 11 = 5.5; to the nearest units = 6 Middle = ¼ x 11 = 2.75; to the nearest units = 3 Youngest = 1/6 x 11 = 1.75; to the nearest units = 2 2. 12 Let n = number of cars ½ n + 1/3 n + ¼ n = 13; get the LCD 13/12 n = 13 n = 13 x 12/13 n = 12 3. The answer is 28; very practical one 4. 4 1/2 minutes (4 and 30 seconds) Don’t believe me, then go cut one yourself. 5. Nothing. How can you store something into a hole. 6. Both will cost the same. 7. 2 hours. Speed = distance x time 1km/hr = 1km x time 1km/hr x 1/1km = time 1hr = time the train is completely inside the tunnel and will take another hour to completely pass through it. 8. Procedure: a. Use the 7-min and 11-min hour glass at the same time. b. Once the 7-min glass hour is consumed, turn the 11-min glass hour upside down. ( 11 min – 7 min = 4). c. Start boiling the egg. When the 11- min glass hour is done, turn it again upside down. (4 min + 11 min = 15 min). 9. Solution: Cross the river carrying the rabbit with you. Leave the carrot and cross back. Its now the carrot’s turn, but this time carry back the rabbit as you return to get the wolf. Bring the wolf in, leaving behind the goat. Lastly, return and get the goat. Whooh! Seems a hard work. 10. On the 76th jump. N = number of jump. 9 n – 7 n = 150 n = 150/2 = 75 On the 75th jump, both dog and rabbit are on the same footing. #### 11 comments: 1. Waaa! I really hate math. I was just reading through the questions and it pains my head already! Hahaha!!! But after check the answers, they are easy! I guess, I'm just really stubborn with math. 2. Ow, I'm really not good at math! But come to think of it, the answers are really easy. :) 3. i was going to try to solve the questions all the way, pero halfway through i gave up hahaha 4. I hate Math papaleng ha ha..Though I pass all my Math subject coz its a requirement to my college course. 5. OMG! Math you said???? You're barking at the wrong person ahaha. Papaleng, I swear, I didn't know how I finished my degree but somehow I got through without failing any of my Math and Math related courses haha. By the way, why are you shying away from smoothies? Please know that my smoothies concoction are 70% veggies and 30% fruits, no other additives :-) 6. My sincere apologies, your title made me jump in the comment box. Hahahahahaha! I. HATE. MATHEMATICS!!! 7. ahhh.. problem solving my favorite, makes my brain awaken from its rusty years... thanks for this..i love math its in my nature to solve such a nice and confusing problems. 8. I am okay with Math but not fond of the complicated problems like algebra and such lol. 9. I am not good in Math Papaleng, numbers gives me headaches 10. Your Math questions remind me of my son's MTAP competitions. I'd rather see the answer myself than figure out the answers. Lol! 11. These are questions that I'd rather avoid if I can but can't since I see similar questions in my children's assignments.

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https://multi-converter.com/watt-hours-to-megawatt-hours

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# Watt Hours to Megawatt Hours Convert W*h to MW*h Change to Megawatt Hours to Watt Hours Share: ## How to convert Watt Hours to Megawatt Hours 1 [Watt Hours] = 1.0E-6 [Megawatt Hours] [Megawatt Hours] = [Watt Hours] / 1000000 To convert Watt Hours to Megawatt Hours divide Watt Hours / 1000000. ## Example 61 Watt Hours to Megawatt Hours 61 [W*h] / 1000000 = 6.1E-5 [MW*h] ## Conversion table Watt Hours Megawatt Hours 0.01 W*h1.0E-8 MW*h 0.1 W*h1.0E-7 MW*h 1 W*h1.0E-6 MW*h 2 W*h2.0E-6 MW*h 3 W*h3.0E-6 MW*h 4 W*h4.0E-6 MW*h 5 W*h5.0E-6 MW*h 10 W*h1.0E-5 MW*h 15 W*h1.5E-5 MW*h 50 W*h5.0E-5 MW*h 100 W*h0.0001 MW*h 500 W*h0.0005 MW*h 1000 W*h0.001 MW*h

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CC-MAIN-2024-22

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https://library.exemplars.com/tasks/assessment/ms.-harley-rides-to-school

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Ms. Harley Rides to School Ms. Harley is a teacher who saves money by riding her motorcycle to school in the morning and back home in the afternoon. It costs Ms. Harley nine cents a mile to ride her motorcycle. Ms. Harley knows the distance from her house in Greenville to Lakeland is three and forty-five hundredths miles. The distance from Lakeland to Centerville is five and forty-eight hundredths miles. The distance from Centerville to Sunrise City is one and seven hundredths miles. The distance from Sunrise City to her school is one and five tenths miles. How many total miles does Ms. Harley ride to school and back home in one day? Ms. Harley rides to school and back home five days each week for four weeks. Ms. Harley has a gas budget of fifty dollars. Does Ms. Harley stay within her budget? Show all your mathematical thinking. Assessment Plan Formal Mathematical Language and Symbolic Notation A student may independently select a printed number line, number chart, ten frames, graph paper, etc. as they work on a task. Suggested materials Engagement Image: Teachers may project the image below to launch this task for their students, define nouns, promote discussion, access prior knowledge, and inspire engagement and problem solving. Click image to enlarge Solutions tabs Expert This student does not meet the standard. Scoring Rationale Novice The student's strategy of listing the miles Ms. Harley rides to school in decimals to the thousandths and subtracting $0.09 from$50.00 does not work to solve the first and second parts of the task. The student's first answer, "She drives 12.030 miles," is not correct. The student's second answer, "She has enough to drive," is not correct as it is based on incorrect reasoning. Novice The student does not demonstrate correct reasoning and proof of the underlying concepts of the task. The student is not able to notate decimals to the hundreds and tenths place. It is not clear if the student's notation—1.500, represents one and five-tenths or one and five hundreds as the student lists one and seven hundredths as 1.700. The student does not understand that the miles Ms. Harley rides to school have to include total miles for a round trip. The student does not show correct reasoning that the total miles for 20 round trips has to be multiplied by $0.09 to determine if the cost does not exceed$50.00. Practitioner The student makes the mathematically relevant observation, "Lakeland to Centerville is most miles and costs the most gas." Apprentice The student's table is appropriate to the task but is not accurate. The student omits a decimal point for 1.50 miles. The student also omits a dollar sign for $0.14 and$0.80. Apprentice , This student does not meet the standard. Scoring Rationale Practitioner The student correctly uses the mathematical terms miles, days, weeks, cost from the task. The student also correctly uses the term table. The student correctly uses the mathematical notation 3.45, 5.48, 1.07, 1.50, 11.50, 8.93, 10.00, 23.00, $.09,$41.40, $50.00,$18.60. Apprentice The student attempts to find the difference between $50.00 and the cost of the 20 round trips,$41.40, but the student miscalculates and arrives at an incorrect connection. The student's statement, "Mrs. Harley reminds me of my book where a boy runs away on a harley," is not considered a mathematically relevant connection. Apprentice The student's table is appropriate to the task but is not accurate. The student's fourth column should be labeled "total miles," "running total of miles," or "total miles rode." Apprentice This student meets the standard. Scoring Rationale Practitioner The student's strategy of using a number line to show the distance in miles Ms. Harley rides between locations from home to school works to solve the first part of the task. The student solves the rest of the task by computing the number of miles she drives in a round trip, in five days, four weeks and, how much money Ms. Harley uses for gas. The student's answers, "23 miles," and "she does not go over her budget," are correct. Expert The student makes mathematically relevant Practitioner connections. The student states, "Lakeland to Centerville is most distance between towns or school 5.48 miles," and "no distance is not in decimals. She is very careful when she measures distances." The student makes an Expert connection by using calculation to explain how fractions can replace decimals and arrive at the same answer of 23 miles. The student states "I see 11 1/2 is 11.50 miles to school + 11 1/2 is 11.50 miles to home = 22 2/2 = 23 miles too." Practitioner The student's number line is appropriate to the task and accurate. All labels are included, the intervals are accurate, and the "jumps" are correct. Practitioner , This student meets the standard. Scoring Rationale Practitioner The student's table is appropriate to the task and accurate. All labels are included and all entered data is correct. Practitioner , This student exceeds the standard. Scoring Rationale Expert The student makes mathematically relevant Practitioner connections. The student states, "Lakeland to Centerville is longest riding part," and "$8.60 under budget for more miles." The student makes Expert connections. The student includes the equivalent mixed numbers for "miles in decimals as fractions" and "total miles in decimals as fractions" on their table. The student justifies their decisions. The student states, "11.50 if only 50% of ms Harley's driving. 11.50 x 2 is 23 miles," "11.50 + 11.50 is 23 miles—the same, I am correct," "11.50 = 11 50/100 so I think it is correct." The students uses two different strategies for computing$41.40 calling them, "thinking one" and "thinking two" and stating, "$41.40 =$41.40 I am correct." The student also supports their understanding that, "$.09 is$.01 from $.10 which is 1/10 of a dollar or 10% of$1.00," and "$.09 is 9/100 of$1.00. I like equivalent stuff." The student ends their solution by stating, "Sunrise City to school is 1.50 miles. That is 1 1/2 miles from 1 5/10 or 1 50/100. It is equivalent again." Expert The student's table is appropriate to the task and accurate. All labels are included and all extended data is correct. The student extends their thinking to include mixed numbers in the table and to compare 11.50 from the table to 50% and 1.50 from the table to 1 1/2 and 1 5/10 in their solution. Expert , , This student exceeds the standard. Scoring Rationale Expert The student's strategy of using a number line and calculation to show the total distance in miles Ms. Harley rides between locations from home to school and home, works to solve the first part of the task. The student's strategy of calculating the cost of gas to ride 23 miles and the cost for riding 20 days, works to solve the second part of the task.The student's answers, "3 miles," and "Mrs Harley does not go over her budget," are correct. The student continues their solution to include percents and time measurement. Expert The student demonstrates correct reasoning of the underlying concepts of the task. The student correctly uses decimal notation to define the four distances in hundredths and tenths of a mile, and the total miles Ms. Harley travels to school and home in one day and 20 days. The student demonstrates correct reasoning by computing and using money notation to determine $41.40 as the total cost of gas needed for 20 days and comparing that total to$50.00. The student also demonstrates understanding of the concepts of fractions, percents and time measurement. The student justifies their understanding of comparing time to miles per hour and decimals and reaches a conclusion. Expert The student correctly uses the mathematical terms miles, distance, total, days, weeks, cost from the task. The student also correctly uses the terms number line time, per, miles per hour/mph, time, hour, min., more, decimals, fraction. The student correctly uses the mathematical notation 3.45, 5.48, 1.07, 1.50, 11.50, 23.00, .575, .5, 1.0, $.09,$2.07, $41.40,$50.00, 1/2, 1/4, 50%, 25%. <. Expert The student solves the task and makes the Expert connection of extending their thinking to miles per hour and how this concept relates to the task. The student states, "If she drives 40 mph you can find the time she rides." The student defines 40 mph and determines "20 miles is 1/2 hour or 50% of a hour or 30 min.," "10 miles is 1/4 hour or 25% of a hour or 15 min.," "So 11.50 miles is about 15 min. (1 way) and 23 miles is about 30 min. (round trip)." The student divides 23.00 miles by 40 miles per hour for a quotient of .575 which the student rounds to 6. The student states, "I think the 6 means 1/2 hour on a clock," The student diagrams a clock and states, "But .545 < 6 and 20 miles is 1/2 40 mph so 30 mins, 20 < 23 so it takes a little more time to ride like 34 min." The student continues their explanation. "I know .575 is like decimals. .5 + .5 = 1.0 so .575 is a little more like 23 miles is a little more. So .5 is 1/2 hour about a round trip. So .25 is 1/4 hour about 1 way." The student aligns decimals and fractions to percents. ".5 + .5 is 1 hour. 1/2 + 1/2 is 1 hour. 50% + 50% is 1 hour." The student concludes, "my clock idea was wrong becaus I was thinking the number 6 on a clock and not mph fractions!!!" Expert The student's table is appropriate to the task and accurate. All labels are included and all entered data is correct. The student extends their thinking to include mixed numbers in the table and to compare 11.50 from the table to 50% of 23.00, and 1.50 from the table to 1 1/2 and 1 5/10 in their solution. The student also diagrams a clock to indicate 1/2 an hour representing 30 minutes.

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Switch to: TJX Companies (NYSE:TJX) Days Inventory 62.41 (As of Apr. 2014) TJX Companies's inventory for the three months ended in Apr. 2014 was \$3,208 Mil. TJX Companies's cost of goods sold for the three months ended in Apr. 2014 was \$4,678 Mil. Hence, TJX Companies's days inventory for the three months ended in Apr. 2014 was 62.41. TJX Companies's days inventory declined from Apr. 2013 (63.45) to Apr. 2014 (62.41). Inventory can be measured by Days Sales of Inventory (DSI). TJX Companies's days sales of inventory (DSI) for the three months ended in Apr. 2014 was 44.98. Inventory turnover measures how fast the company turns over its inventory within a year. TJX Companies's inventory turnover for the three months ended in Apr. 2014 was 1.46. Inventory to revenue ratio determines the ability of a company to manage their inventory levels. It measures the percentage of Inventories the company currently has on hand to support the current amount of Revenue. TJX Companies's inventory to revenue ratio for the three months ended in Apr. 2014 was 0.49. Definition Days Inventory indicates the number of days of goods in sales that a company has in the inventory. TJX Companies's Days Inventory for the fiscal year that ended in Jan. 2014 is calculated as Days Inventory = Inventory / Cost of Goods Sold * Days in Period = 2966.49 / 19605.037 * 365 = 55.23 TJX Companies's Days Inventory for the quarter that ended in Apr. 2014 is calculated as: Days Inventory = Inventory / Cost of Goods Sold * Days in Period = 3208.46 / 4678 * 91 = 62.41 * All numbers are in millions except for per share data and ratio. All numbers are in their own currency. Explanation An increase of Days Inventory may indicate the company's sales slowed. 1. Inventory can be measured by Days Sales of Inventory (DSI). TJX Companies's Days Sales of Inventory for the three months ended in Apr. 2014 is calculated as Days Sales of Inventory (DSI) = Inventory / Revenue * Days in Period = 3208.46 / 6491.176 * 91 = 44.98 2. Inventory Turnover measures how fast the company turns over its inventory within a year. TJX Companies's Inventory Turnover for the three months ended in Apr. 2014 is calculated as Inventory Turnover = Cost of Goods Sold / Average Inventory = 4678 / 3208.46 = 1.46 3. Inventory to Revenue determines the ability of a company to manage their inventory levels. It measures the percentage of Inventories the company currently has on hand to support the current amount of Revenue. TJX Companies's Inventory to Revenue for the three months ended in Apr. 2014 is calculated as Inventory to Revenue = Inventory / Revenue = 3208.46 / 6491.176 = 0.49 * All numbers are in millions except for per share data and ratio. All numbers are in their own currency. Be Aware A lot of business are seasonable. It makes more sense to compare Days Inventory from the same period in the previous year instead of from the previous quarter. Related Terms Historical Data * All numbers are in millions except for per share data and ratio. All numbers are in their own currency. TJX Companies Annual Data Jan05 Jan06 Jan07 Jan08 Jan09 Jan10 Jan11 Jan12 Jan13 Jan14 DaysInventory 75.59 70.70 72.66 72.18 66.26 61.75 62.93 63.90 59.40 55.23 TJX Companies Quarterly Data Jan12 Apr12 Jul12 Oct12 Jan13 Apr13 Jul13 Oct13 Jan14 Apr14 DaysInventory 54.97 63.56 64.02 65.71 49.74 63.45 63.26 67.56 47.78 62.41 Get WordPress Plugins for easy affiliate links on Stock Tickers and Guru Names | Earn affiliate commissions by embedding GuruFocus Charts GuruFocus Affiliate Program: Earn up to \$400 per referral. ( Learn More)

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## Partner Practice.pdf - Section 3: Partner Practice Partner Practice.pdf Partner Practice.pdf # Determining Solutions Unit 8: Equations Lesson 1 of 11 ## Big Idea: How can we prove equality? In this lesson students determine if a given number is a solution to an equation. Skill mastery is a focus. Print Lesson 11 teachers like this lesson Standards: Subject(s): Math, algebraic expression, Algebra, variable, solution, substitution 65 minutes ### Carla Seeger ##### Similar Lessons ###### Equivalent Numerical Expressions, Day 2 of 2 6th Grade Math » Intro to 6th Grade Math & Number Characteristics Big Idea: How can you represent the area of a diagram using numerical expressions? Students connect their knowledge of area and equivalent expressions to the commutative and distributive properties for day 2 of this investigation. Favorites(10) Resources(35) Somerville, MA Environment: Urban ###### Distributive Property 6th Grade Math » Properties of Math Big Idea: Students will compare the distributive property to sending invitations at a birthday party. Favorites(14) Resources(13) Brooklyn, NY Environment: Urban ###### Mathematical Properties in Action 6th Grade Math » Expressions Big Idea: No Trespassing! Understanding that mathematics has boundaries, rules called properties that make mathematics predictable. Favorites(7) Resources(18) Jonesboro, GA Environment: Urban sign up or Something went wrong. See details for more info Nothing to upload details close

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# Free Domino Addition and Subtraction Printables Share and Pin for later! 108 This post may contains affiliate links.  This means if you buy something through a link in this post, I will make a small commission at no cost to you.  This allows me to keep bringing you great content. Practicing addition and subtraction facts are a fundamental part of elementary school math. But, children can often get tired of just worksheet after worksheet of practice problem. So, as homeschool moms, we’ve got to change it up to keep things interesting! Today, I’d like to share with you one way that I get my first grader to practice her math facts without just another boring worksheet. I created these domino addition and subtraction worksheets for just these occasions. You can download them here. Related Post: Smartick Online Math Program Review Also, these worksheets aren’t THAT much different than a traditional worksheet, it gives my child a lot of things that are lacking in traditional worksheets. First, she gets to choose the dominoes she uses, so she is essentially choosing the addition or subtraction problems she practices. A little choice can go a long way with young children. Second, she is physically handling items in her hands. This simple act engages more of the brain and helps students retain information better. There are two free printables in the download, one for addition and one for subtraction. But, after you complete those worksheets, you will see how easy it is to continue the process using plain notebook paper. Related Post: Sort-A-Scene: Long Vowel Sounds I have also seen this process done using dice. The student rolls the dice and then creates a subtraction or addition statement from the numbers on the dice. To create problems with larger numbers, you can simply add more dice.

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## tadhanala 3 years ago -4√x+9 (end of sqrt) = 20 1. 03453660 $-4\sqrt{x+9} = 20$ 2. 03453660 is this the question?? Yes 4. 03453660 ok so squaring bothsides we get 16(x+9) = 400 x+9 = 400/16 x+9 = 25 x = 25 - 9 x = 16 --------------> required solution Thank you! 6. 03453660 welcome

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# Clip line to triangle in 2D? This topic is 3659 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. ## Recommended Posts Hi there, the last day I thought about how I could clip a line to a triangle in 2D. I have a triangle ABC and a line PQ. Now I want the line P'Q' that is clipped to the triangle (e. g. has no extend outside the triangle) - if the line is completely outside this should be found out. I thought that I test for both points P and Q of the line if they are inside my triangle (via barycentric cooridnates). So the simplest case is both are inside and I have to do nothing :). The nexst case is P is in and Q is out (or vice versa) - what to do now? check the line for intersections with every triangle edge and get the new line PQ' (P'Q resp. if other way round)? Third case is both, P and Q, are outside and I need to check if the line intersects the trinagle and clip it. How to do this? Again I could check the line for intersection with every edge of the triangle. I think I could come up with a naive solution (the one above) - but I looks pretty slow to me. Are there any algorithms that do what I want? Thank you very much, Tom ##### Share on other sites the standard clipping method would be to clip the segment using the infinite lines passing through the triangle edges. You keep clipping your segment with each edge you test against. That ultimately will reduce your segment to the portion inside. You can do some basic culling using the segment end points to reject cases. [Edited by - oliii on September 17, 2008 8:44:53 AM] ##### Share on other sites well, thanks for your reply. I can not really see how the approach you mentioned has to be done. If I caluclate the intersections between my segment PQ and all 3 infinite lines I end up with 3 inersection points. How do I know which intersections are the ones being my clipped segment? ##### Share on other sites Quote: Original post by VooDooTomIf I caluclate the intersections between my segment PQ and all 3 infinite lines I end up with 3 inersection points. How do I know which intersections are the ones being my clipped segment? Take your original line and clip it against one infinite line, then take that output and clip it against the next infinite line etc. You only have to deal with one intersection point at a time, and your line segment will only get smaller until you've got your final result. This approach will work for any convex hull, just make sure to generate your infinite lines consistently so you know which half is "inside" and which is "outside". ##### Share on other sites You'll need to clip the line to each edge of the 2d triangle assuming that each edge has a sort of "normal", pointing, for example, to the inside of the triangle. So, starting with the end points of your line, you will test the first edge. If both points are "out" then jump out (the line is outside) if both in then feed them to the next edge if they cross, find the intersection and feed the "in" point and the intersection to the next edge Do for the 3 edges and the resulting output vertices are your clipped line. It can be extended in 3d space and with n planes. EDIT: cool OrangyTang! same reply same time ;) ##### Share on other sites Hi there, thank you for your explanations - I think now I got it :) My solution for all convex polygons is: bool clip_line_to_triangle(const point3f vertices[], int num_vertices, point3f &p, point3f &q) { point3f normal = cross( normalize(vertices[1]-vertices[0]), normalize(vertices[2]-vertices[1])); point3f n1; point3f n2; bool p_outside; bool q_outside; int index2; // go through all edges for (int i = 0; i < num_vertices; ++i) { index2 = (i+1)%num_vertices; n1 = cross(normalize(p-vertices),normalize(vertices[index2]-p)); n2 = cross(normalize(q-vertices),normalize(vertices[index2]-q)); p_outside = dot(normal,n1) < -0.001f; q_outside = dot(normal,n2) < -0.001f; if (p_outside) { if (!q_outside) { line_line_intersect(vertices, vertices[index2], p, q, p); // save the intersection in p } else { // if both points are "outside" of the edge, we can leave return false; } } else { if (q_outside) { line_line_intersect(vertices, vertices[index2], p, q, q); // save the intersection in q } } } return true;} Edit: Found a mistake, corrected it. Hope this works :) [Edited by - VooDooTom on September 17, 2008 10:49:04 AM] 1. 1 2. 2 3. 3 Rutin 18 4. 4 JoeJ 14 5. 5 • 14 • 10 • 23 • 9 • 33 • ### Forum Statistics • Total Topics 632631 • Total Posts 3007538 • ### Who's Online (See full list) There are no registered users currently online ×

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Thursday December 5, 2013 # Posts by Rhea Total # Posts: 55 Accounting In 2014 ABC Company reported net income of \$100,000. What would be the effect on retained earnings on ABC Company's balance sheet and on its 2015 income statement if it didn't record a closing entry? Accounting What is the journal entry for the following? Stan opened a bank account in the name of SSRC and deposited \$10,000 of his savings into the account. Accounting Cadzow Inc purchases all of its inventory on credit. On January 1, 2008 Cadzow had \$1,750,000 of Inventory. Cost of goods Sold during 2008 was \$5,650,000. The beginning and ending balances in Cadzow’s Accounts Payable account on January 1, 2008 and December 31, 2008 were ... Accounting How do you calculate the 'Capital stock at the end of the year' with the following information? Revenues: \$375,000 Expenses: \$297,000 Net Income: \$78,000 Retained earnings at the beginning of the year: 0 Retained earnings at the end of the year: \$68,000 Liabilities at ... Statistics How do you differentiate between equal and unequal variances when conducting a t-test for comparing two populations? URGENT Statistics In performing two-tailed hypothesis test with v=20, you obtain a t-statistic of 2.41. The p-value is: Between 2% and 5%. I need help understanding how this range was gotten. I know that the t-statistic is between t.025 and t.01 and since this is a 2-tailed test these t-values ... Physics A 63 canoeist stands in the middle of her canoe. The canoe is 3.0 long, and the end that is closest to land is 2.6 from the shore. The canoeist now walks toward the shore until she comes to the end of the canoe. Suppose the canoeist is 3.3 from shore when she reaches the end o... Statistics - M/C In a version of the game of roulette, a steel ball is rolled onto a wheel that contains 19 red, 19 black and 2 green slots. If the ball is rolled 25 times, the probability that it falls into the green slots two or more times: a) is 5%. b) is 35.8%. c) is 12.7%. d) cannot be de... Stats Twenty-three students wrote a statistics examination having a maximum of 50 marks. The mark distribution is given in the following stem-and-leaf diagram: 0 9 1 25 2 01335889 3 001369 4 02248 5 0 Q1 is equal to: a) 15 b) 21 c) 23 d) None of the above THE ANSWER IS: C Please Exp... Stats A test has 15 true or false questions and 10 multiple choice questions (each with 4 choices). All questions are weighted equally. Jack has not studied at all for the test and randomly guesses. 1. What is the probability that Jack gets 96% on the test? a. 0.000000001 b. 0.00000... Pages: <<Prev | 1 | 2 | 3 | 4 | 5 | 6 | Next>> Search Members

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My Math Forum exercise problem IEEE 754 floating point User Name Remember Me? Password Computer Science Computer Science Forum October 21st, 2012, 03:45 AM #1 Newbie   Joined: Oct 2012 Posts: 2 Thanks: 0 exercise problem IEEE 754 floating point Hi Everyone, I need some help on how to convert decimal numbers in to IEEE 754 (single) floating point notation. For example, given a number 1995,5, then I do: 1995 to binary is 111 1100 1011 0,5 to binary is 0,1 Together we have: 111 1100 1011,1 After standardising, we have 1,11110010111 x 2^10(dec) and and then it's clear on howto convert it to IEEE 754. But now I have an excercise like -0,000000012. How do you solve this kind of exercise manually. We may not use a calculator. I'm especially interested on how to standardize this number? For hours I've been searching for the answer with no result... Any help would be great. Best regards! October 21st, 2012, 11:15 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: exercise problem IEEE 754 floating point Exactly the same, but flip the sign bit. October 22nd, 2012, 05:13 AM   #3 Newbie Joined: Oct 2012 Posts: 2 Thanks: 0 Re: exercise problem IEEE 754 floating point Quote: Originally Posted by CRGreathouse Exactly the same, but flip the sign bit. It's not about the sign bit. Assume 0,000000012 without a sign. So what now? Exact the same? 0,000000012 x 2 = 0,000000024 0,000000012 x 2 = 0,000000048 0,000000012 x 2 = 0,000000072 0,000000012 x 2 = 0,000000144 0,000000012 x 2 = 0,000000288 0,000000012 x 2 = 0,000000576 0,000000012 x 2 = 0,000001152 0,000000012 x 2 = 0,000002304 ... You see, it's not the most pretty and quickest method. I would like to write 0,000000012 as a power of two, like 1,... x 2^n. (Preferably without using a calculator.) Someone (else) ? October 22nd, 2012, 05:28 AM #4 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: exercise problem IEEE 754 floating point If you know your powers of two, this is just the sum of adjacent powers of two (shifted appropriately). So you shouldn't need more than a single addition to see how far to shift it (and possibly a second if that was the wrong amount, to get the significand). June 14th, 2017, 12:30 AM #5 Newbie   Joined: Jun 2017 From: Vietnam Posts: 1 Thanks: 0 10110010000110011001100110011001 Tags 754, exercise, floating, ieee, point, problem , , , , , , ### write 0,000000012 Click on a term to search for related topics. Thread Tools Display Modes Linear Mode Similar Threads Thread Thread Starter Forum Replies Last Post abady-1 Number Theory 5 September 21st, 2013 02:08 PM Primalscientist Computer Science 9 June 2nd, 2011 06:29 AM Chengpu Real Analysis 3 June 2nd, 2010 11:37 AM Chengpu Linear Algebra 0 May 23rd, 2010 04:55 PM RonnieStokie Algebra 3 December 12th, 2007 09:36 PM Contact - Home - Forums - Cryptocurrency Forum - Top

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# Linear Project Model – College Algebra Curve-fitting Project – Linear Model (due at the end of Week 5) Instructions For this assignment, collect data exhibiting a relatively linear trend, find the line of best fit, plot the data and the line, interpret the slope, and use the linear equation to make a prediction. Also, find r2 (coefficient of determination) and r (correlation coefficient). Discuss your findings. Your topic may be that is related to sports, your work, a hobby, or something you find interesting. If you choose, you may use the suggestions described below. Linear Model Example and Technology Tips are provided in separate documents. Tasks for Linear Regression Model (LR) (LR-1) Describe your topic, provide your data, and cite your source. Collect at least 8 data points. Label appropriately.  (Highly recommended: Post this information in the Linear Model Project discussion as well as in your completed project. Include a brief informative description in the title of your posting. Each student must use different data.) The idea with the discussion posting is two-fold: (1) To share your interesting project idea with your classmates, and (2) To give me a chance to give you a brief thumbs-up or thumbs-down about your proposed topic and data. Sometimes students get off on the wrong foot or misunderstand the intent of the project, and your posting provides an opportunity for some feedback. Remark: Students may choose similar topics, but must have different data sets. For example, several students may be interested in a particular Olympic sport, and that is fine, but they must collect different data, perhaps from different events or different gender. (LR-2) Plot the points (x, y) to obtain a scatterplot. Use an appropriate scale on the horizontal and vertical axes and be sure to label carefully. Visually judge whether the data points exhibit a relatively linear trend. (If so, proceed. If not, try a different topic or data set.) (LR-3) Find the line of best fit (regression line) and graph it on the scatterplot. State the equation of the line. (LR-4) State the slope of the line of best fit. Carefully interpret the meaning of the slope in a sentence or two. (LR-5) Find and state the value of r2, the coefficient of determination, and r, the correlation coefficient. Discuss your findings in a few sentences. Is r positive or negative? Why? Is a line a good curve to fit to this data? Why or why not? Is the linear relationship very strong, moderately strong, weak, or nonexistent? (LR-6) Choose a value of interest and use the line of best fit to make an estimate or prediction. Show calculation work. (LR-7) Write a brief narrative of a paragraph or two. Summarize your findings and be sure to mention any aspect of the linear model project (topic, data, scatterplot, line, r, or estimate, etc.) that you found particularly important or interesting. You may submit all of your project in one document or a combination of documents, which may consist of word processing documents or spreadsheets or scanned handwritten work, provided it is clearly labeled where each task can be found. Be sure to include your name. Projects are graded on the basis of completeness, correctness, ease in locating all of the checklist items, and strength of the narrative portions. Here are some possible topics: • Choose an Olympic sport — an event that interests you. Go to http://www.databaseolympics.com/ and collect data for winners in the event for at least 8 Olympic games (dating back to at least 1980). (Example: Winning times in Men’s 400 m dash). Make a quick plot for yourself to “eyeball” whether the data points exhibit a relatively linear trend. (If so, proceed. If not, try a different event.) After you find the line of best fit, use your line to make a prediction for the next Olympics (2014 for a winter event, 2016 for a summer event ). • Choose a particular type of food. (Examples: Fish sandwich at fast-food chains, cheese pizza, breakfast cereal) For at least 8 brands, look up the fat content and the associated calorie total per serving. Make a quick plot for yourself to “eyeball” whether the data exhibit a relatively linear trend. (If so, proceed. If not, try a different type of food.) After you find the line of best fit, use your line to make a prediction corresponding to a fat amount not occurring in your data set.) Alternative: Look up carbohydrate content and associated calorie total per serving. • Choose a sport that particularly interests you and find two variables that may exhibit a linear relationship. For instance, for each team for a particular season in baseball, find the total runs scored and the number of wins. Excellent websites: http://www.databasesports.com/  and http://www.baseball-reference.com/ *NEEDS TO BE ORIGINAL WORK COMPLETED. NO DUPLICATE WORK FROM OTHER WEBSITES OR WORK THAT HAS BEEN SOLD TO OTHER CLIENTS WITHIN THE LAST 6 MONTHS.*

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# 177 cm to inch converter ## FAQs on 177 cm to inch ### How many inches are in a cm? If you wish to convert 177 centimeters to a number in inches, first you need to know how many inches 1 cm is equal to. This is how I will tell you directly one cm is equal to 0.3937 inches. ### How to convert 1 cm to inches? To convert 1 centimeter into inches, you need to multiply 1cm with a conversion factor of 0.3937. This makes it much easier to convert 177 cm to inches. So 1 cm to inches = 1 times 0.3937 = 0.3937 inches. Based on this, you can answer the following question very lightly and simply. • What is one centimeter into inches? • What is cm to inches conversion formula? • How many inches equals 1 cm? • What does 1 cm equal to in inches? ### Implication of centimeter Centimeter is an International Standard Unit of Length. It is equal to one hundredth of one millimeter. It’s roughly equivalent to 39.37 inches. ### Definition of Inch Anglo-American units of length are in inches. 12 inches equals one foot, and 36 inches is equivalent to one yard. According to modern standards, one inch equals 2.54 cm. ### How do I convert 177 cm to inches? By the above, you have fully grasped cm to inches. Below are the relevant formulas: Value in inches = value in cm × 0.3937 So, 177 cm to inches = 177 cm × 0.3937 = 6.96849 inches This formula will allow you to answer the following questions: • What is 177 cm in inches? • How do I convert cm to inches? • How to translate 177 cm to inch? • How to measure cm to inches? • What size are 177 cm into inches? cm inch 176.2 cm 6.936994 inch 176.3 cm 6.940931 inch 176.4 cm 6.944868 inch 176.5 cm 6.948805 inch 176.6 cm 6.952742 inch 176.7 cm 6.956679 inch 176.8 cm 6.960616 inch 176.9 cm 6.964553 inch 177 cm 6.96849 inch 177.1 cm 6.972427 inch 177.2 cm 6.976364 inch 177.3 cm 6.980301 inch 177.4 cm 6.984238 inch 177.5 cm 6.988175 inch 177.6 cm 6.992112 inch 177.7 cm 6.996049 inch 177.8 cm 6.999986 inch Deprecated: Function get_page_by_title is deprecated since version 6.2.0! Use WP_Query instead. in /home/nginx/domains/becalculator.com/public/wp-includes/functions.php on line 5413

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# Problem C - Snakes Problem C - Snakes ## Problem C - Snakes Buffalo Bill wishes to cross a 1000x1000 square field. A number of snakes are on the field at various positions, and each snake can strike a particular distance in any direction. Can Bill make the trip without being bitten? Assume that the southwest corner of the field is at (0,0) and the northwest corner at (0,1000). The input consists of a line containing n <= 1000, the number of snakes. A line follows for each snake, containing three real numbers: the (x,y) location of the snake and its strike distance. The snake will bite anything that passes closer than this distance from its location. Bill must enter the field somewhere between the southwest and northwest corner and must leave somewhere between the southeast and northeast corners. If Bill can complete the trip, give coordinates at which he may enter and leave the field. If Bill may enter and leave at several places, give the most northerly. If there is no such pair of positions, print "Bill will be bitten." ``````3 500 500 499 0 0 999 1000 1000 200 `````` ``````Bill enters at (0.00, 1000.00) and leaves at (1000.00, 800.00). `````` ``````/* use of random() portable among: Solaris, SunOS, DECUnix, Linux */ #include <stdio.h> #include <stdlib.h> char jane[200], john[200]; int janei, johni; main(){ int i,j; gets(jane); gets(john); for (j=janei=johni=0;j<1000 && strlen(jane)&&strlen(john);j++){ if (jane[janei] == john[johni]) { if (random()/141%2 == 0) { /* jane wins */ printf("Snap! for Jane: "); for (i=strlen(jane);i>janei;i--) jane[i+johni+1] = jane[i]; strncpy(jane+janei+1,john,johni+1); strcpy(john,john+johni+1); janei = janei + johni + 2; johni = 0; for (i=janei-1;i>=0;i--) printf("%c",jane[i]); printf("\n"); }else{ /* john wins */ printf("Snap! for John: "); for (i=strlen(john);i>johni;i--) john[i+janei+1] = john[i]; strncpy(john+johni+1,jane,janei+1); strcpy(jane,jane+janei+1); johni = johni + janei + 2; janei = 0; for (i=johni-1;i>=0;i--) printf("%c",john[i]); printf("\n"); } }else{ janei++; johni++; } if (!jane[janei]) janei = 0; if (!john[johni]) johni = 0; } if (!strlen(jane)) printf("John wins.\n"); else if (!strlen(john)) printf("Jane wins.\n"); else printf("No winner after %d turns\n",j); } `````` ``````/* use of random() portable among: Solaris, SunOS, DECUnix, Linux */ #include <stdio.h> #include <stdlib.h> char jane[200], john[200]; int janei, johni; main(){ int i,j; gets(jane); gets(john); for (j=janei=johni=0;j<1000 && strlen(jane)&&strlen(john);j++){ if (jane[janei] == john[johni]) { if (random()/141%2 == 0) { /* jane wins */ printf("Snap! for Jane: "); for (i=strlen(jane);i>janei;i--) jane[i+johni+1] = jane[i]; strncpy(jane+janei+1,john,johni+1); strcpy(john,john+johni+1); janei = janei + johni + 2; johni = 0; for (i=janei-1;i>=0;i--) printf("%c",jane[i]); printf("\n"); }else{ /* john wins */ printf("Snap! for John: "); for (i=strlen(john);i>johni;i--) john[i+janei+1] = john[i]; strncpy(john+johni+1,jane,janei+1); strcpy(jane,jane+janei+1); johni = johni + janei + 2; janei = 0; for (i=johni-1;i>=0;i--) printf("%c",john[i]); printf("\n"); } }else{ janei++; johni++; } if (!jane[janei]) janei = 0; if (!john[johni]) johni = 0; } if (!strlen(jane)) printf("John wins.\n"); else if (!strlen(john)) printf("Jane wins.\n"); else printf("No winner after %d turns\n",j); } ``````

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# Issac Physcis Watch Announcements #1 The planet Mogg is completely spherical, with radius 2.3×106m Calculate the gravitational field strength at a height of 100km above the surface of the planet. Use the information given in question F5.6 and give your answer to 2 significant figures. (F5.6 --At a distance of 1.0×107m from the centre of planet Mogg, the gravitational field strength due to Mogg is 2.1Nkg−1. Calculate the gravitational field strength at a distance of 5.0×107m) 0 2 years ago #2 Solve to find the mass then just plug it into the formula 0 2 years ago #3 You can also use proportionality g=GM/r^2 since M is constant and G is constant, g is inversely proportional to r^2 so g1r12=g2r22 here g1 = 2.1Nkg−1 and r1=1.0×107m g2 = ?, r2= 100 x103 + 2.3×106 0 #4 Thank You 0 #5 (Original post by BobbJo) You can also use proportionality g=GM/r^2 since M is constant and G is constant, g is inversely proportional to r^2 so g1r12=g2r22 here g1 = 2.1Nkg−1 and r1=1.0×107m g2 = ?, r2= 100 x103 + 2.3×106 Thank You 0 #6 How would you use the information in questions F5.6 and F5.7, calculate the gravitational field strength due to planet Mogg at a distance of 3.0x10^6 m from the centre? F5.7 (The planet Mogg is completely spherical, with radius 2.3×106m Calculate the gravitational field strength at a height of 100km above the surface of the planet. Use the information given in question F5.6 and give your answer to 2 significant figures. (F5.6 --At a distance of 1.0×107m from the centre of planet Mogg, the gravitational field strength due to Mogg is 2.1Nkg−1. Calculate the gravitational field strength at a distance of 5.0×107m) 0 #7 (Original post by BobbJo) You can also use proportionality g=GM/r^2 since M is constant and G is constant, g is inversely proportional to r^2 so g1r12=g2r22 here g1 = 2.1Nkg−1 and r1=1.0×107m g2 = ?, r2= 100 x103 + 2.3×106 Thank you 0 X new posts Back to top Latest My Feed ### Oops, nobody has postedin the last few hours. Why not re-start the conversation? see more ### See more of what you like onThe Student Room You can personalise what you see on TSR. Tell us a little about yourself to get started. ### Poll Join the discussion #### Do you have the space and resources you need to succeed in home learning? Yes I have everything I need (209) 57.26% I don't have everything I need (156) 42.74%

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# How prove this integral $\int\limits_0^1 \int\limits_0^1 \ln\Gamma(x+y^3)\,dx\,dy =-\frac 7 {16}+\frac{1}{2}\ln 2\pi$ show that $$I=\int_0^1 \int_0^1 \ln\Gamma(x+y^3) \, dx \, dy =-\frac 7 {16} + \frac 1 2 \ln 2\pi$$ where $$\Gamma(a)=\int_0^\infty x^{a-1}e^{-x} \, dx$$ then $$I=\int_0^1 \int_0^1 \ln\left(\int_0^\infty t^{x+y^3-1}e^{-t} \, dt\right) \, dx \, dy$$ Then I can't works,Thank you • This is just going off intuition, but the $\frac{1}{2} \ln 2 \pi$ could possibly arise from Stirling's Approximation. This makes sense because the Gamma function is intrinsically related to the factorial. Sep 24, 2013 at 4:00 • This is art for art's sake because the Maple code $$Digits := 17; evalf(Int(ln(GAMMA(y^3+x)), [x = 0 .. 1, y = 0 .. 1]), 15)$$ outputs $0.481438533204673$. Sep 24, 2013 at 4:34 Let $\displaystyle\;\;f(u) = \int_0^1 \log\Gamma(z+u) \,dz,\;\;$ we have: $$f'(u) = \int_0^1 \frac{\Gamma'(z+u)}{\Gamma(z+u)}\,dz = \Big[\log\Gamma(z+u)\Big]_{z=0}^1 = \log\frac{\Gamma(u+1)}{\Gamma(u)} = \log u$$ Integrate this gives us $f(u) = f(0) + u\log u - u$. Now $$f(0) = \int_0^1\log\Gamma(z)dz = \frac12\int_0^1\log(\Gamma(z)\Gamma(1-z)) \, dz =\frac12 \int_0^1\log\frac{\pi}{\sin\pi z} \, dz\\ =\frac12\left(\log\pi - \frac{1}{\pi}\int_0^{\pi}\log \sin\theta \, d\theta\right) \stackrel{\color{blue}{[1]}}{=} \frac12\log(2\pi)$$ This gives us $$f(u) = \frac12\log(2\pi) + u\log u - u$$ and hence \begin{align} I = \int_0^1 f(y^3) \, dy = & \int_0^1 \big(\frac12\log(2\pi) + y^3 \log(y^3) - y^3\big) \, dy\\ = & \frac12\log(2\pi) + \left[\frac{3}{16}y^4(\log(y^4)-1) - \frac14 y^4\right]_0^1\\ = & \frac12\log(2\pi) - \frac{7}{16} \end{align} Notes • $\color{blue}{[1]}$ We are using the result $$\frac 1 \pi \int_0^\pi \log\sin\theta \, d\theta = -\log 2,$$ For a proof, see answers of this question. Using $$\int_0^1 \ln\Gamma\left(x+\alpha\right)\ dx =\frac{1}{2}\ln2\pi+\alpha \log \alpha -\alpha\quad;\quad \alpha \geq 0,$$ and $$\int_0^1 x^\alpha \ln^n x\ dx=\frac{(-1)^n n!}{(\alpha+1)^{n+1}}, \qquad\text{for }\ n=0,1,2,\ldots$$ then $$\int_0^1 \ln\Gamma\left(x+y^3\right)\ dx=\frac{1}{2}\ln2\pi+3y^3 \ln y -y^3$$ and \begin{align} \int_0^1\int_0^1 \ln\Gamma\left(x+y^3\right)\ dx\ dy&=\int_0^1 \left(\frac{1}{2}\ln2\pi+3y^3 \ln y -y^3\right)\ dy\\ &=\frac{1}{2}\ln2\pi-\frac{3}{4^2}-\frac14\\ &=\large\color{blue}{\frac{1}{2}\ln2\pi-\frac{7}{16}}.\tag{Q.E.D.} \end{align}

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Posted on ## Advanced Data Reshaping in Python and R This note is a simple data wrangling example worked using both the Python data_algebra package and the R cdata package. Both of these packages make data wrangling easy through he use of coordinatized data concepts (relying heavily on Codd’s “rule of access”). The advantages of data_algebra and cdata are: • The user specifies their desired transform declaratively by example and in data. What one does is: work an example, and then write down what you want (we have a tutorial on this here). • The transform systems can print what a transform is going to do. This makes reasoning about data transforms much easier. • The transforms, as they themselves are written as data, can be easily shared between systems (such as R and Python). Posted on Categories Administrativia, Statistics, Tutorials8 Comments on Update on coordinatized or fluid data ## Update on coordinatized or fluid data We have just released a major update of the `cdata` R package to CRAN. If you work with `R` and data, now is the time to check out the `cdata` package. Continue reading Update on coordinatized or fluid data Posted on ## Introduction In teaching thinking in terms of coordinatized data we find the hardest operations to teach are joins and pivot. One thing we commented on is that moving data values into columns, or into a “thin” or entity/attribute/value form (often called “un-pivoting”, “stacking”, “melting” or “gathering“) is easy to explain, as the operation is a function that takes a single row and builds groups of new rows in an obvious manner. We commented that the inverse operation of moving data into rows, or the “widening” operation (often called “pivoting”, “unstacking”, “casting”, or “spreading”) is harder to explain as it takes a specific group of columns and maps them back to a single row. However, if we take extra care and factor the pivot operation into its essential operations we find pivoting can be usefully conceptualized as a simple single row to single row mapping followed by a grouped aggregation. Posted on 1 Comment on Coordinatized Data: A Fluid Data Specification ## Introduction It has been our experience when teaching the data wrangling part of data science that students often have difficulty understanding the conversion to and from row-oriented and column-oriented data formats (what is commonly called pivoting and un-pivoting). Real trust and understanding of this concept doesn’t fully form until one realizes that rows and columns are inessential implementation details when reasoning about your data. Many algorithms are sensitive to how data is arranged in rows and columns, so there is a need to convert between representations. However, confusing representation with semantics slows down understanding. In this article we will try to separate representation from semantics. We will advocate for thinking in terms of coordinatized data, and demonstrate advanced data wrangling in `R`.

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# question ## I have to write this date to handle my query Date = Dec.24,2015 For example if substring(price_dt,1,3)='Dec' then 12+'-'+substring(price_dt,5,6 How to write this in an expression like above my expression. 1 comment Up to 2 attachments (including images) can be used with a maximum of 512.0 KiB each and 1.0 MiB total. You have some good answers below. This web site runs by you voting and marking the best answers. For each helpful answer below, indicate this by clicking on the thumbs up symbol next to those answers. If any one answer lead to a solution, indicate this by clicking on the check mark next to that answer. This helps indicate your solution for anyone else with the same question. 0 Likes 0 · · very similar to this question: [ https://ask.sqlservercentral.com/questions/92630/need-to-get-date-and-time-in-format-of-20120817133.html][1] Here is what you can do (you will have to finish of the CASE, I couldn't be bothered, sorry): DECLARE @TEST AS CHAR(11) SET @TEST = 'Dec.24,2015' SELECT @TEST SELECT RIGHT(@TEST, 4) , SUBSTRING(@TEST, 5, 2) , CASE WHEN LEFT(@TEST, 3) = 'JAN' THEN 1 WHEN LEFT(@TEST, 3) = 'FEB' THEN 2 ..... WHEN LEFT(@TEST, 3) = 'DEC' THEN 12 END, CONVERT(DATE, RIGHT(@TEST, 4) + CASE WHEN LEFT(@TEST, 3) = 'JAN' THEN '1' WHEN LEFT(@TEST, 3) = 'FEB' THEN '2' .... WHEN LEFT(@TEST, 3) = 'DEC' THEN '12' END + SUBSTRING(@TEST, 5, 2)) [1]: https://ask.sqlservercentral.com/questions/92630/need-to-get-date-and-time-in-format-of-20120817133.html 1 comment Up to 2 attachments (including images) can be used with a maximum of 512.0 KiB each and 1.0 MiB total. Thanks you so much GAZZ 0 Likes 0 ·

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# Open Set, Closed Set: Definition Share on An open set contains its boundary; it is a generalization of an open interval. A closed set does not contain its boundary and is a generalization of a closed interval. In topology, a closed set is defined an one whose complement is open. ## Open Set / Closed Set Examples Every open interval is also an open set [1]. For example, the interval (3, 5) is open because any x-value in the set will be between 3 and 5. In other words, if you choose a number very close to one of the boundaries (3 or 5), there will always be a set of numbers surrounding it that does not contain the boundary. Let’s say you choose 3.001. The numbers 3.00001 and 3.01 are: • In the interval [3, 5], • Surround 3.001, • Do not contain the boundary. You could continue choosing number ad infinitum and never reach the boundary. This leads to an alternative definition of an open set, which is in terms of distance. A set (a, b) is open if it contains all numbers “sufficiently close” to a and b 2. ## Properties of Open Set / Closed Set • The complement of an open set is closed. For example, [3, 5] is closed because its complement is two open sets (-∞ 3) ∪ (5, ∞). • Every union of open sets (the smallest set that contains both sets) is open. • Every finite intersection of open sets is open. However, the fact that the complement of an open set is closed does not mean that “closed set” and “open set” are antonyms. Sets can be open, closed, both, or neither [3]. *Note: A complement is all elements, from a universal set, that are not in the set of interest. For example, if your universal set is {1, 2, 3, 4} then the complement of {1, 2} is {3, 4}. ## References [1] Knapp, A. (2005). Basic Real Analysis. Birkhäuser Boston. [2] A Short Introduction to Metric Spaces: Section 1: Open and Closed Sets. Retrieved August 4, 2021 from: https://math.hws.edu/eck/metric-spaces/open-and-closed-sets.html [3] Lamb, E. (2013). Can a Closed Set Be Open? Can an Open Set Be Closed? When Math and Language Collide. Retrieved August 4, 2021 from: https://blogs.scientificamerican.com/roots-of-unity/can-a-closed-set-be-open-can-an-open-set-be-closed-when-math-and-language-collide/ CITE THIS AS: Stephanie Glen. "Open Set, Closed Set: Definition" From CalculusHowTo.com: Calculus for the rest of us! https://www.calculushowto.com/open-set-closed-set-definition/ --------------------------------------------------------------------------- Need help with a homework or test question? With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. Your first 30 minutes with a Chegg tutor is free!

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## lgbasallote 3 years ago "All the names of a class were written on separate tickets. Ten tickets were selected after the names were jumbled inside a can...." This is an example of simple random sampling right? 1. charlotte123 Yes I believe so :D Since its random ;D 2. lgbasallote well...i know it's random....i just don't know the specific type of random sampling 3. charlotte123 Isnt there only one type? :O do u have choices lol? :P 4. lgbasallote it could be clustered random sampling....since they were grouped first... or maybe stratified random sampling since i don't know what it means.... 5. lgbasallote no there isn't one type and no choices 6. KingGeorge I would probably argue that they're looking for clustered random sampling. They first divided some population up into "classes" and from this particular class, they made a simple random sampling. I see how this is confusing though. Since a clustered random sampling by definition has a simple random sampling in it... 7. vf321 Taking AP Stats, eh @Igbasallote? It's SRS. 8. lgbasallote clustered random sampling has something to do with grouping right @KingGeorge ? 9. lgbasallote @vf321 not taking it....it's complicated anyway why SRS? 10. vf321 One sec let me take my notes out with precise definitions. 11. KingGeorge clustered random sampling is when you split the population into multiple groups/clusters, and then take a simple random sample. By saying this was from a "class" it implied to me that they had divided the overall population into multiple "classes"/groups. 12. lgbasallote yes. my thoughts too 13. KingGeorge It's that fact that confuses the question a little for me. Since any example of clustered random sampling is an example of simple random sampling as well. 14. lgbasallote a lottery is a simple random sampling though... 15. vf321 Def 1. SRS is a sample selected from a population that ensures that EVERY possible sample of desired size has the same chance of being selected (i.e., random number generator - but, the College Board counts the shuffled names on tickets as random) Def 2. A population can be divided into non-overlapping subgroups called clusters which are internally heterogenous. Random selection of several clusters and then assessment of all internal individuals is cluster sampling. 16. lgbasallote ...so how is it not cluster nor random? 17. vf321 You are taking ONE sample from your ticket pool, and each ticket has an equal chance of being drawn, assuming you take them at the same time, and do so randomly. You are NOT dividing the class into, say, desk groups and randomly choosing entire desk groups for your sample. QED, SRS. 18. vf321 **QED was necessary for style points. 19. KingGeorge Ah. It makes more sense now. In a cluster sampling, you also have to take a sample of each cluster. Hence, this can't be CRS, so it must be SRS. 20. KingGeorge ^^I think that's the right idea. Feel free to shoot me down if it's wrong. 21. lgbasallote by SRS we're talking about simple? or stratified? 22. KingGeorge Simple I think. 23. vf321 Simple of course. Stratified sampling can be thought of as homogenous clustering. 24. lgbasallote oh..i thought SRS meant stratified 25. vf321 And stratification would result in an internal SRS for each strata. 26. lgbasallote that was why i was confused with the definition 27. vf321 Well are you all clear now? 28. lgbasallote what is stratified random sampling then? 29. lgbasallote @vf321 ? 30. vf321 I told you, didn't I? "Stratified sampling can be thought of as homogenous clustering," but where each such homogenous cluster has an "internal SRS for each strata." I.e., you don't use the entire strata as your sample. 31. lgbasallote i meant....how does it look like...i not good with understanding stat words 32. lgbasallote you choose part of the cluster? 33. lgbasallote or you divide a population into different clusters and then you select one cluster? 34. vf321 Stratified sampling: I want to observe high school student's attitude towards school assemblies. I know that there may be varying attitudes over grade level. Strata: Freshmen, Sophomores, Juniors, Seniors. Take a SRS (simple RS) of each strata (make sure size of SRS is proportional to grade population): 30 rand selected fresh, 20 r.s. soph., 25 r.s. juniors, 20 r.s. seniors. Sample = 30 + 20 + 25+ 20 35. vf321 This is done so that I have a sample that represents my population well. A whole SRS of the entire high school of size 95 can end up with, say, 50 sophomores, which may skew the results. 36. lgbasallote ohhh 37. lgbasallote but simple random sampling takes all of the population into account? 38. vf321 yes look at my definition above 39. lgbasallote like i said..im not good with stat words...just clarifying

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# Ncert solution maths class 12. NCERT Solutions for Class 12 Maths 2018-08-06 Ncert solution maths class 12 Rating: 8,5/10 1856 reviews ## NCERT Solutions for Class 12 Maths The council generally acts as the Secretariat of the National Development Group for Educational Innovations. Register for our free webinar class with best mathematics tutor in India. The class 12 is really important for the students as the future of the students depend upon the marks secured by them in this examination. Q11 : is equal to A. Therefore, in order to make learning an enjoyable and effective experience, try to create an affinity towards the subject. Invertible matrices and proof of the uniqueness of inverse, if it exists; Here all matrices will have real entries. Elementary properties of inverse trigonometric functions. Next ## NCERT Solutions for Class 12 Maths Here you will learn about all the vector algebra and the types. Note: This page was being slower due to excess use by the visitors. In this chapter we will see the solutions for a applications of determinants. To answer such type of questions, the fundamental concepts must be made clear. Derivatives of logarithmic and exponential functions. Next ## NCERT Solutions For Class 12 Maths Basically, it helps student to solve more. You will find out of integrals can be used to find the areas of parabola, ellipse, etc. All Inverse Trigonometric Functions Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the types given in the syllabus and problems based on them. Calculate the total earning by the hoarding in a month. Next ## ncert solutions for class 12 maths pdf download You will learn how arbitary constants can be used to solve a particular solution. We are planning to upload class 12 R D Sharma, P K Garg, R S Aggarwal book solutions on this website that will be done with in the session 2018 — 2019. Leaving space 5 cm wide for the gate on one side. Cartesian and vector equation of a plane. Find the ratio of speed of Hamid to the speed of Akhtar. The solutions are very helpful during individual or group studies, teaching students how to best approach a problem. Find the ratio of a Present age of father to the present age of son. Next ## NCERT Solutions for Class 12 Maths Chapter 12 Exercise 12.1, 12.2 Misc Write any one value reflected in the problem. Ncert solution class 12 Mathematics includes text book solutions from both part 1 and part 2. It will surely boost up your marks in the board exam. They used this for trade and commerce with different parts of the world. Concept of exponential and logarithmic functions. Main points to be recovered Relations and Functions 1. Next ## NCERT solutions for class 12 Mathematics Adjoint and inverse of a square matrix. Answer : Adding 1 and 2 , we obtain Hence, the correct answer is B. Thanks a lot and have a great day. Just like R D Sharma, All in One for Mathematics is also very good book with ample practice questions. After learning the basics of matices you will move forward to advanced a part of that like: addition, multiplication, transpose, scalar multiplication, etc Determinants Now comes the most important chapter of this class 12 mathematics: determinants. Find the maximum number of cakes which can be made from 5 kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes. Next ## NCERT SOLUTIONS FOR CLASS 6 MATHS EXERCISE 12.1 Answer : By second fundamental theorem of calculus, we obtain Hence, the correct answer is C. Differential Equations 9 — summary: Definition, order and degree, general and particular solutions of a differential equation. There increasing and decreasing functions, approximation with a maximum and minimum derivatives. Q42 : is equal to A. Both the products are processed on two different machines. Write in the comment section for any error or any solution related queries from the exercise. Next ## NCERT Solutions Class 12 Maths Free PDF Download The available capacity of first machine is 12 hours and that of second machine is 9 hours per day. Q19 : Show that if f and g defined as and Answer : Adding 1 and 2 , we obtain Q20 : The value of A. These solutions must be focused properly for a deeper understanding of chapters included in the class 12 textbooks. Concept of exponential and logarithmic functions. Find the ratio of the cost of a pen to the cost of a ball pen. Next ## NCERT Solutions for Class 9 Maths Chapter 12 Heron Formula 12.1, 12.2 The solutions have been devised by some of the best teachers in the country. Then you will find the equation of a curve that is passing through a specific location with the help of given parameter. Linear Programming 12 — summary: Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming L. This would ultimately lead to a good score on their board exam. After that you will be learning about binary operation, composite function, inverse function and so on. Determinants 4 — summary: Determinant of a square matrix up to 3 x 3 matrices , properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle. Next

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# Well Control: Activity 2 1) The Volumetric Method is being employed to bring a gas influx to surface because circulation was impossible – no pipe in the hole. During a bleed step the choke operator should adjust the choke to accomplish what? a. Allow SICP to rise by the calculated amount. b. Allow SICP to fall by the calculated amount. c. Hold SICP constant at the proper Pchoke value. d. Bleed the calculated volume in a timely manner. 2) A driller observes a warning sign for a kick. Why is it better to continue pumping while raising the pipe to the shut-in position? a. To minimize downtime. b.To minimize the amount of influx by keeping the annular pressure loss as long as possible. c. The driller should shut-off the pump before picking up to identify the influx as soon as possible. d. To prevent sticking the pipe. 3) The well is shut-in on a gas kick and while preparing to begin the Wait and Weight Method, both SIDPP and SICP have risen by 300 psi due to gas migration. Before beginning to circulate, what must be done if constant bottom hole pressure is required? a. Bleed SICP back to the original shut-in value. b. Bleed small amounts of mud through the choke until the SIDPP is back to the original shut-in value. c. Bleed a “few barrels” of mud out of the annulus and see what happens. d. Do nothing – carry the 300 psi as a safety factor. 4) A vertical well with a surface BOP stack is shut-in after a gas kick has been taken. The bit is 950 ft off bottom and the influx is calculated to be from bottom to 300 ft above bottom. Shut-in drill pipe pressure is 450 psi. What will the most likely shut-in casing pressure be? a. The same as the shut-in drill pipe pressure. b. Higher than the shut-in drill pipe pressure. c. Lower than the shut-in drill pipe pressure. d. Impossible to say if the exact location is not known. 5) The principle involved in the CONSTANT BOTTOM HOLE PRESSURE method of well control is to maintain a pressure that is: a. Equal to the slow rate circulating pressure. b. At least equal to the formation pressure. c. Equal to the shut-in drill pipe pressure. d. At least equal to the shut-in casing pressure. 6) A vertical well with a surface BOP stack is shut-in after a kick. The pressure readings are as follows: Shut-in Drill Pipe Pressure = 680 psi Shut-in Casing Pressure = 890 psi What is the reason for the difference in these two pressures? a. The influx is in the drill pipe. b. The influx has a lower density than the drilling fluid. c. The influx has a higher density than the drilling fluid. d. The BOP was closed too fast which caused trapped pressure 7) Formation fluids can flow into the well if: a. Formation pressure is greater than hydrostatic pressure. b. Hydrostatic pressure is greater than formation pressure. c. Answer “a” and the formation must have permeability. d. Answer “b” and the formation must have porosity. 8) A well is brought on choke correctly and afterward it is realized that the initial circulating pressure is higher than anticipated. This is diagnosed as a plugged jet. It is decided to proceed with this higher ICP and correct the FCP calculation. (Wait and Weight Method). Use the data below, calculate the corrected FCP. Observed ICP = 1500 psi Kill weight mud = 13.5 ppg Calculated ICP = 1150 psi Original weight mud = 12.0 ppg SIDPP = 600 psi a. 619 psi         b. 1092 psi         c. 1013 psi        d. 782 psi 9) At what point during a well kill operation would you expect the highest pressure at the casing shoe? a. At initial shut-in. b. When the top of the gas reaches the shoe. c. When the kill weight mud reaches the bit. d. Any of the above could be correct depending on wellbore geometry 10) From the following list, which “two” are considered advantages that the Wait and Weight Method of Well Control has over the Drillers Method of Well Control? (Choose two answers) a.The Wait and Weight Method provides less "on choke" circulating time. b. The Wait and Weight Method always provides lower equivalent pressures at the casing shoe. c. Since the Wait and Weight Method is a "one circulation kill", less barite is utilized making it the cheaper method of killing a well. d. When the drill string volume is "less" than the annular open hole volume, the Wait and Weight Method will provide lower pressures at the casing shoe. NB: We are very thankful to the well control community. We will be very happy to receive your comments or objections for sharing this content. Facebook page Drilling Course , E-mail: drilling.course@gmail.com

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# Category: Optimization ## Inverse Problem (Part 3) In the two previous posts I wrote about inverse problems (part 1 and part 2). For a proper introduction into inverse problems I refer to these posts. In my last post about inverse problems, I have showed you how to describe a prediction (classification problem) in terms of an inverse problem and how to solve ## Inverse Problem (Part 2) In the last post I have written about inverse problems. A simplified toy example was presented, which showed you how to translate this problem into an optimization problem. Optimization problems can be solved with multiple algorithms, e.g. gradient descent or evolutionary algorithms. This article presents a more sophisticated inverse problem. We want to classify images ## Inverse Problem (Part 1) The process of calculating the causal factors from an observation is called inverse problem. An inverse problem is much harder to solve than the corresponding forward counterpart, which is calculating the observation from the causal factors. Many problems in science and math are inverse problems. They can be found in optics, radar, acoustics, communication theory, ## Image deblurring (Part 2) This article is a follow up to my last article Image debluring (Part 1). There I wrote about the specific problem of image deblurring. The problem is to find the original image, which is convolved with a known point spread function. This can be solved with an interactive optimization procedure. My intention to write about ## Image deblurring (Part 1) Image deblurring is the process of removing artifacts from images. An out of focus camera or movement during the exposure can cause these artifacts. This is often modeled as a convolution of the undistorted image with a point spread function. Deblurring is the inversion of this model. Inverse problems are often solved in an iterative

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# Cubic Yard/Hour to Cubic Feet/Day Converter 1 Cubic Yard/Hour = 648 Cubic Feet/Day ## One Cubic Yard/Hour is Equal to How Many Cubic Feet/Day? The answer is one Cubic Yard/Hour is equal to 648 Cubic Feet/Day and that means we can also write it as 1 Cubic Yard/Hour = 648 Cubic Feet/Day. Feel free to use our online unit conversion calculator to convert the unit from Cubic Yard/Hour to Cubic Feet/Day. Just simply enter value 1 in Cubic Yard/Hour and see the result in Cubic Feet/Day. Manually converting Cubic Yard/Hour to Cubic Feet/Day can be time-consuming,especially when you don’t have enough knowledge about Volume Flow units conversion. Since there is a lot of complexity and some sort of learning curve is involved, most of the users end up using an online Cubic Yard/Hour to Cubic Feet/Day converter tool to get the job done as soon as possible. We have so many online tools available to convert Cubic Yard/Hour to Cubic Feet/Day, but not every online tool gives an accurate result and that is why we have created this online Cubic Yard/Hour to Cubic Feet/Day converter tool. It is a very simple and easy-to-use tool. Most important thing is that it is beginner-friendly. ## How to Convert Cubic Yard/Hour to Cubic Feet/Day (yd3/h to ft3/day) By using our Cubic Yard/Hour to Cubic Feet/Day conversion tool, you know that one Cubic Yard/Hour is equivalent to 648 Cubic Feet/Day. Hence, to convert Cubic Yard/Hour to Cubic Feet/Day, we just need to multiply the number by 648. We are going to use very simple Cubic Yard/Hour to Cubic Feet/Day conversion formula for that. Pleas see the calculation example given below. $$\text{1 Cubic Yard/Hour} = 1 \times 648 = \text{648 Cubic Feet/Day}$$ ## What Unit of Measure is Cubic Yard/Hour? Cubic Yard/Hour or Cubic Yard per Hour is a unit of measurement for volumetric flow rate. It is defined as movement of a cube in one hour whose all sides are equal to 1 yard in length. ## What is the Symbol of Cubic Yard/Hour? The symbol of Cubic Yard/Hour is yd3/h. This means you can also write one Cubic Yard/Hour as 1 yd3/h. ## What Unit of Measure is Cubic Feet/Day? Cubic Feet/Day or Cubic Feet per Day is a unit of measurement for volumetric flow rate. It is defined as movement of a cube in one day whose all sides are equal to 1 foot in length. ## What is the Symbol of Cubic Feet/Day? The symbol of Cubic Feet/Day is ft3/day. This means you can also write one Cubic Feet/Day as 1 ft3/day. ## How to Use Cubic Yard/Hour to Cubic Feet/Day Converter Tool • As you can see, we have 2 input fields and 2 dropdowns. • From the first dropdown, select Cubic Yard/Hour and in the first input field, enter a value. • From the second dropdown, select Cubic Feet/Day. • Instantly, the tool will convert the value from Cubic Yard/Hour to Cubic Feet/Day and display the result in the second input field. Cubic Yard/Hour 1 Cubic Feet/Day 648 # Cubic Yard/Hour to Cubic Feet/Day Conversion Table Cubic Yard/Hour [yd3/h]Cubic Feet/Day [ft3/day]Description 1 Cubic Yard/Hour648 Cubic Feet/Day1 Cubic Yard/Hour = 648 Cubic Feet/Day 2 Cubic Yard/Hour1296 Cubic Feet/Day2 Cubic Yard/Hour = 1296 Cubic Feet/Day 3 Cubic Yard/Hour1944 Cubic Feet/Day3 Cubic Yard/Hour = 1944 Cubic Feet/Day 4 Cubic Yard/Hour2592 Cubic Feet/Day4 Cubic Yard/Hour = 2592 Cubic Feet/Day 5 Cubic Yard/Hour3240 Cubic Feet/Day5 Cubic Yard/Hour = 3240 Cubic Feet/Day 6 Cubic Yard/Hour3888 Cubic Feet/Day6 Cubic Yard/Hour = 3888 Cubic Feet/Day 7 Cubic Yard/Hour4536 Cubic Feet/Day7 Cubic Yard/Hour = 4536 Cubic Feet/Day 8 Cubic Yard/Hour5184 Cubic Feet/Day8 Cubic Yard/Hour = 5184 Cubic Feet/Day 9 Cubic Yard/Hour5832 Cubic Feet/Day9 Cubic Yard/Hour = 5832 Cubic Feet/Day 10 Cubic Yard/Hour6480 Cubic Feet/Day10 Cubic Yard/Hour = 6480 Cubic Feet/Day 100 Cubic Yard/Hour64800 Cubic Feet/Day100 Cubic Yard/Hour = 64800 Cubic Feet/Day 1000 Cubic Yard/Hour648000 Cubic Feet/Day1000 Cubic Yard/Hour = 648000 Cubic Feet/Day # Cubic Yard/Hour to Other Units Conversion Table ConversionDescription 1 Cubic Yard/Hour = 0.00021237634944 Cubic Meter/Second1 Cubic Yard/Hour in Cubic Meter/Second is equal to 0.00021237634944 1 Cubic Yard/Hour = 18.35 Cubic Meter/Day1 Cubic Yard/Hour in Cubic Meter/Day is equal to 18.35 1 Cubic Yard/Hour = 0.764554857984 Cubic Meter/Hour1 Cubic Yard/Hour in Cubic Meter/Hour is equal to 0.764554857984 1 Cubic Yard/Hour = 0.0127425809664 Cubic Meter/Minute1 Cubic Yard/Hour in Cubic Meter/Minute is equal to 0.0127425809664 1 Cubic Yard/Hour = 18349316.59 Cubic CM/Day1 Cubic Yard/Hour in Cubic CM/Day is equal to 18349316.59 1 Cubic Yard/Hour = 764554.86 Cubic CM/Hour1 Cubic Yard/Hour in Cubic CM/Hour is equal to 764554.86 1 Cubic Yard/Hour = 12742.58 Cubic Centimeter/Minute1 Cubic Yard/Hour in Cubic Centimeter/Minute is equal to 12742.58 1 Cubic Yard/Hour = 212.38 Cubic Centimeter/Second1 Cubic Yard/Hour in Cubic Centimeter/Second is equal to 212.38 1 Cubic Yard/Hour = 18349.32 Liter/Day1 Cubic Yard/Hour in Liter/Day is equal to 18349.32 1 Cubic Yard/Hour = 764.55 Liter/Hour1 Cubic Yard/Hour in Liter/Hour is equal to 764.55 1 Cubic Yard/Hour = 12.74 Liter/Minute1 Cubic Yard/Hour in Liter/Minute is equal to 12.74 1 Cubic Yard/Hour = 0.21237634944 Liter/Second1 Cubic Yard/Hour in Liter/Second is equal to 0.21237634944 1 Cubic Yard/Hour = 18349316.59 Milliliter/Day1 Cubic Yard/Hour in Milliliter/Day is equal to 18349316.59 1 Cubic Yard/Hour = 764554.86 Milliliter/Hour1 Cubic Yard/Hour in Milliliter/Hour is equal to 764554.86 1 Cubic Yard/Hour = 12742.58 Milliliter/Minute1 Cubic Yard/Hour in Milliliter/Minute is equal to 12742.58 1 Cubic Yard/Hour = 212.38 Milliliter/Second1 Cubic Yard/Hour in Milliliter/Second is equal to 212.38 1 Cubic Yard/Hour = 4847.38 Gallon/Day [US]1 Cubic Yard/Hour in Gallon/Day [US] is equal to 4847.38 1 Cubic Yard/Hour = 201.97 Gallon/Hour [US]1 Cubic Yard/Hour in Gallon/Hour [US] is equal to 201.97 1 Cubic Yard/Hour = 3.37 Gallon/Minute [US]1 Cubic Yard/Hour in Gallon/Minute [US] is equal to 3.37 1 Cubic Yard/Hour = 0.056103896103896 Gallon/Second [US]1 Cubic Yard/Hour in Gallon/Second [US] is equal to 0.056103896103896 1 Cubic Yard/Hour = 4036.29 Gallon/Day [UK]1 Cubic Yard/Hour in Gallon/Day [UK] is equal to 4036.29 1 Cubic Yard/Hour = 168.18 Gallon/Hour [UK]1 Cubic Yard/Hour in Gallon/Hour [UK] is equal to 168.18 1 Cubic Yard/Hour = 2.8 Gallon/Minute [UK]1 Cubic Yard/Hour in Gallon/Minute [UK] is equal to 2.8 1 Cubic Yard/Hour = 0.046716265942821 Gallon/Second [UK]1 Cubic Yard/Hour in Gallon/Second [UK] is equal to 0.046716265942821 1 Cubic Yard/Hour = 115.41 Barrel/Day [Petrol, US]1 Cubic Yard/Hour in Barrel/Day [Petrol, US] is equal to 115.41 1 Cubic Yard/Hour = 4.81 Barrel/Hour [Petrol, US]1 Cubic Yard/Hour in Barrel/Hour [Petrol, US] is equal to 4.81 1 Cubic Yard/Hour = 0.080148423005566 Barrel/Minute [Petrol, US]1 Cubic Yard/Hour in Barrel/Minute [Petrol, US] is equal to 0.080148423005566 1 Cubic Yard/Hour = 0.0013358070500928 Barrel/Second [Petrol, US]1 Cubic Yard/Hour in Barrel/Second [Petrol, US] is equal to 0.0013358070500928 1 Cubic Yard/Hour = 0.11541372912801 Kilobarrel/Day [Petrol, US]1 Cubic Yard/Hour in Kilobarrel/Day [Petrol, US] is equal to 0.11541372912801 1 Cubic Yard/Hour = 5.43 Acre Foot/Year1 Cubic Yard/Hour in Acre Foot/Year is equal to 5.43 1 Cubic Yard/Hour = 0.014876032843512 Acre Foot/Day1 Cubic Yard/Hour in Acre Foot/Day is equal to 0.014876032843512 1 Cubic Yard/Hour = 0.00061983470181299 Acre Foot/Hour1 Cubic Yard/Hour in Acre Foot/Hour is equal to 0.00061983470181299 1 Cubic Yard/Hour = 0.00001033057836355 Acre Foot/Minute1 Cubic Yard/Hour in Acre Foot/Minute is equal to 0.00001033057836355 1 Cubic Yard/Hour = 1.7217630605916e-7 Acre Foot/Second1 Cubic Yard/Hour in Acre Foot/Second is equal to 1.7217630605916e-7 1 Cubic Yard/Hour = 620464.2 Ounce/Day [US]1 Cubic Yard/Hour in Ounce/Day [US] is equal to 620464.2 1 Cubic Yard/Hour = 25852.67 Ounce/Hour [US]1 Cubic Yard/Hour in Ounce/Hour [US] is equal to 25852.67 1 Cubic Yard/Hour = 430.88 Ounce/Minute [US]1 Cubic Yard/Hour in Ounce/Minute [US] is equal to 430.88 1 Cubic Yard/Hour = 7.18 Ounce/Second [US]1 Cubic Yard/Hour in Ounce/Second [US] is equal to 7.18 1 Cubic Yard/Hour = 645805.66 Ounce/Day [UK]1 Cubic Yard/Hour in Ounce/Day [UK] is equal to 645805.66 1 Cubic Yard/Hour = 26908.57 Ounce/Hour [UK]1 Cubic Yard/Hour in Ounce/Hour [UK] is equal to 26908.57 1 Cubic Yard/Hour = 448.48 Ounce/Minute [UK]1 Cubic Yard/Hour in Ounce/Minute [UK] is equal to 448.48 1 Cubic Yard/Hour = 7.47 Ounce/Second [UK]1 Cubic Yard/Hour in Ounce/Second [UK] is equal to 7.47 1 Cubic Yard/Hour = 24 Cubic Yard/Day1 Cubic Yard/Hour in Cubic Yard/Day is equal to 24 1 Cubic Yard/Hour = 0.016666666666667 Cubic Yard/Minute1 Cubic Yard/Hour in Cubic Yard/Minute is equal to 0.016666666666667 1 Cubic Yard/Hour = 0.00027777777777778 Cubic Yard/Second1 Cubic Yard/Hour in Cubic Yard/Second is equal to 0.00027777777777778 1 Cubic Yard/Hour = 648 Cubic Feet/Day1 Cubic Yard/Hour in Cubic Feet/Day is equal to 648 1 Cubic Yard/Hour = 27 Cubic Feet/Hour1 Cubic Yard/Hour in Cubic Feet/Hour is equal to 27 1 Cubic Yard/Hour = 0.45 Cubic Feet/Minute1 Cubic Yard/Hour in Cubic Feet/Minute is equal to 0.45 1 Cubic Yard/Hour = 0.0075 Cubic Feet/Second1 Cubic Yard/Hour in Cubic Feet/Second is equal to 0.0075 1 Cubic Yard/Hour = 1119744 Cubic Inch/Day1 Cubic Yard/Hour in Cubic Inch/Day is equal to 1119744 1 Cubic Yard/Hour = 46656 Cubic Inch/Hour1 Cubic Yard/Hour in Cubic Inch/Hour is equal to 46656 1 Cubic Yard/Hour = 777.6 Cubic Inch/Minute1 Cubic Yard/Hour in Cubic Inch/Minute is equal to 777.6 1 Cubic Yard/Hour = 12.96 Cubic Inch/Second1 Cubic Yard/Hour in Cubic Inch/Second is equal to 12.96 1 Cubic Yard/Hour = 29908.31 Pound/Day [Gasoline]1 Cubic Yard/Hour in Pound/Day [Gasoline] is equal to 29908.31 1 Cubic Yard/Hour = 0.3461609981761 Pound/Second [Gasoline]1 Cubic Yard/Hour in Pound/Second [Gasoline] is equal to 0.3461609981761 1 Cubic Yard/Hour = 20.77 Pound/Minute [Gasoline]1 Cubic Yard/Hour in Pound/Minute [Gasoline] is equal to 20.77 1 Cubic Yard/Hour = 1246.18 Pound/Hour [Gasoline]1 Cubic Yard/Hour in Pound/Hour [Gasoline] is equal to 1246.18 1 Cubic Yard/Hour = 13566.18 Kilogram/Day [Gasoline]1 Cubic Yard/Hour in Kilogram/Day [Gasoline] is equal to 13566.18 1 Cubic Yard/Hour = 0.15701597204745 Kilogram/Second [Gasoline]1 Cubic Yard/Hour in Kilogram/Second [Gasoline] is equal to 0.15701597204745 1 Cubic Yard/Hour = 9.42 Kilogram/Minute [Gasoline]1 Cubic Yard/Hour in Kilogram/Minute [Gasoline] is equal to 9.42 1 Cubic Yard/Hour = 565.26 Kilogram/Hour [Gasoline]1 Cubic Yard/Hour in Kilogram/Hour [Gasoline] is equal to 565.26 1 Cubic Yard/Hour = 6.48 Hundred Cubic Feet/Day1 Cubic Yard/Hour in Hundred Cubic Feet/Day is equal to 6.48 1 Cubic Yard/Hour = 0.27 Hundred Cubic Feet/Hour1 Cubic Yard/Hour in Hundred Cubic Feet/Hour is equal to 0.27 1 Cubic Yard/Hour = 0.0045 Hundred Cubic Feet/Minute1 Cubic Yard/Hour in Hundred Cubic Feet/Minute is equal to 0.0045 1 Cubic Yard/Hour = 0.000075 Hundred Cubic Feet/Second1 Cubic Yard/Hour in Hundred Cubic Feet/Second is equal to 0.000075 1 Cubic Yard/Hour = 0.000648 Million Cubic Feet/Day1 Cubic Yard/Hour in Million Cubic Feet/Day is equal to 0.000648

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Get Inspire insights from former attendees in our AMA discussion thread on Inspire Buzz. ACEs and other community members are on call all week to answer! alteryx Community # Weekly Challenges Solve the challenge, share your solution and summit the ranks of our Community! Also available in | Français | Português | Español | 日本語 ###### IDEAS WANTED Want to get involved? We're always looking for ideas and content for Weekly Challenges. ## Challenge #161: Triangles, Triangles, Triangles 8 - Asteroid Challenge #161 solved! "Every triangle is a love triangle when you love triangles." - James Acaster, 2018 Spoiler 8 - Asteroid My Solution: Alteryx Spoiler Fun Challenge! 8 - Asteroid 8 - Asteroid 8 - Asteroid My solution: 8 - Asteroid Nice! 11 - Bolide This was a tricky one! The first attempt I made I kept getting 515 triangles, and I have no idea which one I was missing. So, I tried again and got the correct answer with a much simpler workflow. Spoiler 7 - Meteor Nice 🙂 10 - Fireball

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# What tools are used to measure dry ingredients? ## What tools are used to measure dry ingredients? Graduated and adjustable measuring cups are used to measure dry ingredients, such as flour, sugar, oats, rice and solid ingredients, such as shortening and peanut butter. The single measure cups are generally found nested in a graduated set of ¼ cup, 1/3 cup, ½ cup, and 1 cup measures. ## What is the measure of 1 ounce? oz. or oz. fl.) is a unit of volume equal to about 28.4 ml in the imperial system or about 29.6 ml in the US system. The fluid ounce is sometimes referred to simply as an “ounce” in applications where its use is implicit, such as bartending. What is used to mix ingredients? Whisks are vary efficient for combing liquid ingredients. they are used for mixing wet and dry ingredients together. ### What are the three basic ways of measuring ingredients? By now you’ve figured out there are three primary kitchen tools for measuring: measuring spoons, liquid measuring cups, and dry measuring cups. A kitchen scale is also helpful for measuring ingredients, as it can be used to measure pasta that doesn’t fit into measuring cups or for more precise amounts. ### How do you measure dry ingredients? HOW TO MEASURE DRY INGREDIENTS. When measuring dry powders like flour, granulated sugar, baking powder, baking soda, or salt, you want to place your measuring cup or spoon over a canister, sink, or sheet of parchment paper. Then, lightly spoon in the ingredient, until it is overflowing the cup. How do you measure 1 oz dry? Two dry tablespoons make up 1 dry ounce. 6 tsp #### What is the most accurate way to measure dry ingredients? Here are some helpful measuring tips. 1. Dry ingredients (like flour and sugar) should be measured using flat-cup measures. Ingredients should be level. 2. Spoon measures must be measured with the correct sized spoons. A level spoon is essential. 3. Liquid ingredients should be measured in jugs. How many teaspoons is 1 oz of powder? 11.53 tsp ## How much of a cup is a tablespoon? There are 16 tablespoons in one cup. ## How do you convert dry ounces to teaspoons? Conversion formula of oz to tsp 1. By multiplication. Number of ounce US multiply(x) by 6, equal(=): Number of teaspoon. 2. By division. Number of ounce US divided(/) by 0. equal(=): Number of teaspoon. 3. By multiplication. 24 oz(s) * 6 = 144 tsp(s) 4. By division. 24 oz(s) / 0.= 144 tsp(s) How do you measure dry ingredients by weight? To measure ingredients by weight, start by placing your mixing bowl on top of your scale and hitting the “tare” or “zero” button. This will account for the weight of the bowl and set your scale’s counter back to zero. Now add your flour by spooning it into the bowl until it hits 22.5 ounces. ### How many spoons is 4 oz? Convert 4 Ounces to Tablespoons fl oz tbsp 4.00 8 4.01 8.02 4.02 8.04 4.03 8.06 ### How many tablespoons are in a dry ounce? Dry/Weight Measure Ounces 3 teaspoons 1 tablespoon 1/2 ounce 1 tablespoon 3 teaspoons 1/2 ounce 2 tablespoons 1/8 cup 1 ounce 4 tablespoons 1/4 cup 2 ounces How many teaspoon is 4 oz? Convert 4 Ounces to Teaspoons fl oz tsp 4.00 24 4.01 24.06 4.02 24.12 4.03 24.18 #### What is used to level off dry ingredients? For dry ingredients such as flour, sugar or spices, heap the ingredient into the spoon over a canister or waxed paper. With a metal spatula or flat side of a knife, level with the rim of the spoon. For shortening or butter, spread into spoon and level off. #### How can I measure 3 ounces? Measure the right amount with your palm. One palm size portion equals 3 oz., or one serving. Snacking can add up. What are the 3 steps to measuring dry ingredients? How to Measure Dry Ingredients 1. Step 1: Get Your Tools Ready. Get some dry measuring cups and measuring spoons. 2. Step 2: Measuring by Volume. 3. Step 3: Measuring Spoons. 4. Step 4: Measuring Brown Sugar. 5. Step 5: Measure by Weight. 6. Step 6: Zero Out the Scale. 7. Step 7: Select Grams or Ounces. 8. Step 8: You’ve Mastered Measuring. ## Does 2 tablespoons equal 1 ounce? 1 US fluid ounce = 2 US tablespoons. ## How do you measure wet and dry ingredients? Here’s a good rule of thumb to follow—when measuring dry ingredients, use dry measuring cups or weigh them with a scale. For liquids, stick to a liquid measuring cup. What are the example of dry ingredients? Here are some of the dry ingredient examples used in baking: • Baking Flour or All-Purpose Flour. • Sugar (Castor or brown) • Cocoa Powder. • Baking Soda. • Baking Powder. • Spices. • Yeast. • Salt. ### What do you call a tool that is sometimes called mixing spoon? Wooden spoon – is also called mixing spoon which comes in various sizes suitable for different types of mixing. OTHER BAKING TOOLS. 1. ### Is 1 oz the same as 1 fl oz? 1 ounce (oz) = 0.fluid ounces (fl oz). Ounce (oz) is a unit of Weight used in Standard system. Fluid Ounces (fl oz) is a unit of Volume used in Standard system. The US fluid ounce, defined as 1/128 US gallon, equals to milliliters. How many cups does 4 oz equal? 0.5 cup #### Which utensil is used for leveling ingredients? used for leveling off dry ingredients when measuring; used for spreading icing on cakes tined fork tool used to hold meat while carving it or to spear food and pick up eye level: Measuring spoons are used for both _____ingredients: liquid and dry : Use a narrow metal spatula OR the back of a _____to scrape (level) off … #### How do I cut down in measurements? Breaking everything down into tablespoons and teaspoons makes dividing measurements a little easier and helpful to know what cup measurements are made of. 1. 1 cup = 16 tablespoons. 2. 3/4 cup = 12 tablespoons. 3. 1/2 cup = 8 tablespoons. 4. 1/3 cup = 5 tablespoons plus 1 teaspoon. 5. 1/4 cup = 4 tablespoons. 6. 1 tablespoon = 3 teaspoons. How many tablespoons are in an ounce of taco seasoning? 2 Tablespoons ## How much is 4 oz of meat? 4 oz of raw, lean meat is about 3 ounces after cooking. 3 oz of grilled fish is the size of a checkbook. A medium apple, peach, or orange is about the size of a tennis ball. ## Is an ounce the same as a tablespoon? 1 Tablespoon (tbsp) is equal to 0.5 fluid ounce (oz). To convert tablespoons to fluid ounces, multiply the tablespoon value by 0.5 or divide by 2. For example, to convert 5 tbsp to oz (fluid), multiply 5 by 0.5, that makes 2.5 fl oz is 5 tbsp.

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Fine Tuning Bait and Switch Jeff Lowder at Secular Outpost, argues against William Lane Craig's fine tuning argument. His objective is to show that even if the argument is valid it doesn't establish probability for God. Lowdwer's syllogism of the argument: 1. The life-permitting nature of the universe’s initial conditions is either the result of chance, necessity or design. (Premise) 2. It is not the result of chance or necessity. (Premise) 3. Therefore, it is the result of design. (From 1 and 2) This argument is clearly valid, i.e., the conclusion follows from the premises. We want to know the probability of (3). The probability of (3) will depend upon the probability of (2). If we have a very weak degree of belief that (2) is true, say we think Pr(2)=0.25, then, by itself, this argument only warrants the belief Pr(3)=0.25. N.B. I’m not claiming that (2) has an exact numerical probability equal to 0.25; that value is simply an example to illustrate the point.[1] Excluding it as a result of chance means showing the improbability of a given variable. For example hitting the target levels necessary for large open bodies of water on a planet. If that is extremely improbable then it's less likely that it "just happened" as the result of chance. The very fact of target levels and the extreme improbability of hitting them all argues against necessity. The universe did not have to turn out as it did. as Paul Davies Tells us: Paul Davies: "You might be tempted to suppose that any old rag-bag of laws would produce a complex universe of some sort, with attendant inhabitants convinced of their own specialness. Not so. It turns out that randomly selected laws lead almost inevitably either to unrelieved chaos or boring and uneventful simplicity. Our own universe is poised exquisitely between these unpalatable alternatives, offering a potent mix of freedom and discipline, a sort of restrained creativity. The laws do not tie down physical systems so rigidly that they can accomplish little, but neither are they a recipe for cosmic anarchy. Instead, they encourage matter and energy to develop along pathways of evolution that lead to novel variety-what Freeman Dyson has called the principle of maximum diversity: that in some sense we live in the most interesting possible universe." "Some scientists have tried to argue that if only we knew enough about the laws of physics, if we were to discover a final theory that united all the fundamental forces and particles of nature into a single mathematical scheme, then we would find that this superlaw, or theory of everything, would describe the only logically consistent world. In other words, the nature of the physical world would be entirely a consequence of logical and mathematical necessity. There would be no choice about it. I think this is demonstrably wrong. There is not a shred of evidence that the universe is logically necessary. Indeed, as a theoretical physicist I find it rather easy to imagine alternative universes that are logically consistent, and therefore equal contenders for reality." [2] We can eliminate necessity and even Andre Linde himself tells us the probabilities are overwhelmingly against life, meaning it is most unlikely that the universe's life bearing aspect would come about randomly.[3] That means premise two checks out and thus the argument is valid. But I think Lowder is attacking the soundness by brining arguing that the fine turning argument doesn't include all relevant material, that will change the probability factors. At this point he's going to pull an interesting bait and switch. He's going to transpose fine tuning into design argument so he can argue the counter design argument. But first he brings up the idea that FT dies not reflect all the data: Second, such arguments fail to embody all of the relevant, available evidence. .... It may well be the case that, by itself, the life-permitting nature of the universe’s initial conditions does make it more probable than not that the universe is designed. But that doesn’t entail that, all things considered, the total available, relevant evidence makes it more probable than not that the universe is designed. In order to defend that claim, you have to look at all of the evidence, including the evidence of evolution, biological role of pain and pleasure, nonresistant nonbelief, etc. And once you do that, it’s far from obvious that the total evidence favors theism, much less Christian theism. What he's calling "relevant data is anti-design data, FT is a from of design but does it have the same implications such that anti-design evidence would  count against it? Most of us know that evolution is not counter evidence to God. God can use evolution so how is that counter? There is the extinction aspect. The cruelty of nature. He fleshes some of it out thusly: We also know that so much of our universe is hostile to life due to things such as containing vast amounts of empty space, temperatures near absolute zero, cosmic radiation, and so forth. Given that our universe is life-permitting, the fact that so much of it is hostile to life is much more probable on no-design than on design. So once all of the evidence about cosmic life-permitting conditions has been fully stated, however, it’s far from obvious that facts about cosmic “fine-tuning” favor design over non-design. That only matters because he's brining in the conventional design arguments or bait and witch. In the conventional design argument the argument turns u[on things looking designed fitting together and seeming like the result of a plan. That's why empty space life threatening aspects are taken as counter design evidence they don't paper life so they are not part of a plan. All he's really doing there is to turn the conditions that make life improbable (counts for FT) into evidence for unplanned universe. That's because he switched arguments. In FT the only appearance of planning is so many totally improbable things working out. All that empty space bad water and so on is actually pro design if the deign is FT. In other words with FT the only aspects of design are where the target levels are hit and how overwhelming  the odds against hitting them. None of his counter design stuff really matters. see my FT argument on Religious a priori More on this in comment section. Please join me there and comment. [1] Jeffery Jay Lowder, "WLC Denies That Anyone Has Ever Died a Sincere Seeker Without Finding God" Secular Out Post, January 2, 2016 (blog URL) all quotations from Lowder will be from this source. [2] Paul Davies  "Physics and The Mind of G: The Tempelton Prize Address,"First Things, August 5 (1995) On line URL: [3] Andre Linde,"The Self  Reproducing Inflationary Universe, Scientifi9c American Nov 19994, 48-55 Now Linde is confident that the new inflationary theires will explain all of this, and indeed states that their purpose is to revolve the ambiguity with which cosmologists are forced to cope. His co-author in inflationary theory. Physicist Paul Steinhardt, had doubts about it as early as his first paper on the subject (1982). He admits that the point of the theory was to eliminate fine tuning (a major God argument), but the theory only works if one fine tunes the constants that control the inflationary period. John Horgan, “Physicist slams Cosmic Theory he Helped Conceive,” Scientific American Blogs, December 1, 2014. on line, URL http://blogs.scientificamerican.com/cross-check/physicist-slams-cosmic-theory-he-helped-conceive/ accessed 10/5/15. Horgan interviews Steinhardt. “The whole point of inflation was to get rid of fine-tuning – to explain features of the original big bang model that must be fine-tuned to match observations. The fact that we had to introduce one fine-tuning to remove another was worrisome. This problem has never been resolved." Anonymous said… JH: Excluding it as a result of chance means showing the improbability of a given variable. For example hitting the target levels necessary for large open bodies of water on a planet. If that is extremely improbable then it's less likely that it "just happened" as the result of chance. The very fact of target levels and the extreme improbability of hitting them all argues against necessity. Given an infinite universe, such as the one we live in, even the extremely unlikely is certain to happen. And indeed to have happened an infinite number of times. With regards to the laws of the universe, we need only suppose an infinite number of tries and it becomes a certainty that even the most unlikely will appear an infinite number of times (I think Linde's view is similar). By the way, Linde's paper is available on line here. Pix Unknown said… From my reading, no one knows if the U is spatially infinite, or only about 50 billion ly in size, currently. One can argue that, given the incomprehensible unlikelihood of complex imtelligent life appearing anywhere, at any time, in an undesigned universe, then the U must be infinite, to balance the probabilities. But in that case the hidden premise is "since we know the U isn't designed", and therefore begs the question (on its knees with real tears). This comment has been removed by the author. This comment has been removed by the author. Given an infinite universe, such as the one we live in, even the extremely unlikely is certain to happen. that's not the issue, The issue is it's so unlikely to happen that it's really likely the game is fixed, We are not talking about actual proof but probability. And indeed to have happened an infinite number of times. With regards to the laws of the universe, we need only suppose an infinite number of tries and it becomes a certainty that even the most unlikely will appear an infinite number of times It doesn't work that way. we don't have infinite chancres because universe had initiate duration of existence,ewe are headed for heat death and we have a starting time, and abunch of that is eaten up in plank time (I think Linde's view is similar) I know I;ve read it many ties use to link to it, Anonymous said… KW: From my reading, no one knows if the U is spatially infinite, or only about 50 billion ly in size, currently. One can argue that, given the incomprehensible unlikelihood of complex imtelligent life appearing anywhere, at any time, in an undesigned universe, then the U must be infinite, to balance the probabilities. But in that case the hidden premise is "since we know the U isn't designed", and therefore begs the question (on its knees with real tears). The reason for thinking the universe is infinite is the curvature of space (or lack thereof). It is not to account for life, so there is no question begging here. https://cosmosmagazine.com/space/how-big-is-the-universe But it does not have to be infinite, it just has to be incomprehensibly large for an incomprehensibly unlikelihood event to become almost certain. We have good evidence that it is at least incomprehensibly large, and possibly infinite. What evidence do you have that complex intelligent life is incomprehensibly unlikely? Pix Anonymous said… JH: that's not the issue, The issue is it's so unlikely to happen that it's really likely the game is fixed, We are not talking about actual proof but probability. Actually it is a very important part of the issue. If the universe is infinite, then no matter how unlikely an event - or sequence of events - it will necessarily happen an infinite number of times. Saying it is unlikely does not help you at all. It could be a 1 in 10^1000 event, it will still happen an infinite number of times. There is no eed to fix the game at all. JH: It doesn't work that way. we don't have infinite chancres because universe had initiate duration of existence,ewe are headed for heat death and we have a starting time, and abunch of that is eaten up in plank time We have infinite chances if the universe is spatially infinite. Pix Anonymous said... KW: From my reading, no one knows if the U is spatially infinite, or only about 50 billion ly in size, currently. One can argue that, given the incomprehensible unlikelihood of complex imtelligent life appearing anywhere, at any time, in an undesigned universe, then the U must be infinite, to balance the probabilities. But in that case the hidden premise is "since we know the U isn't designed", and therefore begs the question (on its knees with real tears). The reason for thinking the universe is infinite is the curvature of space (or lack thereof). It is not to account for life, so there is no question begging here. https://cosmosmagazine.com/space/how-big-is-the-universe But it does not have to be infinite, it just has to be incomprehensibly large for an incomprehensibly unlikelihood event to become almost certain. We have good evidence that it is at least incomprehensibly large, and possibly infinite. What evidence do you have that complex intelligent life is incomprehensibly unlikely? Pix that doesn't help you because the larger you make it the more level of FT targets to be hit, so you are just diving the probability against it up. If you want to take our solar system as Representative (we don't know it is), not much life. no intelligent life, Anonymous said... JH: that's not the issue, The issue is it's so unlikely to happen that it's really likely the game is fixed, We are not talking about actual proof but probability. Actually it is a very important part of the issue. If the universe is infinite, then no matter how unlikely an event - or sequence of events - it will necessarily happen an infinite number of times. Saying it is unlikely does not help you at all. It could be a 1 in 10^1000 event, it will still happen an infinite number of times. There is no eed to fix the game at all. JH: It doesn't work that way. we don't have infinite chancres because universe had initiate duration of existence,ewe are headed for heat death and we have a starting time, and abunch of that is eaten up in plank time We have infinite chances if the universe is spatially infinite. no. Let' say we have game where X' have Pdq' that attach to then, You have to build up a large supply of X' but if you have too many P' and Q your X's die you sayI have 100, yes but 500 P and Q. so yourX's will die. that;okIm getting 100 more X but that;s 500 more P andQ I know I;ll get infinite X, yes but infinite P and Q evidence for FT here is the argument a I irreverent argue it Ny FT argument im-skeptical said… He admits that the point of the theory was to eliminate fine tuning (a major God argument), but the theory only works if one fine tunes the constants that control the inflationary period. Joe, You have it all wrong. This has nothing to do with the theistic clams about the divinely fine-tuned universe. It is about the fact that the previous theory (big bang) was unlikely to produce a flat universe. The new theory (inflation) resolves that problem, because it naturally drives toward a flat universe. In tour fevered mind, you see a phrase like "fine tuning" and the only thing you can think of is "Yes! God did it!" And you imagine a group of atheist scientists sitting around a table trying to come up with a way to eliminate God from science. But that's not how real science works. I will quote from Guth, the primary author of the theory: The conventional Big Bang theory without inflation really only worked if you fed into it initial conditions which were highly finely tuned to make it just right to produce a universe like the one we see. Inflationary theory gets around this flatness problem because inflation changes the way the geometry of the universe evolves with time. They were not thinking about how to get rid of God. That's a stupid idea that only a theist like yourself would believe. m-skeptical said... He admits that the point of the theory was to eliminate fine tuning (a major God argument), but the theory only works if one fine tunes the constants that control the inflationary period. Joe, You have it all wrong. This has nothing to do with the theistic clams about the divinely fine-tuned universe. It is about the fact that the previous theory (big bang) was unlikely to produce a flat universe. The new theory (inflation) resolves that problem, because it naturally drives toward a flat universe. no because BB did produce a flat universe, flat universe better for CA btw, but he say It is to get rid of fine tuning then use fine tuning to help so he doesn't just mean any fine tuning but the God argument, In tour fevered mind, you see a phrase like "fine tuning" and the only thing you can think of is "Yes! God did it!" And you imagine a group of atheist scientists sitting around a table trying to come up with a way to eliminate God from science. But that's not how real science works. I just explained why it clerical mean that (backed up by things Martian Rees said). but even if it doesn't it doesn't matter because the real optimist they have to use fine tuning to make the theory work, o the methodology is valid, I will quote from Guth, the primary author of the theory: The conventional Big Bang theory without inflation really only worked if you fed into it initial conditions which were highly finely tuned to make it just right to produce a universe like the one we see. Inflationary theory gets around this flatness problem because inflation changes the way the geometry of the universe evolves with time. it does it by employing the thing they are trying to get rid of. Now you want to remove the very motive for the guy giving up on it. The story was inventor of theory gives up on it,because of this fine tuning hypocrisy thing, you are trying to pretend the story is not about that it says clearly it is. They were not thinking about how to get rid of God. That's a stupid idea that only a theist like yourself would believe. doesn't even matter the point is the same 11/07/2017 06:49:00 PM Delete you have not answered by X's thing, which proves that assuming an infinite universe doen't help. you just get infinite more target levels to have to hit, Anonymous said… JH: no. Let' say we have game where X' have Pdq' that attach to then, You have to build up a large supply of X' but if you have too many P' and Q your X's die you sayI have 100, yes but 500 P and Q. so yourX's will die. that;okIm getting 100 more X but that;s 500 more P andQ I know I;ll get infinite X, yes but infinite P and Q You have contrived an example in which the probability of winning is zero, so that is not analogous to what we were discussing. Here is a better example, with randomness so there is a finite probability of winning: Let us say we have a game where we have to roll ten dice. If they all come up six, I win, otherwise I lose. The chances of winning are 1 in 6^10, i.e., a probability of 0.000000016. We can be pretty sure I will lose, right? Except I get to play a billion times. The probability of losing a single game is 0.99999998346. The probability of losing every game out of a billion is 0.000000066 (0.99999998346^1000000000). Turns out that if I play enough times I am virtually certain to win at least once. And as the number of games heads to infinity, the probability of winning at least once becomes more and more of a certainty. Pix Anonymous said... JH: no. Let' say we have game where X' have Pdq' that attach to then, You have to build up a large supply of X' but if you have too many P' and Q your X's die you sayI have 100, yes but 500 P and Q. so yourX's will die. that;okIm getting 100 more X but that;s 500 more P andQ I know I;ll get infinite X, yes but infinite P and Q You have contrived an example in which the probability of winning is zero, so that is not analogous to what we were discussing. Ooop silly me Here is a better example, with randomness so there is a finite probability of winning: Let us say we have a game where we have to roll ten dice. If they all come up six, I win, otherwise I lose. The chances of winning are 1 in 6^10, i.e., a probability of 0.000000016. We can be pretty sure I will lose, right? Except I get to play a billion times. The probability of losing a single game is 0.99999998346. The probability of losing every game out of a billion is 0.000000066 (0.99999998346^1000000000). Turns out that if I play enough times I am virtually certain to win at least once. And as the number of games heads to infinity, the probability of winning at least once becomes more and more of a certainty. Pix 2 thints (1) you don't get to play a billion games,there's a finite window although really long. bigbang and heat death. (2) the no win scenario is not that unanalogous because there are so many target levels and they all have to be hit just right. you are trying to equate infinite space with infinite chance this not true, going infinite doesn't get you more chances for fine turning, im-skeptical said… no because BB did produce a flat universe - Big Bang was never a real theory. When they tried to works out the physics it didn't work. That's what Steinhardt was talking about. And that's why they needed a better theory. There is no cosmologist today that I'm aware of who thinks Big Bang is valid. I honestly don't know why theists are so desperate to cling to it. If your superstition tells you that God created the universe, then why couldn't he use inflation? At least that works better. As it is, you are no better than Thomists, with their Medieval theories of act and potency. Anonymous said… JH: (1) you don't get to play a billion games,there's a finite window although really long. bigbang and heat death. But there is infinite space to do it in. It is like playing the game a billion times simultaneously, rather than one after the other. JH: (2) the no win scenario is not that unanalogous because there are so many target levels and they all have to be hit just right. you are trying to equate infinite space with infinite chance this not true, going infinite doesn't get you more chances for fine turning, Actually it is very close to that. In each game, you have 10 target level that have to be hit just right (i.e., roll a six). Maybe you can argue life is more improbable targets and more of them (and maybe not). However, this galaxy alone has about a hundred billion stars and there could be an infinite number of galaxies, so the principle holds. Or for a fine tuned universe, each game is analogous to one of an infinite number of universes in the multiverse. Pix Actually it is very close to that. In each game, you have 10 target level that have to be hit just right (i.e., roll a six). Maybe you can argue life is more improbable targets and more of them (and maybe not). However, this galaxy alone has about a hundred billion stars and there could be an infinite number of galaxies, so the principle holds. Or for a fine tuned universe, each game is analogous to one of an infinite number of universes in the multiverse. except in real life there are hundreds of target levels. they bet you can do is maybe I say maybe a minuscule chance, that's a good reason to believe in God it;s much more parsemonius. Anonymous said… 1. It does not matter how many targets or how small the probabilities of each, in an infinite universe, it will still happen infinitely. 2. What is the basis for your claim of a "minuscule chance"? Pix Anonymous said... 1. It does not matter how many targets or how small the probabilities of each, in an infinite universe, it will still happen infinitely. ye sure does, Every fact that contribute to life bearing universe be exactly right to get to life and each one has to go through a gauntlet of trials like Daniel Boone being tried by the Native Americans. Increasing the number of chances just means increasing the number of gauntlets. 2. What is the basis for your claim of a "minuscule chance"? Pix Anonymous said… JH: ye sure does, Every fact that contribute to life bearing universe be exactly right to get to life and each one has to go through a gauntlet of trials like Daniel Boone being tried by the Native Americans. Increasing the number of chances just means increasing the number of gauntlets. They certainly decrease the probability. But as long as the probability is greater than zero, then it will still happen infinitely in an infinite universe. Pix Anonymous said… http://religiousapriori.blogspot.com/2015/10/fine-tuning-argument-part-1.html All I am seeing there is a bunch of quotes, some from over sixty years ago. In particular from the Linde article (which I think is 94, not 97), you have quoted him presenting the issues with the current model, but neglected to mention that that same paper proposes a solution to those problems! Pix All I am seeing there is a bunch of quotes, some from over sixty years ago. In particular from the Linde article (which I think is 94, not 97), you have quoted him presenting the issues with the current model, but neglected to mention that that same paper proposes a solution to those problems! no I did not neglect to mention it,I've written about it,I ay mention it on page two or nay have forgotten to link to it,I'll get back with you, They certainly decrease the probability. But as long as the probability is greater than zero, then it will still happen infinitely in an infinite universe. no both sets are creased so it stay the sane, you to circumvent all those thing like plank density and distance from the sun, here's one thing I found myself saying about his answer that is on my blog: "Now Linde is confident that the new inflationary theires will explain all of this, and indeed states that their purpose is to revolve the ambiguity with which cosmologists are forced to cope. The Scalar field is suppossed to explain all of this; but these inflationary models are still on the drawing board. Moreover, he never says where scalar fields come from, what makes them, and indeed never illustrates how they solve the initial problem of where it all came form in the first palce. Finally, it seems that scalar fields would be a design feature that should troulbe Linde as much as the initial problems, since he compares them the circuit breaker of a house which keeps the uiverse from heating up too fast before it can expand. Moreover, they might be argitrary necessiteis (see argument I)." Anonymous said… JH: no both sets are creased so it stay the sane, you to circumvent all those thing like plank density and distance from the sun, Show us the maths, then. that' a ridiculous answer, every chance for life to thri e ha to go through the sane set of possible failure, im-skeptical said… Don't bother asking Joe to show the math. At best, he'll google another quote and spit it at you, but never understand a word of it. Linde's discrepancy of 60 orders of magnitude is, of course, a problem with the big bang theory. It had already been resolved by 1980. Does Joe discuss the solution to issues that have been raised with inflation theory, and how they have been resolved? No, because he really doesn't understand any of this stuff. For him, it's good enough to find some quote from decades ago that he thinks supports his GodDidIt thesis, and put that in his article. m-skeptical said... Don't bother asking Joe to show the math. At best, he'll google another quote and spit it at you, but never understand a word of it. I have no evidence that you know jack shit about science,all I see you do is whine about how we don't fall at Yoruba feet and all your bull shit without question, when you do talk about stuff like Quantum theory you spout the usual atheist drivel from message boards, Linde's discrepancy of 60 orders of magnitude is, of course, a problem with the big bang theory. It had already been resolved by 1980. Does Joe discuss the solution to issues that have been raised with inflation theory, and how they have been resolved? No, because he really doesn't understand any of this stuff. For him, it's good enough to find some quote from decades ago that he thinks supports his GodDidIt thesis, and put that in his article. here the deceiver play another of his favorite games,misdirection. He points out an aspect he might be right about but neglects to inform it has nothing to do with the issue, Linde's article assumes that correction genius, so you are not saying anything, that does not circumvent the aspects of fine tuning that the discusses,those assume the correction too. Look at the ploy Px has opened up here, Yew I am not a scientific researcher I don't do math at that level, neither does he neither does the genius Skepie It' totally unreasonable to expect that. No reason why quoting experts such a Collins isn't enough especially when they have not done any original research on the issue, either.they have no math, Does Joe discuss the solution to issues that have been raised with inflation theory, and how they have been resolved? did you bring that issue up before? no you did not, you did not bring up. No reason why it should be mentioned because My argument had nothing to do with inflationary theory,why should not be discussed? you makeout like that mean I have something to hide?? you are being deceptive, you already drug us off the real issue of the Op because the bait and switch you never mentioned,you are a pervericator. you the coward who refuses to debate, you are a liar,a coward and a God hater, No, because he really doesn't understand any of this stuff. he reaches for the easy insult solution rather than be honest, in fact we ha struck inflation glancing blow when I said they want to get rid of fine tuning he just forgot to include the fact that one of the inventors of the theory withdrew support because it needs fine tuning to work, but that' what they wanted to get rid of. For him, it's good enough to find some quote from decades ago that he thinks supports his GodDidIt thesis, and put that in his article. he assigning motives to me that he wants you to think I have, that is ad hom argument It' deceptive and it damages people's reputations it's extremely unethical, WE DON'T ARGUE THAT WAY HERE do it again and you are history Anonymous said… JH: Look at the ploy Px has opened up here, Yew I am not a scientific researcher I don't do math at that level, neither does he neither does the genius Skepie I did the maths. here it is again: Here is a better example, with randomness so there is a finite probability of winning: Let us say we have a game where we have to roll ten dice. If they all come up six, I win, otherwise I lose. The chances of winning are 1 in 6^10, i.e., a probability of 0.000000016. We can be pretty sure I will lose, right? Except I get to play a billion times. The probability of losing a single game is 0.99999998346. The probability of losing every game out of a billion is 0.000000066 (0.99999998346^1000000000). Turns out that if I play enough times I am virtually certain to win at least once. And as the number of games heads to infinity, the probability of winning at least once becomes more and more of a certainty. Pix im-skeptical said… I have no evidence that you know jack shit about science - I have no evidence that you know how to make a logical argument, let alone understand what scientists say. No reason why it should be mentioned because My argument had nothing to do with inflationary theory,why should not be discussed? - See my comment of 11/07/2017 06:49:00 PM. The only reason I bring it up is because you did. you the coward who refuses to debate, you are a liar,a coward and a God hater - And you argue entirely from emotion. Whenever you can't stand up to the criticisms brought against your arguments, this is how you respond. in fact we ha struck inflation glancing blow when I said they want to get rid of fine tuning he just forgot to include the fact that one of the inventors of the theory withdrew support because it needs fine tuning to work - I told you before, Big Bang was superseded by inflation BECAUSE IT DIDN'T WORK. And only a theist would describe as being fine-tuned. And yes, Steinhardt noted that a VERSION of the inflation theory has a similar issue, but that's not true of all versions. In particular, the time-unbounded version advanced by Hawking does not have the problem that Steinhardt refers to. You can whine all you want about scientists trying to push God out of science, but they're always trying to find theories that work better. That's what science does. So just go on whining. Anonymous said... JH: Look at the ploy Px has opened up here, Yew I am not a scientific researcher I don't do math at that level, neither does he neither does the genius Skepie I did the maths. here it is again: Here is a better example, with randomness so there is a finite probability of winning: Let us say we have a game where we have to roll ten dice. If they all come up six, I win, otherwise I lose. The chances of winning are 1 in 6^10, i.e., a probability of 0.000000016. We can be pretty sure I will lose, right? Except I get to play a billion times. The probability of losing a single game is 0.99999998346. The probability of losing every game out of a billion is 0.000000066 (0.99999998346^1000000000). Turns out that if I play enough times I am virtually certain to win at least once. And as the number of games heads to infinity, the probability of winning at least once becomes more and more of a certainty. Px you are doing the math on my example, my example is extremely simplistic and it i probably very crude,(I invented it myself that should give you a clue). But you are not doing the real math on fine tuning which has been done by gobs of scientists who all agree it is a problem for them. Morton Rees(may have name wrong) the crayola astronomer of England was depressed for years because he could not shake God. he said it, he said "looks like there has to be a God" he was an atheist, m-skeptical said... I have no evidence that you know jack shit about science - I have no evidence that you know how to make a logical argument, let alone understand what scientists say. but that; because you don't know logic, people who know logic know immediately if know it or not No reason why it should be mentioned because My argument had nothing to do with inflationary theory,why should not be discussed? - See my comment of 11/07/2017 06:49:00 PM. The only reason I bring it up is because you did. you the coward who refuses to debate, you are a liar,a coward and a God hater - And you argue entirely from emotion. Whenever you can't stand up to the criticisms brought against your arguments, this is how you respond. again let the reader judge, those who know argument will see immediately i argue from reason and evidence, you do not you argue from whining about your status, in fact we ha struck inflation glancing blow when I said they want to get rid of fine tuning he just forgot to include the fact that one of the inventors of the theory withdrew support because it needs fine tuning to work - I told you before, Big Bang was superseded by inflation BECAUSE IT DIDN'T WORK. that prove you know shit about science, Saying Big bang didn't work is ludicrousness, for one thing they kept the big bang as part of inflationary theory. Secondly, I quoted the guy who invented the theory saying the purpose was to get rid of fine tuning, they used fine tuning to get rid of it, that's why the abandoned inflation, And only a theist would describe as being fine-tuned. And yes, Steinhardt noted that a VERSION of the inflation theory has a similar issue, but that's not true of all versions. the major one, if only a theist would use that term they why did Seknhardt say it was fine tuned? Is he a theist? In particular, the time-unbounded version advanced by Hawking does not have the problem that Steinhardt refers to. You can whine all you want about scientists trying to push God out of science, but they're always trying to find theories that work better. That's what science does. So just go on whining. Hawking's version is also considered a dead version it' not used, it also deputes upon gravity and laws of physics which he can't accout for deosn;t even try, YOU STILL IGNORE THE BAIT AND WITCH YOU CAN'T DISCUS THE REAL ISSUES BECAUSE YOU ARE SO HUNG UP ON BEING SEEN AS ALL KNOWING , book review in Gardion on Rees book https://www.theguardian.com/science/2012/jun/08/just-six-numbers-martin-rees-review "One can marvel, almost indefinitely, at the balance between the nuclear forces and the astoundingly feeble but ultimately inexorable power of gravity, giving us N, a huge number involving 36 zeroes, and nod gratefully each time one is told that were gravity not almost exactly 1036 times weaker then we wouldn't be here. One can gasp at the implications of the density parameter Ω (omega), which one second after the big bang could not have varied from unity by more than one part in a million billion or the universe would not still be expanding, 13.7bn years on. But who'd have thought that we also needed D for dimension to equal three, because without that value the show would never have got on the road? We go up the stairs, down the hall or across the living room so often that we tend to imagine that those are the only imaginable dimensions, but there could have been just two, for instance, or perhaps four. Had there been four dimensions, gravitational and other forces would have varied inversely as the cube of the distance rather than the square, and the inverse cube law would be an unforgiving one. Any orbiting planet that slowed for whatever reason in its orbit would swiftly plunge into the heart of its parent star; any planet that increased its speed ever so slightly would spiral madly into the cold and the dark. Under the inverse square law, however, a planet that speeds up ever so slightly – or slows down – simply shifts to a very slightly different orbit. That is, we owe the stability of the solar system to the fact that spacetime has, on the macroscale, only three physical dimensions. All six values featured in this book permit something significant to happen, and to go on happening. Take for instance Q, the one part in 100,000 ratio between the rest mass energy of matter and the force of gravity. Were this ratio a lot smaller, gas would never condense into galaxies. Were it only a bit smaller, star formation would be slow and the raw material for future planets would not survive to form planetary systems. Were it much bigger, stars would collapse swiftly into black holes and the surviving gas would blister the universe with gamma rays." Anonymous said… JH: Px you are doing the math on my example, my example is extremely simplistic and it i probably very crude,(I invented it myself that should give you a clue). But you are not doing the real math on fine tuning which has been done by gobs of scientists who all agree it is a problem for them. Morton Rees(may have name wrong) the crayola astronomer of England was depressed for years because he could not shake God. he said it, he said "looks like there has to be a God" he was an atheist, I was doing the maths on a model. That is what we do in science. If you can say that there is a specific issue with the model that affects the result for our purposes, then what is it? If you cannot say what that issue is, thenyou have to accept that the model is good enough for our purpose, and the conclusion is sound. That is how science is done, Joe. All those quotes you have, thery are conbsidering a single game, and concluding it is so unlikely as to be impossible. There are not considering an infinite number of games. Pix im-skeptical said… if only a theist would use that term they why did Seknhardt say it was fine tuned? Is he a theist? - That's the only reason he would use terminology like that. I think he is a theist. You don't hear other physicists saying that. What they say is IT DOESN'T WORK, and the need a better theory that does work. Hawking's version is also considered a dead version it' not used, it also deputes upon gravity and laws of physics which he can't accout for deosn;t even try, - Joe, you have no idea what you're talking about. Anonymous said... JH: Px you are doing the math on my example, my example is extremely simplistic and it i probably very crude,(I invented it myself that should give you a clue). But you are not doing the real math on fine tuning which has been done by gobs of scientists who all agree it is a problem for them. Morton Rees(may have name wrong) the crayola astronomer of England was depressed for years because he could not shake God. he said it, he said "looks like there has to be a God" he was an atheist, I was doing the maths on a model. That is what we do in science. If you can say that there is a specific issue with the model that affects the result for our purposes, then what is it? If you cannot say what that issue is, thenyou have to accept that the model is good enough for our purpose, and the conclusion is sound. That is how science is done, Joe. All those quotes you have, thery are conbsidering a single game, and concluding it is so unlikely as to be impossible. There are not considering an infinite number of games. you are a professional academic and a scintillate you know better, you are not dialing with a real level of scientific acumen in challenging my little rink a dink example and you are arid to take on guys like Linde and Paul Davies. my model is done by me not a real scientist, there are much better hmodels you are afarid of them, im-skeptical said... if only a theist would use that term they why did Seknhardt say it was fine tuned? Is he a theist? - That's the only reason he would use terminology like that. I think he is a theist. You don't hear other physicists saying that. What they say is IT DOESN'T WORK, and the need a better theory that does work. Martin Rees is not a theist and he ues the term fine tuning, he yas we have to be careful in using it but he does use it, he says it's true Hawking's version is also considered a dead version it' not used, it also deputes upon gravity and laws of physics which he can't accout for deosn;t even try, - Joe, you have no idea what you're talking about. https://arxiv.org/abs/hep-th/0610199 "Given the observed cosmic acceleration, Leonard Susskind has presented the following argument against the Hartle-Hawking no-boundary proposal for the quantum state of the universe: It should most likely lead to a nearly empty large de Sitter universe, rather than to early rapid inflation. Even if one adds the condition of observers, they are most likely to form by quantum fluctuations in de Sitter and therefore not see the structure that we observe. Here I present my own amplified version of this argument and consider possible resolutions, one of which seems to imply that inflation expands the universe to be larger than 10^{10^{10^{122}}} Mpc." https://science.howstuffworks.com/dictionary/famous-scientists/physicists/stephen-hawking3.htm "Biographer and science writer Kitty Ferguson said the no-boundary proposal is less accepted than Hawking radiation. "To this day there are many people in physics who don't accept it as something in physics that can be used as part of other theories -- you can't use it as a starting off point to go somewhere else," Ferguson said. In more recent years, Hawking has doubted the possibility of a "theory of everything" existing, an all-encompassing theory of theoretical physics that would explain pretty much everything [source: Sample]. He's also a skeptic on finding the Higgs boson, an elusive particle thought to give subatomic particles mass." died you read those quotes genius? do you see the biographer saying a lot people don't accept hawking no boundary do you see that.??"? I proved you wrong, Anonymous said… JH: you are a professional academic and a scintillate you know better, you are not dialing with a real level of scientific acumen in challenging my little rink a dink example and you are arid to take on guys like Linde and Paul Davies. my model is done by me not a real scientist, there are much better hmodels you are afarid of them, If you have a better model, present it. I am not afraid to address them because the same argument will apply. If you have an infinite number of attempts, even the most improbably event becomes a certainty. Pix Anonymous said… While there are challenges to the inflation model, a lot of the top cosmologists still hold to it, as a recent response to an article in Scientific American shows. Pix im-skeptical said… died you read those quotes genius? do you see the biographer saying a lot people don't accept hawking no boundary do you see that.??"? I proved you wrong, - The only thing you showed is that there are some who disagree, as Pix pointed out. But we already knew that. What puzzles me is how you can think that by googling an article that presents a different view, you can think that the whole world should just conclude that Joe's uninformed opinions must be true after all - because he cites an article. The only thing you showed is that there are some who disagree, as Pix pointed out. But we already knew that. What puzzles me is how you can think that by googling an article that presents a different view, you can think that the whole world should just conclude that Joe's uninformed opinions must be true after all - because he cites an article. some physics who disagree you can show none who agree,if it was proven they could not disagree, who disagrees with scientific fact? Anonymous said... While there are challenges to the inflation model, a lot of the top cosmologists still hold to it, as a recent response to an article in Scientific American shows. Pix you have thee problems you have not answered, (1) you cant show why inflation beats fine tuning (2)Steionhardt is one of the primary authors of the theory (3) the basis of his rejection prove fine tuning works because they used fine tuning to secure inflationary theory If you have a better model, present it. I am not afraid to address them because the same argument will apply. If you have an infinite number of attempts, even the most improbably event becomes a certainty. px why didn't you watch the you tube video I linked to? that gives you Ree model im-skeptical said… some physics who disagree you can show none who agree,if it was proven they could not disagree, who disagrees with scientific fact? - This is where the real difference between science and faith becomes so apparent. With faith-based belief, all you have to do is find someone whose opinion you agree with, and then you have all the basis you need for belief. It's true just because some philosopher says so, and you agree with what he says. Evidence be damned. This explains why you think all you have to do is find some article on google that agrees (or seems to agree) with you, and you can then act like your ideas are not subject to dispute. But science doesn't work like that. There are different theories, and which of those we should accept is not simply a matter of opinion. The minute someone produces empirical evidence that disconfirms a theory, then we abandon or change the theory. It is not determined by faith, but by evidence. Is inflation theory a matter of faith for me (as you so often claim that my science-based beliefs are just misplaced faith)? No. I don't stake my life on any one theory, and if a better one comes along, that's fine with me. You said earlier that big bang is included in inflation theory, just to show that I didn't know what I was talking about. But you are wrong. True, there is still a period of expansion of matter from a tiny initia condition (and this actually follows the inflation period), but the theory itself is very different. For example, big bang entails a singularity, and inflation doesn't. The only people who still believe in a singularity are theists, as far as I know. Why do they cling to that? Theists latched onto big bang theory from the outset, because it seems to agree with their opinion that God created the universe. For them, it is a matter of faith. And that implies that people like you will be resistant to the inevitable advancements of science that might supersede it. And make no mistake, there are theists in the scientific community, whose work is influenced by their religious faith. In the long run evidence, not faith, will determine who is right. Anonymous said… JH: you have thee problems you have not answered, (1) you cant show why inflation beats fine tuning Infinity beats fine-tuning. JH: (2)Steionhardt is one of the primary authors of the theory You think he and his two fellow authors areright, and the thirty three top cosmologists who disagree are wrong because..? ... He agrees with the conclusion you want to arrive at. JH: px why didn't you watch the you tube video I linked to? that gives you Ree model Rees is talking about a single attempt, a single play of the game. He does not consider infinite plays of the game, infinite universes in a multiverse. Again and again you fail to address the issue of infinity - or indeed give any indication you have a clue about it at all. Pix - This is where the real difference between science and faith becomes so apparent. With faith-based belief, all you have to do is find someone whose opinion you agree with, and then you have all the basis you need for belief. No it's not, this is the difference in being ignorant and arrogant and obligated. You know jack shit about theology you have no training you think stuff about it that's real self serving, because your atheist brain washers tell you to think it. But you have no idea what you are talking aout, It's true just because some philosopher says so, and you agree with what he says. you are indulging in nightly inflammatory insulting attacks on personality and not reasoning about the argument, you really can't handle argument. Evidence be damned. This explains why you think all you have to do is find some article on google that agrees (or seems to agree) with you, and you can then act like your ideas are not subject to dispute. it' called documentation .ie Trump you can't stand a free exchange of ideas. you have to be right regardless of the facts. You can't stand it when I prove you wrong. I use expert opinion in published sources available to all and you are whining about it because you can't research, But science doesn't work like that. There are different theories, and which of those we should accept is not simply a matter of opinion. argument does work like that,I quoted three major scientists you don't have the gumption to quote one,so you are whining. The minute someone produces empirical evidence that disconfirms a theory, then we abandon or change the theory. It is not determined by faith, but by evidence. Is inflation theory a matter of faith for me (as you so often claim that my science-based beliefs are just misplaced faith)? No. I don't stake my life on any one theory, and if a better one comes along, that's fine with me. you have no evidence that Hawking's theory is accepted, it not a proven fact it just theory,it has not won major support, Skep You said earlier that big bang is included in inflation theory, just to show that I didn't know what I was talking about. But you are wrong. True, there is still a period of expansion of matter from a tiny initia condition (and this actually follows the inflation period), but the theory itself is very different. For example, big bang entails a singularity, and inflation doesn't. The only people who still believe in a singularity are theists, as far as I know. wrong, you are trying to meld inflation with Hawking-Hurtle, some inflationary models have no boundary condition not all, Why do they cling to that? Theists latched onto big bang theory from the outset, because it seems to agree with their opinion that God created the universe. For them, it is a matter of faith. And that implies that people like you will be resistant to the inevitable advancements of science that might supersede it. And make no mistake, there are theists in the scientific community, whose work is influenced by their religious faith. In the long run evidence, not faith, will determine who is right. that' really a stupid move trying to impose your own assumptions upon the other side then argue with that that is really a straw man argument, (1) It doesn't make any kind of difference if that is the reason why they like it. That has nothing to do with what models are used. (2) I've seen creationists who think the big bang theory opposed to creation for that reason oppose it, Its stupid but true, (3) You just proved my point about how physicists change theory to get rid of God arguments, 11/13/2017 10:17:00 AM Delete Anonymous said... JH: you have thee problems you have not answered, (1) you cant show why inflation beats fine tuning Infinity beats fine-tuning. why? assertion is not proof JH: (2)Steionhardt is one of the primary authors of the theory You think he and his two fellow authors areright, and the thirty three top cosmologists who disagree are wrong because..? the three inventor of the theory are above those 33 they are the students these are the teachers, there's only one royal astronomer, ... He agrees with the conclusion you want to arrive at. JH: px why didn't you watch the you tube video I linked to? that gives you Ree model Rees is talking about a single attempt, a single play of the game. He does not consider infinite plays of the game, infinite universes in a multiverse. you have not made it clear that you are talking about multiverse or just infinite space, he i assuming infinite chances, these FT gautlet would apply anytime, all other univeres would require FT, I have at lest 10 arguments on mutiverse Again and again you fail to address the issue of infinity - or indeed give any indication you have a clue about it at all. Anonymous said… Pix: Infinity beats fine-tuning. JH: why? assertion is not proof I already said why. See my post on 11/07/2017 12:42:00 AM. Or from 11/07/2017 12:48:00 AM. Or 11/08/2017 01:28:00 AM. Or 11/08/2017 08:11:00 AM. In fact virtually all my posts... Which I suppose goes to show that either you did not read them or did not understand them. JH: the three inventor of the theory are above those 33 they are the students these are the teachers, there's only one royal astronomer, So you are calling Linde, Guth, Hawking, Rees and Vilenkin the students (two of whom you have cited already in defence of your claims), and Ijjas, Steinhardt and Loeb the teachers? What is your basis for considering those three to be better authorities? Other then they happen to agree with your preconceived ideas... JH: you have not made it clear that you are talking about multiverse or just infinite space, he i assuming infinite chances, these FT gautlet would apply anytime, all other universe would require FT, I have at lest 10 arguments on mutiverse It is not clear if you are talking about the fundamental laws and constants of the universe or the improbability of life. The multiverse covers the first, the infinite universe the second. Either way the game has an infinite number of plays, and so even the most improbable event is certain to happen. JH: I just answered it again, you have never answered that argument, Reinforcing my view that either you did not read them or did not understand them. Pix Anonymous said… JH: Unless we know the rate at which life bearing is produced, just having a bunch of universes proves nothing. This applies both to parallel universes and to planets of our own universe. Again the demand for proof. How often do you demand your opponents give proof, whilst your own theory offers only hints and suggestions and maybes? If we have infinite universes we do not need to know the rate they are produced at. We just need to know the probability is greater than zero. In fact, it is the fine-tuning argument fort God that has top know the hit rate. If the hit rate is 22%, then it fails. JH: One might be tempted to think that doesn't matter because the statistics indicate there must be lots of life bearing planets out there. Yet the important point is the atheists are the one's saying don't believe without empirical proof. They will challenge the believer to show "just one" fact supporting God. Yet they believe this with no empirical proof Again the demand for proof! In reality atheists demand empirical evidence, and accept these things cannot be proven. The multiverse is a possible solution to the fine-tuning problem, just as God is a possible solution. Neither are proven. JH: Futhermore, the best mechanism for multiverses that last, actually requires fine-tuning itself. The chaotic inflationary model - which seeks to avoid fine-tuning by positing that the initial conditions vary at random over the superspace of the Higgs fields - also fine-tunes its parameters, as Earman has pointed out: "The inflationary model can succeed only by fine-tuning its parameters, and even then, relative to some natural measures on initial conditions, it may also have to fine-tune its initial conditions for inflation to work." Some inflation models indicate eternal inflation, and they imply that within the universe there are regions that are not expanding such as the region where we live. This then is one particular multiverse model, and it is this that Steinhardt disagrees with (and those thirty three lesser cosmologists like Linde, Guth, Hawking, Rees and Vilenkin accept, but hey, what do those idiots know, right?). Another multiverse model is where there are entirely separate universes spawning with different initial conditions. This is the model that explains fine-tuning. By the way, there are ideas as to how inflation might solve fine-tuning without the multiverse: "One of the most severe challenges for inflation arises from the need for fine tuning. In new inflation, the slow-roll conditions must be satisfied for inflation to occur. The slow-roll conditions say that the inflaton potential must be flat (compared to the large vacuum energy) and that the inflaton particles must have a small mass.[clarification needed][93] New inflation requires the Universe to have a scalar field with an especially flat potential and special initial conditions. However, explanations for these fine-tunings have been proposed. For example, classically scale invariant field theories, where scale invariance is broken by quantum effects, provide an explanation of the flatness of inflationary potentials, as long as the theory can be studied through perturbation theory." Pix Anonymous said… JH: The whole issue of the objection to the multiverse is nothing but an inverse of the gambler's fallacy: " Some people think that if you roll the dice repeatedly and don't get double sixes, then you are more likely to get double sixes on the next roll. They are victims of the notorious gambler's fallacy. In a 1987 article in Mind, the philosopher Ian Hacking sees a kindred bit of illogic behind the Many Universes Hypothesis. Suppose you enter a room and see a guy roll a pair of dice. They come up double sixes. You think, "Aha, that is very unlikely on a single roll, so he must have rolled the dice many times before I walked into the room." You have committed what Hacking labels the inverse gambler's fallacy." Compare to the theist who walks into the room to see the guy roll two sixes. "Aha, that is very unlikely on a single roll, so God must have done it." Which is the fallacy? Which is more analogous to our discussion? JH: Plantinga puts it as follows: "Well, perhaps all this is logically possible (and then again perhaps not). As a response to a probabilistic argument, however, it's pretty anemic. How would this kind of reply play in Tombstone, or Dodge City? "Waal, shore, Tex, I know it's a leetle mite suspicious that every time I deal I git four aces and a wild card, but have you considered the following? Possibly there is an infinite succession of universes, so that for any possible distribution of possible poker hands, there is a universe in which that possibility is realized; we just happen to find ourselves in one where someone like me always deals himself only aces and wild cards without ever cheating. So put up that shootin' arn and set down 'n shet yore yap, ya dumb galoot." Again, we can compare to the theist, who claims God dealt him that unlikely hand. JH: The multiverse is a desperate catch-all explanation that could explain away any evidence for anything by simply inflating the probabilistic resources to infinity, and it is also the most flagrant violation of Occam's razor ever. Occam really said "do not multiply entities beyond necessity," yet the Multiversers are doing just that merely for the purpose of answering this argument. Compare to the theist, who is invoking a supernatural entity. Hmm, we better reject that as fast as possible, right? JH: Arbitrary necessities are illogical. That is one a contingency is put over as a necessity. That is what is being done with the multiverse, they are pretending that this whole mutliverse needs no explanation, it's just bound to happen, it's necessary. But it's really just magnifying a string of endless contingencies into a giant arbitrary necessity. So that would be like God then? An entity that is just bound to happen, is necessary? JH: At this point we can bring in Platinga's Possible words argument. Is it possible that in one of those other universes there would be a God like the one Anselm speaks of? The answer as to be "yes." If not the atheist must show why not. ... And yet it is absurd to think that a necessary being would be limited to just one reality. God has to be God in all reality. Great shifting of the burden of proof there. Is God possible? Well... There is no sign of God in this universe Therefore it is not unreasonable to conclude God is not present in this universe. If God exists in one universe he must be present in them all. Therefore God does not exist in any universe. Therefore the existence of God is an impossibility! Pix im-skeptical said… You know jack shit about theology you have no training you think stuff about it that's real self serving, because your atheist brain washers tell you to think it. But you have no idea what you are talking aout - Now, there's the difference between you and me. I don't claim to be an expert in theology, and I don't try to tell you what theologists' theories are, that way you try to tell be about science. All I can say about religion is what I learned growing up as a Catholic, and what is obvious to any observer. it' called documentation .ie Trump you can't stand a free exchange of ideas. - It is a free exchange of ideas. Too bad you only listen to one side, and automatically reject those that you don't like, Trump. argument does work like that,I quoted three major scientists you don't have the gumption to quote one,so you are whining. - There is a place for argumentation is science, but when it comes down to evidence, the argument is settled. This is unlike your theistic arguments that don't depend on evidence, and will never be settled you have no evidence that Hawking's theory is accepted, it not a proven fact it just theory,it has not won major support - There you go with your "proof" again. How many times do I have to tell you that theories are never proven absolutely. We accept the ones that work the best. Cosmological theory isn't settled like Darwinian evolution, but big bang theory has definitely fallen in favor of some variant of inflation - and no-boundary seems to be the most widely accepted at this point. wrong, you are trying to meld inflation with Hawking-Hurtle, some inflationary models have no boundary condition not all - OK, now I get it. Here's a clue for you: Hawking-Hartle no-boundary theory IS inflation, but you would only know that if you some faint idea of what you were talking about. (1) It doesn't make any kind of difference if that is the reason why they like it. That has nothing to do with what models are used. - It makes all the difference. That's why science works as a means of knowing things, and faith doesn't. (2) I've seen creationists who think the big bang theory opposed to creation for that reason oppose it, Its stupid but true - That's my point. On faith, you can believe whatever you want. It isn't based on evidence. (3) You just proved my point about how physicists change theory to get rid of God arguments - You can believe whatever you want. It isn't based on evidence. And it isn't true. im-skeptical said… It is not clear if you are talking about the fundamental laws and constants of the universe or the improbability of life. The multiverse covers the first, the infinite universe the second. Either way the game has an infinite number of plays, and so even the most improbable event is certain to happen. - I mentioned that Joe has two completely different issues mixed up in his mind. When he talks about Steinhardt's use of the term "fine-tuning", he thinks it is the supposed fine tuning of physical constants that leads to the conditions needed to form life in the universe. I tried to explain to him that this is not the same thing. It is actually the setting of starting conditions for cosmic expansion that would lead to a flat space-time. Totally separate issue, but Joe doesn't grok that. He thinks inflation theory is about the need to have a multiverse in order to bypass the fine-tuning of physical constants. Joe doesn't grok the fact that inflation solves the problem of starting conditions, even it there is just one universe, and THAT's why it is favored - not because scientists are trying to get rid of God. Joe also doesn't grok that a multiverse just happens to be a predicted consequence of the very same quantum theory that is the source of cosmic inflation. You can see this confusion in his linked article "My answers on Multiverse". He just doesn't get what the real discussion is about (at least in scientific circles). im-skeptical said... PX?:It is not clear if you are talking about the fundamental laws and constants of the universe or the improbability of life. The multiverse covers the first, the infinite universe the second. Either way the game has an infinite number of plays, and so even the most improbable event is certain to happen. skep- I mentioned that Joe has two completely different issues mixed up in his mind. When he talks about Steinhardt's use of the term "fine-tuning", he thinks it is the supposed fine tuning of physical constants that leads to the conditions needed to form life in the universe. I tried to explain to him that this is not the same thing. It is actually the setting of starting conditions for cosmic expansion that would lead to a flat space-time. I already apprised you of your error on that are you are to arrogant to listen. You are totally confused about what I said.you brought inflatiomn imto the anthropic arguent, youthojghtit wasansweringit,Iwas ayingwhy inflatioanry gtheory doen;t haveiktshit together yet. But aithappens fine tuningisa genrealapproach thkatworksinanynuer ofwayswith edifferentiues, "In theoretical physics, fine-tuning is the process in which parameters of a model must be adjusted very precisely in order to agree with certain observations...Theories requiring fine-tuning are regarded as problematic in the absence of a known mechanism to explain why the parameters happen to have precisely the observed values that they return. The heuristic rule that parameters in a fundamental physical theory should not be too fine-tuned is called naturalness." (from Wili https://en.wikipedia.org/wiki/Fine-tuning they cite Grinbaum, Alexei (1 February 2012). "Which Fine-Tuning Arguments Are Fine?". Foundations of Physics. 42 (5): 615–631. Bibcode:2012FoPh...42..615G. arXiv:0903.4055 Freely accessible. doi:10.1007/s10701-012-9629-9. Totally separate issue, but Joe doesn't grok that. He thinks inflation theory is about the need to have a multiverse in order to byp I know what it is I've reached it and written on it. you are so imperceptive you can't figure out that when Stienhardt quiets the project because they used fine tuning to get rid of fine tuning he knows what it means even if I don't so it still means they are contradicting themselves. you are so imperceptive, so you not a thinker, Joe doesn't grok the fact that inflation solves the problem of starting conditions, even it there is just one universe, and THAT's why it is favored - not because scientists are trying to get rid of God. Joe also doesn't grok that a multiverse just happens to be a predicted consequence of the very same quantum theory that is the source of cosmic inflation. You can see this confusion in his linked article "My answers on Multiverse". He just doesn't get what the real discussion is about (at least in scientific circles). this pretentious little shallow non thinker loves to assign assign motives to people because he can't cut it on an intellectual level, 11/14/2017 08:37:00 AM Delete JH: I just answered it again, you have never answered that argument, Reinforcing my view that either you did not read them or did not understand them. you never made an answer. Your argument never get around the fact that expanding the number just means you get ore fine tuning to deal with, so you can't get out of the original problem, every time you expand the needs for fine tuning do as well and the odds against life life jut go up more Anonymous Anonymous said... JH: Unless we know the rate at which life bearing is produced, just having a bunch of universes proves nothing. This applies both to parallel universes and to planets of our own universe. Again the demand for proof. How often do you demand your opponents give proof, whilst your own theory offers only hints and suggestions and maybes? that is bull hit, you are playing a game, the fact of it is many people have made explicit models, Rees has gone deep into the math and so have all the others,Collins, de young, Linde, Davies. Those don't go away just because I'm not posting their very words, If we have infinite universes we do not need to know the rate they are produced at. We just need to know the probability is greater than zero. that i BS. look at the planets in our solar systems, one ha life,only one has life,most planets don't have life, you re also missing the argent I'm made that you don't have infatuate chances. You can't prove there;s a multiverse,.If there are antenatal universes you can't prove they are infinte, In fact, it is the fine-tuning argument fort God that has top know the hit rate. If the hit rate is 22%, then it fails. I don't understand that sentence it is strangely garbled. It is absurd to put that on the FTA because we've already proven that just hitting the constants in the fomentation that would allow life is so vastly agaist the odds it's ridiculous not to believe in God, im-skeptical said… This comment has been removed by the author. im-skeptical said… I already apprised you of your error on that are you are to arrogant to listen. You are totally confused about what I said.you brought inflatiomn imto the anthropic arguent ... - No, Joe. You brought it in. Let's look at what YOU said in your article: Answer I. Have to know hit rate for life bearing universes. Answer II.We can never know if other universes exist or not. III. Multiverse Requires Fine Tunning And this is the point where YOU introduce Steinhardt's objection to INFALTION theory. But this has NOTHING to do with that topic that you have been discussing all along. You don't understand what he's talking about. In fact you even quoted him later in the same article saying what the real problem is: Inflation was introduced to produce a universe that looks smooth and flat everywhere. Those are Steinhardt's words, but you ignore them, because you don't even know what he's saying. After all this discussion,you still don't. IM: He thinks inflation theory is about the need to have a multiverse in order to byp... JH: I know what it is I've reached it and written on it. you are so imperceptive you can't figure out that when Stienhardt quiets the project because they used fine tuning to get rid of fine tuning he knows what it means even if I don't so it still means they are contradicting themselves. - Yes, you've written about it. And what you wrote is WRONG, because you don't understand what Steinhardt said. Read the second quote you provided from Steinhardt. His objection was not to the fine tuning that is the subject of your article. It has nothing to do with that. It is about the flatness problem - a completely different issue. It is the fact that the original big bang theory DOESN"T WORK. That's the reason for inflation theory. He said that himself. Read his words again. JH: At this point we can bring in Platinga's Possible words argument. Is it possible that in one of those other universes there would be a God like the one Anselm speaks of? The answer as to be "yes." If not the atheist must show why not. ... And yet it is absurd to think that a necessary being would be limited to just one reality. God has to be God in all reality. Great shifting of the burden of proof there. Is God possible? Well... you have not dealt with the logic of the shift, you are so used to your atheist masters telling you that the theists have the burden of proof You never bothered to question it did you? One only has a burden to prove what one sets out to prove. I only set out to prove that I have a good reason to believe and I did that, There is no sign of God in this universe *Mystical experience and it effect * the way religious experiencing fit the criteria of epistemic judgement *the universality argent on mystical experience *the overweening odds again life bearing universe *Lourdes miracles *feeling of utterdepnedence *modal argument I have 52 of them Therefore it is not unreasonable to conclude God is not present in this universe. when you see the power of God in your life and you know Jesus is real the it;s absurdly stupid to deny it. For those who have not see that I understand and why it see reasonable to deny it but there's so much there it's clear your attitude that keep from seeing, If God exists in one universe he must be present in them all. Therefore God does not exist in any universe. Therefore the existence of God is an impossibility! you have no evidence that he does';t exit here, when you are given evidence that he does you fight like hell to ignore it to the point refusing to even think about it, im-skeptical said… when you see the power of God in your life and you know Jesus is real the it;s absurdly stupid to deny it. For those who have not see that I understand and why it see reasonable to deny it but there's so much there it's clear your attitude that keep from seeing - There's an easy solution to this problem, Joe. Get over you attitude, and then maybe you'll be able to see things more clearly. Anonymous said… JH: you never made an answer. Your argument never get around the fact that expanding the number just means you get ore fine tuning to deal with, so you can't get out of the original problem, every time you expand the needs for fine tuning do as well and the odds against life life jut go up more This is exactly wrong. Think about it, Joe. If you have one chance to roll double six, what is the probability? Now suppose you get to try ten times... Do you think it is more or less likely you will get a double six at least one time. Hopefully, you will realise that the more times you throw the dice, the more likely you are to get double six at some point. It is just like that. im-skeptical said… Joe's "IV. Multivrese is Inverse of Gambler's fallacy" (from his linked article is an example of projecting stupidity on his opponents, as well as a fundamental misunderstanding of their argument. im-skeptical said... Joe's "IV. Multivrese is Inverse of Gambler's fallacy" (from his linked article is an example of projecting stupidity on his opponents, as well as a fundamental misunderstanding of their argument. 11/15/2017 07:36:00 AM Delete show where I misunderstood an argument? but don't shift your positon to pretend thkat i did. Anonymous said... JH: you never made an answer. Your argument never get around the fact that expanding the number just means you get ore fine tuning to deal with, so you can't get out of the original problem, every time you expand the needs for fine tuning do as well and the odds against life life jut go up more This is exactly wrong. Think about it, Joe. If you have one chance to roll double six, what is the probability? Now suppose you get to try ten times... Do you think it is more or less likely you will get a double six at least one time. that does not help you because the odds are agaisnt you, normally if you get more tries it woudl go down but at the same time the task is made more difficult so it doen;t decrease the improbably, Hopefully, you will realist that the more times you throw the dice, the more likely you are to get double six at some point. I know that,I never denied that, you do not understand the reliance of my game to the issues. in the game I describe the subsequent tries are handicapper by the same limitations cropping up again so the odds don't change, It is just like that. no your analogousness wrong, it;not just a simple roll there; a gauntlet of difficulties that are there for every through, even if infinite chances eventually reveal life that;not enough to satisfy me. I'm basing my life on the chance that I could win the lottery,and in a world where mystical experience is good for you and changes your life dramatically for the odds of life bearing universe to be so improbable means good reason to think the game is fixed. im-skeptical said… show where I misunderstood an argument? but don't shift your positon to pretend thkat i did. - Nobody but an idiot thinks that the odds improve for any individual outcome if you try again. The argument is that if there are more tries, the odds are improved that one of them will be successful. But this is not the way you presented it. - Nobody but an idiot thinks that the odds improve for any individual outcome if you try again. The argument is that if there are more tries, the odds are improved that one of them will be successful. But this is not the way you presented it yes it is. No one think otherwise only you are looking for an excuse to criticize, Anonymous said… JH: that does not help you because the odds are agaisnt you, normally if you get more tries it woudl go down but at the same time the task is made more difficult so it doen;t decrease the improbably, That depends on how many tries and what the probability of each try is. Here is this maths. Say that success has a probability of p for one try. The probability of failure for one try is therefore: 1 - p The probability of failure for every try in n turns is: (1 - p)^n And then the probability of at least 1 success in n turns is: 1 - (1 - p)^n We can just plug the numbers in. I am suggesting an infinite number of tries (n = infinity). What probability do you propose? Give a figure, and we can do a calculation. By the way, whatever value of p where p is greater than zero will give a result of 1, so do not worry too much about what it actually is. Pix im-skeptical said… IM: The argument is that if there are more tries, the odds are improved that one of them will be successful. But this is not the way you presented it. JH: yes it is. No one think otherwise only you are looking for an excuse to criticize - These are your own words. "Some people think that if you roll the dice repeatedly and don't get double sixes, then you are more likely to get double sixes on the next roll. They are victims of the notorious gambler's fallacy." So now the question arises: do you even understand what YOU have written? Pix has been trying to explain simple probability to you, and you don't seem to get it. I think this demonstrates my assertion that you are projecting stupidity. BK said… The problem is that Pix is wrong from the outset. He starts in the very first comment with "Given an infinite universe, such as the one we live in, even the extremely unlikely is certain to happen." No, we don't live in an actual infinite universe either in terms of size or time. We live in a universe of finite size which has been around for a finite number of years. So, all of the talk thereafter that supposes that we live in an infinite universe and that there is both time and space for anything to happen is simply false. im-skeptical said… I'm sure that he means the greater reality that spawns multiple universes. It is clear from his discussion that he's talking about multiple or an infinite number of universes. There is confusion in the term 'universe' because it is used to mean different things, including that greater reality. I think it would be better to use a word like 'superverse' to refer to whatever it is that is the progenitor of our universe (and possibly others as well). JH: that does not help you because the odds are agaisnt you, normally if you get more tries it woudl go down but at the same time the task is made more difficult so it doen;t decrease the improbably, Px That depends on how many tries and what the probability of each try is. Here is this maths. Say that success has a probability of p for one try. The probability of failure for one try is therefore: you are till not doing the real math, you are pinning this off of my little example not the real data supplied by Linde Ree Davies and people like that, you have not answered my argument about why you don't get initiate chances. H: yes it is. No one think otherwise only you are looking for an excuse to criticize - These are your own words. "Some people think that if you roll the dice repeatedly and don't get double sixes, then you are more likely to get double sixes on the next roll. They are victims of the notorious gambler's fallacy." So now the question arises: do you even understand what YOU have written? Pix has been trying to explain simple probability to you, and you don't seem to get it. I think this demonstrates my assertion that you are projecting stupidity. you clearly don't get what is being said here, there is now ayany of ny argument could be construed to mean that I think the odds go up odds go up [the more you miss because its "time for it," That's the gambler's fallacy nothing I have said can be taken that way. That statement was taken from a section on y site where I explain the gambler's fallacy. some Atheists used to argue the gambler' fallacy because they didn't understand fine tuning, m-skeptical said... I'm sure that he means the greater reality that spawns multiple universes. It is clear from his discussion that he's talking about multiple or an infinite number of universes. There is confusion in the term 'universe' because it is used to mean different things, including that greater reality. I think it would be better to use a word like 'superverse' to refer to whatever it is that is the progenitor of our universe (and possibly others as well). I have already answered it, there is no empirical evidence for a multi veer,even if there was you can;t prove it's infinite and you can't prove the hit rate for life bearing universes, you are contradicting your claim to being priciest, you have no evidence of an empirical nature against belief in God yet you want people to think you do, Anonymous said… BK: The problem is that Pix is wrong from the outset. He starts in the very first comment with "Given an infinite universe, such as the one we live in, even the extremely unlikely is certain to happen." No, we don't live in an actual infinite universe either in terms of size or time. We live in a universe of finite size which has been around for a finite number of years. So, all of the talk thereafter that supposes that we live in an infinite universe and that there is both time and space for anything to happen is simply false. Just to be clear, I meant specifically infinite in space, not time. So tell me, BK, what is you reason for thinking our universe is finite? I am sure NASA would love to know, as they seem unsure: https://www.nasa.gov/audience/foreducators/5-8/features/F_How_Big_is_Our_Universe.html By the way, I do not need the universe to be infinite, I only need it to be possibly infinite to destroy Joe's argument. Fine-tuning does not prove God if there are other possibilities, and an infinite universe is definitely a possibility. Even if the universe is finite, it could still be big enough to give sufficient "throws of the dice", depending on what the probabilities are - and no one knows what those probabilities are. Furthermore, our universe could be one of an infinite number of universes. Anonymous said… JH: you are till not doing the real math, you are pinning this off of my little example not the real data supplied by Linde Ree Davies and people like that, you have not answered my argument about why you don't get initiate chances. Wrong. That was the real maths. It is the same whether we are talking about throwing two sixes or creating a universe "fine-tuned" for life. The only difference is the value of p. Ironic that this post follows directly from one bemoaning the demise of expertise on the internet. You are doing exactly what JPH was complaining about! Pix So tell me, BK, what is you reason for thinking our universe is finite? I am sure NASA would love to know, as they seem unsure: https://www.nasa.gov/audience/foreducators/5-8/features/F_How_Big_is_Our_Universe.html By the way, I do not need the universe to be infinite, I only need it to be possibly infinite to destroy Joe's argument. Fine-tuning does not prove God if there are other possibilities, and an infinite universe is definitely a possibility. good old Px and his usual unaware self. what did I say about proving the existence of God? show me where I said I'm doing that? the mere possibility of infinite chance is not an argument. I can always suggest the possibility that I'm right, Even if the universe is finite, it could still be big enough to give sufficient "throws of the dice", depending on what the probabilities are - and no one knows what those probabilities are. you keep forgetting what we are arguing about, every new universe has to be fine tinned for bearing life,each new unwiser repeats the same odds. try to liten this tine, Anonymous said… JH: good old Px and his usual unaware self. what did I say about proving the existence of God? show me where I said I'm doing that? the mere possibility of infinite chance is not an argument. I can always suggest the possibility that I'm right, So when you said the following, you were not suggesting "the game is fixed" by an intelligent agent, i.e., God? The argument says simply that the universe must be structured in very exact ways to produce life. It's so exacting as to be totally improbable. Because it's so improbable that gives us a good reason to think the game is fixed. JH: you keep forgetting what we are arguing about, every new universe has to be fine tinned for bearing life,each new unwiser repeats the same odds. Wow, you really have missed the point. Universes spawn randomly. Each universe is different. Some just happen to have the conditions for life, but most do not. If the probability for life-bearing in 1 in a million, then one millionth of the universes will be life-bearing. We necessarily will find ourselves in a life-bearing universe. No fine-tuning, Joe. im-skeptical said… there is now ayany of ny argument could be construed to mean that I think the odds go up odds go up ... some Atheists used to argue the gambler' fallacy because they didn't understand fine tuning - The problem is that you have a real reading comprehension issue. I didn't say that's what you believe. I said you are claiming that's what atheists believe, because you doesn't understand what atheists argue. And you just proved it again. you keep forgetting what we are arguing about, every new universe has to be fine tinned for bearing life,each new unwiser repeats the same odds. ... try to liten this tine, - You don't understand the argument, Joe. Only ONE universe has to support life. NOBODY ever said all universes in a multiverse must be capable of supporting life. That's the stupidest thing I ever heard.

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https://proofwiki.org/wiki/Group_of_Order_15_is_Cyclic_Group/Proof_3

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Group of Order 15 is Cyclic Group/Proof 3 Theorem Let $G$ be a group whose order is $15$. Then $G$ is cyclic. Proof Aiming for a contradiction, suppose $G$ is non-abelian. Let $n_3$ denote the number of elements of $G$ of order $3$. From Number of Elements of Order p in Group of Order pq is Multiple of q, $n_3$ is a multiple of $5$. From Number of Order p Elements in Group with m Order p Subgroups, $n_3$ is a multiple of $2$. Therefore $n_3$ is a multiple of $10$. Let $n_5$ denote the number of elements of $G$ of order $5$. From Number of Elements of Order p in Group of Order pq is Multiple of q, $n_5$ is a multiple of $3$. From Number of Order p Elements in Group with m Order p Subgroups, $n_5$ is a multiple of $4$. Therefore $n_5$ is a multiple of $12$. Together with the identity element which has order $1$, that makes $1 + 12 a + 10 b = 15$ for some positive integers $a$ and $b$. This is impossible. Hence by Proof by Contradiction it follows that $G$ must be abelian. Since $15$ is a product of $2$ distinct primes, by Abelian Group of Semiprime Order is Cyclic, $G$ is cyclic. $\blacksquare$

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# Disco On the disco goes 12 boys and 15 girls. In how many ways can we select four dancing couples? Correct result: n =  16216200 #### Solution: We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you! Tips to related online calculators Would you like to compute count of combinations? ## Next similar math problems: • Competition 15 boys and 10 girls are in the class. On school competition of them is selected 6-member team composed of 4 boys and 2 girls. How many ways can we select students? There are 15 boys and 12 girls at the graduation party. Determine how many four couples can be selected. • Class pairs In a class of 34 students, including 14 boys and 20 girls. How many couples (heterosexual, boy-girl) we can create? By what formula? • Classroom Of the 26 pupils in the classroom, 12 boys and 14 girls, four representatives are picked to the odds of being: a) all the girls b) three girls and one boy c) there will be at least two boys On the menu are 12 kinds of meal. How many ways can we choose four different meals into the daily menu? • Boys and girls There are eight boys and nine girls in the class. There were six children on the trip from this class. What is the probability that left a) only boys b) just two boys • School parliament There are 18 boys and 14 girls in the class. In how many ways can 3 representatives be elected to the school parliament, if these are to be: a) the boys themselves b) one boy and two girls • Two groups The group of 10 girls should be divided into two groups with at least 4 girls in each group. How many ways can this be done? • Boys and girls There are 20 boys and 10 girls in the class. How many different dance pairs can we make of them? • Four-member team There are 14 girls and 11 boys in the class. How many ways can a four-member team be chosen so that there are exactly two boys in it?

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# Day: September 21, 2018 ## Logarithm Formula, Inequalities, Indices and Surds Logarithm Formula, Inequalities, Indices and Surds. UPDATED LINKGo to above linked new page to downloadExamples, Theory and Formulas, Practice Problems and worksheets of all topics of Mathematics.Introduction to logarithm “The Logarithm of a given number to a given base is the index of the power to which the base must be raised in order to equal the … ## Set Theory and Relations Set Theory and Relations Set Theory A set is well defined class or collection of objects. A set is often described in the following two ways. (1) Roster method or Listing method : In this method a set is described by listing elements, separated by commas, within braces {}. The set of vowels of English … ## Characteristics of Monera Characteristics of Monera Monera (Monos – single) includes prokaryotes and shows the following characters : (1) They are typically unicellular organisms (but one group is mycelial). (2) The genetic material is naked circular DNA, not enclose by nuclear envelope. (3) Ribosomes and simple chromatophores are the only subcellular organelles in the cytoplasm. The ribosomes are … ## Living World Nature and Scope of Biology Living World, Nature and Scope of Biology Science : The term science is derived from Latin word scientia which means knowledge. So, the term ‘science’ is used for knowledge gained by actual observation, found correct on verification and put in a systematic manner or science provides us information based on facts. There are several branches …

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http://math.stackexchange.com/questions/109648/if-a-b-and-c-are-both-positive-semi-definite-is-aca-bcb-also-positive-sem

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# If $A-B$ and $C$ are both positive semi-definite, is $ACA-BCB$ also positive semi-definite? If $A-B$ and $C$ are both positive semi-definite, is $ACA-BCB$ also positive semi-definite? Welcome proof, reference, or counter example. No, it's not even true for scalars (aka 1×1 matrices). Take: $$A=0,B=−1,C=1$$ Then $A−B=1$ is positive semi-definite (even positive definite), so is C, but $ACA−BCB=−1$ is not. It extends in every dimension by setting eg. $A = 0, B = - I_n, C = I_n$.

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https://theflyinginn.com/is-16-oz-sour-cream-2-cups

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# Is 16 oz sour cream 2 cups? The cup should have 8 oz and the pound 16 oz. So it would take 2 cups weighed at 8 oz to be 1 lb. The official answer I found on the internet says that it is a little more than 1/2 lb per cup. ## How much cups are in a pound? 16 ounces equals one pound or two cups. This may interest you : Is 30 days a full month? Another way to look at the equivalent is that one cup weighs eight ounces and therefore two cups are equal to 16 ounces, and this is the same weight of one pound – 16 ounces. How many dry cups are there in a pound? Also to discover ## Is 16 oz same as 2 cups? 16 oz = 2 cups You may also be interested in 1 oz 1/8 cups. On the same subject : How much weight can you lose in a month. So you can divide 16 by 8 to get the same answer. How many cups is 16? There are 2 cups in a 16 ounce bag. How many cups are in a 16 oz container? 1 cup is 8 ounces. So there are 2 cups in 16 ounces. Also to discover ## Is 16 oz a pint of sour cream? There are 16 ounces of American sour cream in a pint of American sour cream. On the same subject : Can you make oobleck at home? The easiest way to find an approximate answer when converting pints to liquid ounces is to multiply the number of pints by 19,215. Is 16 oz a dry pint? Dry pint equals 18,618 or 18.62 ounces. With that in mind, here’s a more detailed conversion for ounces to dry pint: 1 oz = 0.05371 pt. Is 16 ounces equal to 1 pint? If we remember, 8 ounces = 1 cup, 2 cups = 1 pint (or 16 ounces = 1 pint). There are usually 2 cups in 1 pint, however, depending on the ingredient, this may change. Is 16 oz sour cream 2 cups? There are 1,875 cups in a bowl of 16 ounces of sour cream. For reference, there are about 15 servings in 16 oz. a bowl of sour cream. One serving is 2 tablespoons. ## How much is an ounce compared to a cup? 1 liquid ounce equals 0. Read also : How many mg in a gram.125004 cups, which is the conversion factor from ounces to cups. How do I measure 1 oz? To measure ounces, choose a liquid or dry measuring cup. If you are measuring liquid, place the measuring cup on a flat surface and pour the liquid into the glass. Be sure to bend over to see the dimensions on the side of the cup. Make sure the fluid reaches the correct measurement. ## Is 8 oz of sour cream the same as 1 cup? 1 cup = 8 fl. oz. Is 8 oz considered 1 cup? Liquid measuring cups show that 1 cup = 8 ounces. But what they actually mean is 1 cup of liquid = 8 liquid ounces. On the same subject : Is there a Friday the 13th movie in 2021? … If the recipe requires the amount of liquid in an ounce, you can measure it in a liquid measuring container. How is a cup of sour cream measured? Weighing sour cream and yoghurt Using a spoon, place the sour cream and yoghurt in a dry measuring cup, then flatten the top by spreading a metal spatula or flat side of a knife over the top of the cup. ## What is half a cup of sour cream? 125 ml is equivalent to 1/2 cup. On the same subject : How much does Cardi B get paid? What is a cup of sour cream? There are 1,875 cups in a bowl of 16 ounces of sour cream. … One cup is equal to 16 spoons. So, 30 tablespoons in 16 oz. a container divided by 16 spoons in one cup is 1,875 cups in 16 oz.

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West Asian Mathematics - History of Math Welcome to Quatr.us Study Guides! # West Asian Mathematics Sumerian multiplication table (2700 BC) April 2016 - Once people in West Asia figured out how to write down numbers, about 3500 BC, they quickly began to want to use cuneiform to write down other mathematical ideas. The earliest example of this that we have is from about 2700 BC. It shows a multiplication table to help people figure out the area of a space by multiplying width by length. The first column is the width, the second is the length, and the third column is the area. It uses a system for writing down large numbers in base 60 (the way our clocks work today). Math book (Babylon, about 2000 BC) This tablet, from about 2000 BC, was a school math book for teaching kids how to calculate inheritance. The problem asks how much each of seven boys would get when their father died, according to Babylonian law. Apparently the law said they should each get a different proportion, with the oldest getting the most and the younger kids less and less. Whoever did the math worked up from the bottom (which was not normal), and also made a mistake in his or her calculations! Here's a Babylonian math problem you could try to solve yourself. Are you as smart as Babylonian kids? By the time of the Babylonians, mathematicians were working out quadratic equations like the Pythagorean Theorem, computing square roots and cube roots, and the factors of sixty (because they often worked in base 60). After the Assyrians formed their empire, mathematical developments seem to have slowed down after this initial rush. But mathematicians continued to work on new ideas. Assyrian mathematicians, working around 1000 BC, first had the idea of dividing the circle into 360 degrees (still working in base 60, so 360=6x60). Thales, working under Lydian political control in Miletus (modern Turkey) in the 630s BC, found ways to calculate when there would be an eclipse of the sun or the moon. Thales also found a way to calculate the height of an Egyptian pyramid by measuring its shadow, and proved various geometrical theorems. Thales' student Anaximander, who was also from Miletus, worked on building a better sundial to measure time. During the Persian Empire, around 500 BC, people first began to use the abacus (nobody knows whether the abacus was invented in Iran or China, or both about the same time, thanks to the beginning of the Silk Road). An abacus is a way of calculating large numbers quickly by moving pebbles along grooves dug into dirt, or beads along wires. With the development of trade and more travel along the Silk Road between China, India, and West Asia, in the 300s BC, Greek mathematicians were able to talk to Persian and Indian mathematicians more easily than before. A lot of new ideas about infinity, patterns of numbers, and exponents came out of these conversations, but most importantly, from Egypt to India, all across West Asia, mathematicians began to work more on proving that theorems were always true in every case. About 150 BC, Hipparchus (born in Nicaea, now in Turkey) worked on developing trigonometry, making lists of sines and cosines. Under Parthian and Sassanian rule, scholars continued to bring together knowledge from the countries around them, especially from India. They built a system of math and astronomy based on their Zoroastrian faith, and, like Ptolemy in Egypt and Arya Bhata in India, used trigonometry to make better predictions of the movements of the planets. Then in the 600s AD, the Arabs conquered West Asia and established the Islamic Empire. Around the same time, Indian numbers revolutionized mathematics. You can read about that here. ## Learn by doing: an abacusA real Babylonian math problemMore about Islamic math Science in Ancient Mesopotamia, by Carol Moss (1999). Easy reading. On the short side. ## African MathematicsIndian MathematicsGreek mathematicsIslamic MathematicsMore West Asian ScienceAncient West AsiaQuatr.us home Karen Carr is Associate Professor Emerita, Department of History, Portland State University. She holds a doctorate in Classical Art and Archaeology from the University of Michigan. Follow her on Instagram, Pinterest, or Twitter, or buy her book, Vandals to Visigoths. Karen Carr is Associate Professor Emerita, Department of History, Portland State University. She holds a doctorate in Classical Art and Archaeology from the University of Michigan. Follow her on Instagram or Twitter, or buy her book, Vandals to Visigoths. Check out our new ebook: Short and Simple: Ancient Greek Myths! - just out! Twenty-five easy to read, illustrated stories, from Pandora to Medea, Icarus, and the Trojan Horse (you can read these online as samples). Get it this week for just \$14.99, five dollars off the regular price of \$19.99. • Author: K.E. Carr • Title: • Site Name: Quatr.us Study Guides • Publisher: Quatr.us • Date Published: Did you find what you needed? Ask your teacher to link to this page so other people can use it too! Send it in and win a Quatr.us "Great Page!" award!

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# math-- algebra posted by . If a pro basketball player has a vertical leap of about 25 inches, what is his hang time? Use the hang-time function V=48T^ I am having major problems here!!! I need help. • math-- algebra - V = 48T^2, 25 = 48T^2, T^2 = 25/48 = 0.52s. T = 0.72s. ## Similar Questions 1. ### algebra IF a pro basketball player has a vertical hang-time of about 35 inches, what is his hang-time? 2. ### ALGEBRA If a pro basketball player has a vertical leap of about 35 inches what is his hang-time? 3. ### algebra-is this right A basketball player has a vertical leap of about 36 in. If the equation d=48t^2 describes his hang time t as a function of his vertical leap d. what is his hang time? 4. ### Algebra If a pro basketball player has a vertical leap of 25 inches, what is his hang time? 5. ### algebra II If a pro basketball player has a vertical leap of about 25 inches, what would his hang time be? 6. ### math If a pro basketball player has a vertical leap of about 35 inches, what is his hang time? 7. ### Math If a pro basketball player has a vertical leap of about 35 inches, what is his hang time? 8. ### algebra If a pro basketball player has a vertical leap of about 20in., what is his hang time? 9. ### algebra 1. If a pro basketball player has a vertical leap of about 20 inches, what is his hang time? 10. ### Algebra Hang time? If a basketball player has a vertical leap of about 30 inches, what is his hang time? More Similar Questions

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## Steel truss 15 m span, Civil Engineering Assignment Help: types of truss of 15 m cantilever with 1000 kg on free end. May be steel or any lightest material aluminium anodized truss. thanks #### Is codes for building design, IS CODES FOR BUILDING DESIGN The codes w... IS CODES FOR BUILDING DESIGN The codes which help engineers to design buildings are following: 1. IS 456-2000. For the design of plain and reinforced concrete it is code #### Is cbr test is an arbitrary test, CBR Test is an arbitrary test', justify. ... CBR Test is an arbitrary test', justify. Explain the procedure for conducting the CBR test in the field. Surcharge loads are used in the CBR test; Describe their significa #### Stabilization of Black Cotton soil, How the stabilization of black cotton ... How the stabilization of black cotton soil was done in field? what are the methods to do that? #### Graphics, 1. Draw the projections of a line AB that is 50 mm long and is pa... 1. Draw the projections of a line AB that is 50 mm long and is parallel to both the HP and the VP. The line is 40 mm above the HP and 25 mm in front of the VP. 2. A line AB, 50 mm #### Cross Section Method, Cut and Fill Calculation Using Cross Section Method Cut and Fill Calculation Using Cross Section Method #### Spun pipes, what is flush joint and confined joint in rcc spun pipes? what is flush joint and confined joint in rcc spun pipes? #### Calculate the resultant hydrostatic force, Five 1m diameter, 2m high cylind... Five 1m diameter, 2m high cylindrical drums filled with earth are placed upright and side-by-side in a straight line across a 5m wide creek to form a simple dam completely blocking #### Explain total dynamic head (tdh), Total Dynamic Head: (TDH) y-axis plo... Total Dynamic Head: (TDH) y-axis plot point related to each x-axis flow rate along the system curve plot. TDH = h a = TSH + h f + v 2 /2g       v 2 / 2g usually small #### Loss of prestress due to elastic shortening of concrete, Loss of Prestress ... Loss of Prestress due to Elastic Shortening of Concrete Due to elastic shortening of  concrete, tendons are able to reduce their stretched length to the same extent upto which

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# Expectation value (quantum mechanics) In quantum mechanics, the expectation value is the probabilistic expected value of the result (measurement) of an experiment. It can be thought of as an average of all the possible outcomes of a measurement as weighted by their likelihood, and as such it is not the most probable value of a measurement; indeed the expectation value may have zero probability of occurring (e.g. measurements which can only yield integer values may have a non-integer mean). It is a fundamental concept in all areas of quantum physics. ## Operational definition Consider an operator ${\displaystyle A}$. The expectation value is then ${\displaystyle \langle A\rangle =\langle \psi |A|\psi \rangle }$ in Dirac notation with ${\displaystyle |\psi \rangle }$ a normalized state vector. ## Formalism in quantum mechanics In quantum theory, an experimental setup is described by the observable ${\displaystyle A}$ to be measured, and the state ${\displaystyle \sigma }$ of the system. The expectation value of ${\displaystyle A}$ in the state ${\displaystyle \sigma }$ is denoted as ${\displaystyle \langle A\rangle _{\sigma }}$. Mathematically, ${\displaystyle A}$ is a self-adjoint operator on a Hilbert space. In the most commonly used case in quantum mechanics, ${\displaystyle \sigma }$ is a pure state, described by a normalized[lower-alpha 1] vector ${\displaystyle \psi }$ in the Hilbert space. The expectation value of ${\displaystyle A}$ in the state ${\displaystyle \psi }$ is defined as (1)      ${\displaystyle \langle A\rangle _{\psi }=\langle \psi |A|\psi \rangle }$. If dynamics is considered, either the vector ${\displaystyle \psi }$ or the operator ${\displaystyle A}$ is taken to be time-dependent, depending on whether the Schrödinger picture or Heisenberg picture is used. The evolution of the expectation value does not depend on this choice, however. If ${\displaystyle A}$ has a complete set of eigenvectors ${\displaystyle \phi _{j}}$, with eigenvalues ${\displaystyle a_{j}}$, then (1) can be expressed as (2)      ${\displaystyle \langle A\rangle _{\psi }=\sum _{j}a_{j}|\langle \psi |\phi _{j}\rangle |^{2}}$. This expression is similar to the arithmetic mean, and illustrates the physical meaning of the mathematical formalism: The eigenvalues ${\displaystyle a_{j}}$ are the possible outcomes of the experiment,[lower-alpha 2] and their corresponding coefficient ${\displaystyle |\langle \psi |\phi _{j}\rangle |^{2}}$ is the probability that this outcome will occur; it is often called the transition probability. A particularly simple case arises when ${\displaystyle A}$ is a projection, and thus has only the eigenvalues 0 and 1. This physically corresponds to a "yes-no" type of experiment. In this case, the expectation value is the probability that the experiment results in "1", and it can be computed as (3)      ${\displaystyle \langle A\rangle _{\psi }=\|A|\psi \rangle \|^{2}}$. In quantum theory, also operators with non-discrete spectrum are in use, such as the position operator ${\displaystyle Q}$ in quantum mechanics. This operator does not have eigenvalues, but has a completely continuous spectrum. In this case, the vector ${\displaystyle \psi }$ can be written as a complex-valued function ${\displaystyle \psi (x)}$ on the spectrum of ${\displaystyle Q}$ (usually the real line). For the expectation value of the position operator, one then has the formula (4)      ${\displaystyle \langle Q\rangle _{\psi }=\int _{-\infty }^{\infty }\,x\,|\psi (x)|^{2}\,dx}$. A similar formula holds for the momentum operator ${\displaystyle P}$, in systems where it has continuous spectrum. All the above formulas are valid for pure states ${\displaystyle \sigma }$ only. Prominently in thermodynamics and quantum optics, also mixed states are of importance; these are described by a positive trace-class operator ${\displaystyle \rho =\sum _{i}\rho _{i}|\psi _{i}\rangle \langle \psi _{i}|}$, the statistical operator or density matrix. The expectation value then can be obtained as (5)      ${\displaystyle \langle A\rangle _{\rho }=\mathrm {Trace} (\rho A)=\sum _{i}\rho _{i}\langle \psi _{i}|A|\psi _{i}\rangle =\sum _{i}\rho _{i}\langle A\rangle _{\psi _{i}}}$. ## General formulation In general, quantum states ${\displaystyle \sigma }$ are described by positive normalized linear functionals on the set of observables, mathematically often taken to be a C* algebra. The expectation value of an observable ${\displaystyle A}$ is then given by (6)      ${\displaystyle \langle A\rangle _{\sigma }=\sigma (A)}$. If the algebra of observables acts irreducibly on a Hilbert space, and if ${\displaystyle \sigma }$ is a normal functional, that is, it is continuous in the ultraweak topology, then it can be written as ${\displaystyle \sigma (\cdot )=\mathrm {Trace} (\rho \;\cdot )}$ with a positive trace-class operator ${\displaystyle \rho }$ of trace 1. This gives formula (5) above. In the case of a pure state, ${\displaystyle \rho =|\psi \rangle \langle \psi |}$ is a projection onto a unit vector ${\displaystyle \psi }$. Then ${\displaystyle \sigma =\langle \psi |\cdot \;\psi \rangle }$, which gives formula (1) above. ${\displaystyle A}$ is assumed to be a self-adjoint operator. In the general case, its spectrum will neither be entirely discrete nor entirely continuous. Still, one can write ${\displaystyle A}$ in a spectral decomposition, ${\displaystyle A=\int a\,\mathrm {d} P(a)}$ with a projector-valued measure ${\displaystyle P}$. For the expectation value of ${\displaystyle A}$ in a pure state ${\displaystyle \sigma =\langle \psi |\cdot \,\psi \rangle }$, this means ${\displaystyle \langle A\rangle _{\sigma }=\int a\;\mathrm {d} \langle \psi |P(a)\psi \rangle }$, which may be seen as a common generalization of formulas (2) and (4) above. In non-relativistic theories of finitely many particles (quantum mechanics, in the strict sense), the states considered are generally normal. However, in other areas of quantum theory, also non-normal states are in use: They appear, for example. in the form of KMS states in quantum statistical mechanics of infinitely extended media,[1] and as charged states in quantum field theory.[2] In these cases, the expectation value is determined only by the more general formula (6). ## Example in configuration space As an example, consider a quantum mechanical particle in one spatial dimension, in the configuration space representation. Here the Hilbert space is ${\displaystyle {\mathcal {H}}=L^{2}(\mathbb {R} )}$, the space of square-integrable functions on the real line. Vectors ${\displaystyle \psi \in {\mathcal {H}}}$ are represented by functions ${\displaystyle \psi (x)}$, called wave functions. The scalar product is given by ${\displaystyle \langle \psi _{1}|\psi _{2}\rangle =\int \psi _{1}^{\ast }(x)\psi _{2}(x)\,\mathrm {d} x}$. The wave functions have a direct interpretation as a probability distribution: ${\displaystyle p(x)dx=\psi ^{*}(x)\psi (x)dx}$ gives the probability of finding the particle in an infinitesimal interval of length ${\displaystyle dx}$ about some point ${\displaystyle x}$. As an observable, consider the position operator ${\displaystyle Q}$, which acts on wavefunctions ${\displaystyle \psi }$ by ${\displaystyle (Q\psi )(x)=x\psi (x)}$. The expectation value, or mean value of measurements, of ${\displaystyle Q}$ performed on a very large number of identical independent systems will be given by ${\displaystyle \langle Q\rangle _{\psi }=\langle \psi |Q|\psi \rangle =\int _{-\infty }^{\infty }\psi ^{\ast }(x)\,x\,\psi (x)\,\mathrm {d} x=\int _{-\infty }^{\infty }x\,p(x)\,\mathrm {d} x}$. The expectation value only exists if the integral converges, which is not the case for all vectors ${\displaystyle \psi }$. This is because the position operator is unbounded, and ${\displaystyle \psi }$ has to be chosen from its domain of definition. In general, the expectation of any observable can be calculated by replacing ${\displaystyle Q}$ with the appropriate operator. For example, to calculate the average momentum, one uses the momentum operator in configuration space, ${\displaystyle P=-i\hbar \,d/dx}$. Explicitly, its expectation value is ${\displaystyle \langle P\rangle _{\psi }=-i\hbar \int _{-\infty }^{\infty }\psi ^{\ast }(x)\,{\frac {d\psi (x)}{dx}}\,\mathrm {d} x}$. Not all operators in general provide a measurable value. An operator that has a pure real expectation value is called an observable and its value can be directly measured in experiment. ## Notes 1. This article always takes ${\displaystyle \psi }$ to be of norm 1. For non-normalized vectors, ${\displaystyle \psi }$ has to be replaced with ${\displaystyle \psi /\|\psi \|}$ in all formulas. 2. It is assumed here that the eigenvalues are non-degenerate. ## References 1. Bratteli, Ola; Robinson, Derek W (1987). Operator Algebras and Quantum Statistical Mechanics 1. Springer. ISBN 978-3-540-17093-8. 2nd edition. 2. Haag, Rudolf (1996). Local Quantum Physics. Springer. pp. Chapter IV. ISBN 3-540-61451-6. The expectation value, in particular as presented in the section "Formalism in quantum mechanics", is covered in most elementary textbooks on quantum mechanics. For a discussion of conceptual aspects, see:

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## Cake Serving By lilym Updated 20 Jul 2009 , 5:34pm by lilym lilym Posted 20 Jul 2009 , 1:07pm post #1 of 3 Does a 12x16 cake with 4" inch heigh is it enough to serve 100? 2 replies indydebi Posted 20 Jul 2009 , 2:15pm post #2 of 3 The nice ting about square or rectangle cakes is that you can do the math to figure the number of servings. If you cut the cake in the industry standard of 1x2x4" pieces, that means this cake will be cut in 12 rows by 8 columns = 96 servings. (A 2-layer 12x18 serves 10 lilym Posted 20 Jul 2009 , 5:34pm post #3 of 3 Thanks, that a relief.

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# Reading and interpreting line graphs ## Lesson details ### Key learning points 1. In this lesson, we will learn to read line graphs accurately in order to make factual statements based on the information displayed. ### Licence This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated. ## Video Share with pupils ## Worksheet Share with pupils ## Starter quiz Share with pupils ### 4 Questions Q1. Every line graph must include which of the following features? A title Correct answer: A title, an X-axis and a Y-axis label A wiggly line An X-axis and a Y-axis label Q2. During the lesson we worked together to interpret different line graphs. Can you identify a suitable synonym for the word 'interpret'? Create Draw Ignore Q3. Look at the line graph below. Which of the following statements is true? All of the above statements are false Correct answer: The temperature decreased over time The temperature stayed the same over time Q4. Look at the blank line graph below. What information would this line graph NOT be able to show us? All of the above How far a person has walked during the day Correct answer: How many hours a person slept for each night during one week How tall a plant has grown in a week ## Exit quiz Share with pupils ### 5 Questions Q1. On a line graph measuring the temperature of a city between 6AM and 6PM, a line gradually going down (decreasing) would indicate which of the following things? That it has started to rain heavily The temperature has remained the same The temperature is gradually getting warmer Q2. On a line graph measuring the distance travelled by a person in a car, a flat line could suggest which of the following statements? Correct answer: The car has a flat tyre The car has increased its speed during the journey The car has turned around and is heading home The car is driving slowly in a 20mph zone Q3. On a line graph measuring temperatures of a city, what would you usually expect to see the data line to be doing during the hours of 6AM and 12PM? Go up and down repeatedly like a wiggly line Stay flat across this time interval Q4. Look carefully at the line graph. Which of the following statements is NOT true? The highest temperature of the day was recorded at 3PM Correct answer: The temperature at midnight was the coldest time of the day The temperature decreased most rapidly between 3PM and 6PM The temperature recorded at 9AM and 6PM was the same Q5. The Line Graph below recorded the average temperature of a country across a 12 month period. However, unfortunately the title has been rubbed out. Looking at the data, can you identify which country the data could represent? Finland Greenland Iceland

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# What is magnetic noise ? Noise and vibrations of electrical machines include electromagnetically-excited sources, aerodynamic sources and mechanical sources. This article briefly explains the origin of magnetic noise and vibrations in electric machines, also called e-NVH in automotive applications. ## What is magnetic noise in electric machines ? Electromagnetic noise and vibrations come from the vibrations of the electric machine active parts in the audible range (20 Hz to 20 kHz) under the excitation of electromagnetic forces, namely magnetostriction and Maxwell forces. A low-speed, high-torque, direct-drive permanent magnet synchronous generator for wind turbine applications may be responsible for a “low frequency” 100 Hz humming noise, while a high-speed brushless DC motor used for instance in model making might create a high-pitch, “high frequency” whining noise up to 8000 Hz. The role of magnetostriction in noise generation can be generally neglected: based on EOMYS consulting experience on more than 200 electrical machines, it is not the root cause of electromagnetic noise and vibrations in rotating machines. Maxwell stress is the formalization of how Maxwell forces arise from electromagnetic fields: it includes well-known attraction/repulsion forces between two magnets, and Laplace forces which apply on current conductors in an external magnetic field. The Maxwell stress tangential net effect on the rotor gives the average electromagnetic torque of the electrical machine, but its tangential and radial harmonics can produce parasitic vibration and acoustic noise. ## Resonance effects When the shape of magnetic forces along the airgap (called a wavenumber) match with a structural mode of the stator and travel at the right speed, vibrations and acoustic noise are amplified significantly: this is the resonance effect. Resonance occurs when the electrical frequency (not the mechanical frequency) of the travelling force wave of wavenumber r match with the circumferential mode (r,0) natural frequency. As an example, the following animation shows the modal shape (2,0) of a stator lamination stack: A rotating radial force of wavenumber r=2 is illustrated here: Resonance occurs when the electrical frequency of this rotating force wave equals the natural frequency of the mode (2,0). The modal participation factor of magnetic forces to rotor and stator structural modes can be more rigourously quantified using the concept of Modal Force Matrix (projection of magnetic force on structural modes). ## Magnetic noise and vibration reduction techniques A special article discusses electromagnetic NVH mitigation techniques at design stage of electric machines. This article deals with techniques such as • topology, pole / slot / phase numbers • winding • skewing • pole magnetization, pole shaping, pole layout, pole width and position • slot and tooth shape / position • stator slot opening • notching • airgap increase • control parameters (e.g. current angle, PID) • harmonic current injection • switching strategies (e.g. SVPWM, DPWM ) • structural response (e.g. lamination to frame coupling, damping) • control of geometrical & magnetic asymmetries EOMYS can help you identifying the root cause of magnetic noise and vibrations, designing and implementing appropriate noise control actions at all design stage of rotating machines. ## Magnetic noise and vibration experimental characterization To know if an electrical machine is noisy because of electromagnetic noise and not because of aerodynamic or mechanical noise, some simple experiments can be carried. In induction machines for instance, electromagnetic noise stops when the machine is current-free (null stator current). For permanent magnet synchronous machines, cancelling the currents does not cancel all sources of magnetic fields ; it is therefore necessary to drive the machine with demagnetized magnets, or carry more detailed spectral analysis to check if the frequency of the acoustic noise match with the theoretical content of harmonic magnetic forces. EOMYS has developped some specialized experimental test methodologies to quickly characterize and troubleshoot e-NVH issues in rotating machines (e.g. spatiogram post-processing). The combination of Manate simulation software and advanced e-NVH tests allows EOMYS to efficiently identify e-NVH sources and transfer paths, and propose a noise mitigation plan.

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Time：2021-10-16 # Functions on tuples • Here’s the code • The following functions are basically applicable to list ``````#Len: get the length of the tuple t = (1,2,3,4,5) len(t)`````` ``````5 `````` ``````#Max, Min: maximum and minimum print(max(t)) print(min(t))`````` ``````5 1 `````` ``````#Tuple: convert or create tuples l = (1,2,3,4,5) t = tuple(l) print(t) t = tuple() print(t)`````` ``````(1, 2, 3, 4, 5) () `````` # Tuple function • Basically common with list ``````#Count: calculates the number of occurrences of the specified data t = (2,1,2,3,45,1,1,2,) print(t.count(2)) #Index: find the index position of the specified element in the tuple print(t.index(45)) #If you need to find more than one number, the first one is returned print(t.index(1))`````` ``````3 4 1 `````` # Tuple variable exchange method • Two variables exchange values ``````#Two variables exchange values a = 1 b = 3 print(a) print(b) print("*" * 20) #Java programmers would write this: c = a a = b b = c print(a) print(b) print("*" * 20) #Python writing a,b = b,a print(a) print(b)`````` ``````1 3 ******************** 3 1 ******************** 1 3 `````` # Set set • Set is a concept in high school mathematics • A certain set of unordered unique data, and each data in the set becomes an element ``````#Definition of set s = set() print(type(s)) print(s) #At this time, there must be a value in braces, otherwise a dict is defined s = {1,2,3,4,5,6,7} print(type(s)) print(s)`````` ``````<class 'set'> set() <class 'set'> {1, 2, 3, 4, 5, 6, 7} `````` ``````#If it is only defined in curly braces, a dict type is defined d = {} print(type(d)) print(d)`````` ``````<class 'dict'> {} `````` # Characteristics of sets • The data of the collection is out of order, that is, indexes and shards cannot be used • The internal data elements of the collection are unique and can be used to exclude duplicate data • The data in the set, STR, int, float, tuple, frozen set, etc., that is, only hashable data can be placed inside # Set sequence operation ``````#Member detection # in，not in s = {4,5,"i", "love", "you"} print(s) if "love" in s: print("Yes") if "haha" not in s: print("Yes")`````` ``````{'you', 4, 5, 'love', 'i'} Yes Yes `````` # Collection traversal operation ``````#For loop s = {4,5,"i", "love", "you"} for i in s: print(i)`````` ``````you 4 5 love i `````` ``````#Collection traversal with tuples s = {(1,2,3,), ("i", "love", "you"), (4,5,6)} for k,m,n in s: print(k, "--", m, "--", n) for k in s: print(k)`````` ``````i -- love -- you 4 -- 5 -- 6 1 -- 2 -- 3 ('i', 'love', 'you') (4, 5, 6) (1, 2, 3) `````` # Connotation of set ``````#General set connotation #The following sets automatically filter out duplicate elements after initialization s = {23,223,233,2,4,5,6,3,4,1,5,3} print(s) #General set connotation ss = {i for i in s} print(ss)`````` ``````{1, 2, 3, 4, 5, 6, 233, 23, 223} {1, 2, 3, 4, 5, 6, 233, 23, 223} `````` ``````#Conditional set connotation sss = {i for i in s if i % 2 == 0} print(sss)`````` ``````{2, 4, 6} `````` ``````#Set connotation of multi cycle s1 = {1,2,3,4} s2 = {"i", "love", "you"} s = {m*n for m in s2 for n in s1} print(s) s = {m*n for m in s2 for n in s1 if n == 2} print(s)`````` ``````{'you', 'youyou', 'love', 'lovelovelovelove', 'lovelovelove', 'lovelove', 'iii', 'youyouyouyou', 'ii', 'i', 'iiii', 'youyouyou'} {'lovelove', 'youyou', 'ii'} `````` # Set functions / functions about sets ``````#Len, Max, Min: consistent with other basic functions s = {23,54,72,3,5,3,3,6,1,543} print(len(s)) print(max(s)) print(min(s))`````` ``````8 543 1 `````` ``````#Set: generate a set l = {1,2,3,4,5,4,3,2,1} s = set(l) print(s)`````` ``````{1, 2, 3, 4, 5} `````` ``````#Add: adds an element to the collection s = {1} print(s)`````` ``````{1, 3} `````` ``````# clear s = {1,2,3,4,5} print(id(s)) s.clear() print(id(s)) #The results show that the clear function empties the data in place`````` ``````1370773843528 1370773843528 `````` ``````#Copy: copy #Remove: remove the specified value and directly change the original value. If the value to be deleted does not exist, an error will be reported #Discard: the value specified in the removal set is the same as remove, but if you want to delete it, no error will be reported s = {23,4,3,5,1,2,3} s.remove(4) print(s) print(s) print("*" * 20) print(s) s.remove(100) print(s)`````` ``````{1, 2, 3, 5, 23} {2, 3, 5, 23} ******************** {2, 3, 5, 23} --------------------------------------------------------------------------- KeyError Traceback (most recent call last) 12 print(s) 13 ---> 14 s.remove(100) 15 print(s) KeyError: 100 `````` ``````#Pop randomly removes an element s = {1,2,3,4,5,6,7} d = s.pop() print(d) print(s)`````` ``````1 {2, 3, 4, 5, 6, 7} `````` ``````#Set function #Intersection: intersection #Difference: difference set #Union: Union #Issubset: check whether a set is another subset #Issuperset: checks whether a set is another superset s1 = {1,2,3,4,5,6} s2 = {5,6,7,8,9} s_1 = s1.intersection(s2) print(s_1) s_2 = s1.difference(s2) print(s_2) s_3 = s1.issubset(s2) print(s_3) s_4 = s1.issuperset(s2) print(s_4)`````` ``````{5, 6} {1, 2, 3, 4} False False `````` ``````#Set mathematical operation s1 = {1,2,3,4,5,6} s2 = {5,6,7,8,9} #The following are not supported s_1 = s1 - s2 print(s_1) s_2 = s1 + s2 print(s_2)`````` ``````{1, 2, 3, 4} --------------------------------------------------------------------------- TypeError Traceback (most recent call last) <ipython-input-45-fac787d752ea> in <module> 7 print(s_1) 8 ----> 9 s_2 = s1 + s2 10 print(s_2) TypeError: unsupported operand type(s) for +: 'set' and 'set' `````` # Frozen set: Frozen set • Freezing means that no modification can be made • Frozenset is a special set ``````#Create s = frozenset() print(type(s)) print(s)`````` ``````<class 'frozenset'> frozenset() `````` # Dict dictionary • Dictionary is a kind of combined data. There is no sequential combined data. The data appears in the form of key value pairs ``````#Dictionary creation #Create empty dictionary 1 d = {} print(type(d)) print(d) #Create empty dictionary 2 d = dict() print(d) #Create a dictionary with values. Each set of data is separated by colons and each pair of key value pairs is separated by commas d = {"one":1, "two":2, "three":3} print(d) #Creating content dictionary with dict 1 d = dict({"one":1, "two":2, "three":3}) print(d) #Creating dictionary with dict 2 #Use key parameters d = dict(one=1, two=2, three=3) print(d) # d = dict( [("one",1), ("two",2), ("three",3)]) print(d)`````` ``````<class 'dict'> {} {} {'one': 1, 'two': 2, 'three': 3} {'one': 1, 'two': 2, 'three': 3} {'one': 1, 'two': 2, 'three': 3} {'one': 1, 'two': 2, 'three': 3} `````` # Characteristics of dictionary • The dictionary is a sequence type, but it is an unordered sequence, so there is no fragmentation and index • Each data in the dictionary consists of key value pairs, namely kV pairs • Key: must be hashable values, such as int, string, float, tuple, but not list, set, dict • Value: any value # Common operations of dictionary ``````#Access data d = {"one":1, "two":2, "three":3} #Note access format #Key values are in brackets print(d["one"]) d["one"] = "eins" print(d) #Delete an operation #Using del operations del d["one"] print(d)`````` ``````1 {'one': 'eins', 'two': 2, 'three': 3} {'two': 2, 'three': 3} `````` ``````#Member detection: in, not in #Key content during member detection d = {"one":1, "two":2, "three":3} if 2 in d: print("value") if "two" in d: print("key") if ("two,2") in d: print("kv")`````` ``````key `````` ``````#Traversal is quite different between python2 and 3, and the code is not general #Use for loop by key value d = {"one":1, "two":2, "three":3} #Use the for loop to access directly by keu value for k in d: print(k, d[k]) #The above code can be rewritten as follows for k in d.keys(): print(k, d[k]) #Access only dictionary values for v in d.values(): print(v) #Note the following special usage for k,v in d.items(): print(k, "--", v)`````` ``````one 1 two 2 three 3 one 1 two 2 three 3 1 2 3 one -- 1 two -- 2 three -- 3 `````` # Dictionary generator ``````d = {"one":1, "two":2, "three":3} #General dictionary generator dd = {k:v for k,v in d.items()} print(dd) #Dictionary generation with constraints dd = {k:v for k,v in d.items() if v % 2 == 0} print(dd)`````` ``````{'one': 1, 'two': 2, 'three': 3} {'two': 2} `````` # Dictionary correlation function ``````#General functions: len, Max, min, Dict #Str (Dictionary): the string format used to return the dictionary d = {"one":1, "two":2, "three":3} print(str(d))`````` ``````{'one': 1, 'two': 2, 'three': 3} `````` ``````#Clear: clear the dictionary #Items: returns the tuple format composed of key value pairs of the dictionary d = {"one":1, "two":2, "three":3} i = d.items() print(type(i)) print(i)`````` ``````<class 'dict_items'> dict_items([('one', 1), ('two', 2), ('three', 3)]) `````` ``````#Keys: a structure that returns the keys of the dictionary k = d.keys() print(type(k)) print(k)`````` ``````<class 'dict_keys'> dict_keys(['one', 'two', 'three']) `````` ``````#Values: similarly, an iterative structure v = d.values() print(type(v)) print(v)`````` ``````<class 'dict_values'> dict_values([1, 2, 3]) `````` ``````#Get: returns the corresponding value according to the specified key. The advantage is that the default value can be generated d = {"one":1, "two":2, "three":3} print(d.get("oner")) #The default value of get is none, which can be set print(d.get("one", 100)) print(d.get("one33", 100)) print(d['on333'])`````` ``````None 1 100 --------------------------------------------------------------------------- KeyError Traceback (most recent call last) <ipython-input-86-f8c01a58018e> in <module> 8 print(d.get("one33", 100)) 9 ---> 10 print(d['on333']) KeyError: 'on333' `````` ``````#From keys: use the specified sequence as the key and a value as the value of all keys in the dictionary l = ["eins", "zwei", "dree"] #Note the type of the fromkeys two parameters #Notice the calling body of fromkeys d = dict.fromkeys(l, "hahahahaha") print(d)`````` ``````{'eins': 'hahahahaha', 'zwei': 'hahahahaha', 'dree': 'hahahahaha'} `````` ## [hematemesis finishing] Super complete golang interview questions collection + golang Learning Guide + golang knowledge map + growth route The brain map is constantly updated. Check the address onlineSubsequent articles and contents will be updated toGitHub projectWelcome to pay attention. Directory (Ctrl + F) Basic introduction Novice 50 mistakes that golang novices often make data type I don’t even know that nil slice is different from empty slice? Then the bat interviewer has to […]

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https://www.expertsmind.com/library/what-price-should-prescotts-managers-set-5496233.aspx

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### What price should prescotts managers set Assignment Help Financial Accounting ##### Reference no: EM13496233 Prescott, Inc., manufactures bookcases and uses an activity-based costing system. Prescott's activity areas and related data follows: Activity Budgeted Cost of Activity Allocation Base Cost Allocation Rate Materials handling \$230,000 Number of parts \$0.50 Assembly 3,200,000 Direct labor hours 16.00 Finishing 180,000 Number of finished units 4.50 "Prescott produced two styles of bookcases in October: the standard bookcase and an unfinished bookcase, which has fewer parts and requires no finishing. The totals for quantities, direct materials costs, and other data follow:" Product Total Units Produced Total Direct Materials Costs Total Direct Labor Costs Total Number of Parts Total Assembling Direct Labor Hours Standard bookcase 3,000 \$36,000 \$45,000 9,000 4,500 Unfinished bookcase 3,500 35,000 35,000 7,000 3,500 Requirements: 1. Compute the manufacturing product cost per unit of each type of bookcase. "2. Suppose that pre-manufacturing activities, such as product design, were assigned to the standard bookcases at \$7 each, and to the unfinished bookcases at \$2 each. Similar analyses were conducted of post-manufacturing activities such as distribution, marketing, and customer service. The post-manufacturing costs were \$22 per standard bookcase and \$14 per unfinished bookcase. Compute the full product costs per unit." 3. Which product costs are reported in the external financial statements? Which costs are used for management decision making? Explain the difference. 4. What price should Prescott's managers set for unfinished bookcases to earn \$15 per bookcase? ### Previous Q& A #### Evaluate the concentrations of all species in a solution Calculate the concentrations of all species in a 0.100 M H3PO4 solution given the following Ka: 7.5 X 10^-3 for H3PO4^- 6.2 X 10^-8 for H2PO4^- and 4.8 X 10^-13 HPO4^2 #### Compute how fast is dan going as his feet hit the ground Dan is gliding on his skateboard at 3.0 m/s. He suddenly jumps backward off the skateboard, kicking the skateboard forward at 8.0 m/s. How fast is Dan going as his feet hit the ground #### What force is keeping the car in the circle A car is moving on a flat horizontal circular track of radius 120 m. The speed of the car is constant, 15m/s. The mass of the car is 1200 kg.  What force is keeping the car in the circle #### Explain preparation of chromium complexes Preparation of chromium complexes such as [Cr(en)3](ClO4)3, the typical starting material is CrCl3 6H2O. When combined with excess ethylenediamine in an appropriate solvent #### Determine the speed of the five-car train Three identical train cars, coupled together, are rolling east at 1.6 m/s . A fourth car traveling east at 4.4 m/s catches up with the three and couples to make a four-car train. What is the speed of the five-car train #### Interest group theory prespective of regulation Critically analyse and evaluate the arguments for, and against, for each of the case studies. Which arguments do you consider to be more compelling #### Calculate the predetermined overhead rate Lu Technology, Co., manufactures CDs and DVDs for computer software and entertainment companies. Lu uses job order costing and has a perpetual inventory system. #### How far up the smooth side will the marble go A uniform marble rolls down a symmetric bowl, starting from rest at the top of the left side. The top of each side is a distance above the bottom of the bowl. How far up the smooth side will the marble go #### Explain the reaction of crcl3 with liquid nh3 The reaction of CrCl3 with liquid NH3 to give yellow [Cr(NH3)6]Cl3 often has a low yield, since the reaction tends to stop with the production of pink [Cr(NH3)5Cl]Cl2 #### Do you think that non-human animals have interests Do you think that non-human animals have interests? ### Similar Q& A #### Create the required general journal entry to record the create the required general journal entry to record the subsequent transactions for the flaherty company.a. incurred #### Give journal entries necessary on september The dividend is payable on October 12 to the stockholders of record on September 30. Give journal entries necessary on September 15, September 30, and October 12, 2010. #### What were the company annual sales and its acp total current assets of \$675,000, and cash and marketable securities of \$100.000 in 2007. What were the company's annual sales and its ACP for that year? #### Questions on accounts receivables Questions on accounts receivables and capital expenditure and When the effective interest method is used to amortize bond premium or discount and question related to trading securities #### Explain the history of corporate accounting responsibility Read and cite at least 5 articles from the popular business and accounting press relating to CSR and discussing current events as they relate to professional ethics for accountants. #### Your ceo read a recent report on the importance of the sox your ceo read a recent report on the importance of the sox act but he acknowledged that he does not know much about it. #### Alfred a 33 percent profits and capital partner in pizzeria alfred a 33 percent profits and capital partner in pizzeria partnership requires help in adjusting his tax basis to #### Prepare the journal entries necessary to correct books Prepare the journal entries necessary in 2010 to correct the books for the following items, assuming that the books have not been closed. Disregard effects of corrections on income tax. #### The current assets and current liabilities for apple the current assets and current liabilities for apple computer inc. and dell inc. are shown as follows at the end of a #### Multiple choice questions on cvp analysis1 sharp company multiple choice questions on cvp analysis.1. sharp company retailer plans to sell 15000 units of product x during the #### Economic ordering quantity computationcalculate the eoqels economic ordering quantity computation.calculate the eoqels for the following two cases.raw material lrmannual demand #### Accounting records for the machine Lee offered for sale \$10,000 a machine that has been purchased for \$17,500. If Whitney paid Lee \$6,000 for the machine, the amount that Whitney would record in the accounting records for the machine is what?

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https://www.unitsconverters.com/en/Gr/Dunam-To-Gr/Pyong/Utu-7530-7535

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Formula Used 1 Grains Per Square Centimeter = 1000 Grain Per Dunam 1 Grains Per Square Centimeter = 3.3058 Grain Per Pyong 1 Grain Per Dunam = 33.058 Grain Per Pyong ## gr/Dunam to gr/Pyong Conversion The abbreviation for gr/Dunam and gr/Pyong is grain per dunam and grain per pyong respectively. 1 gr/Dunam is 33 times bigger than a gr/Pyong. To measure, units of measurement are needed and converting such units is an important task as well. unitsconverters.com is an online conversion tool to convert all types of measurement units including gr/Dunam to gr/Pyong conversion. ## Grain Per Dunam to gr/Pyong Check our Grain Per Dunam to gr/Pyong converter and click on formula to get the conversion factor. When you are converting area density from Grain Per Dunam to gr/Pyong, you need a converter that is elaborate and still easy to use. All you have to do is select the unit for which you want the conversion and enter the value and finally hit Convert. ## gr/Dunam to Grain Per Pyong The formula used to convert gr/Dunam to Grain Per Pyong is 1 Grain Per Dunam = 33.058 Grain Per Pyong. Measurement is one of the most fundamental concepts. Note that we have Grains Per Square Centimeter as the biggest unit for length while Grain Per Square Mile (US Survey) is the smallest one. ## Convert gr/Dunam to gr/Pyong How to convert gr/Dunam to gr/Pyong? Now you can do gr/Dunam to gr/Pyong conversion with the help of this tool. In the length measurement, first choose gr/Dunam from the left dropdown and gr/Pyong from the right dropdown, enter the value you want to convert and click on 'convert'. Want a reverse calculation from gr/Pyong to gr/Dunam? You can check our gr/Pyong to gr/Dunam converter. ## gr/Dunam to gr/Pyong Converter Units of measurement use the International System of Units, better known as SI units, which provide a standard for measuring the physical properties of matter. Measurement like area density finds its use in a number of places right from education to industrial usage. Be it buying grocery or cooking, units play a vital role in our daily life; and hence their conversions. unitsconverters.com helps in the conversion of different units of measurement like gr/Dunam to gr/Pyong through multiplicative conversion factors. When you are converting area density, you need a Grain Per Dunam to Grain Per Pyong converter that is elaborate and still easy to use. Converting gr/Dunam to Grain Per Pyong is easy, for you only have to select the units first and the value you want to convert. If you encounter any issues to convert Grain Per Dunam to gr/Pyong, this tool is the answer that gives you the exact conversion of units. You can also get the formula used in gr/Dunam to gr/Pyong conversion along with a table representing the entire conversion. Let Others Know

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http://www.westfield.wigan.sch.uk/friday-12th-may-2017-2/

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• A • B # Friday 12th May 2017 Hello again and a huge welcome to our blog for this week. We have been a little unhappy this week in English as we have now come to the end of our book, `Voices in the Park'.  Our focus this week was on the characters Charles' mum and Smudge's dad and their 'voices'.  As we did with their children, we thought about what they said and how they said it and what this told us about their characters. Were they similar or different in the way they viewed the experience of going to the park? Why don't you judge for yourselves... Check out the online book here. We told you it was a great read didn't we. How well did you concentrate? Did you spot the clues in the text or the pictures like we did? Why not test yourself and try our online quiz here. In Marvellous Maths, we have been working flat out on shape -in particular, 2D shapes.  We have been looking at those three different triangles (can you remember what they were?), quadrilaterals, parallelograms and rhombuses. Not only did we have to spell them correctly (!) but we have learned their properties so we could compare and classify them too. Psst. Why are some of these words underlined? (There's more to come). In Science, through our topic, `Living Things' we have been looking at branching databases (think trees). Did you know that these are a way of classifying a group of objects. If it has been designed properly, someone else could use the tree to identify one of the objects. It could be used, for example, to classify minibeasts, vegetables or fruit.  These are sometimes called a `binary tree', as there are only two options - 1 and 0.  With this type of tree it is `yes' or `no'. Take a look. On Thursday we went outside to design our own. It was great fun but we did have to chase a couple of our pictures when the wind got involved! Take a look at the pictures below. How would you like to make your own branching database?  Why not try it out here. Drop in next week for more news about our work. Congratulations this week go to Codie M a well deserved winner. Go Codie! Finally, have your say.  Each week you will have a chance to decide on which new song we will learn in next week's whole school assembly.  Click on the link below to take part in an online vote. (Note -this is carried from last week's choices.) Welcome to our website. ........ .Attendance for w/c 3rd July 2017... RW 96%, RF 97%, 1WF 91%, 1W 96%, 1F 90%, 2W 99%, 2F 90%, 3W 99%, 3F 97%, 4W 99%, 4F 95%, 5W 90%, 5F 97%, 6W 91%, 6F 93%. ** Whole School Attendance for w/c 3rd July 2017 was... 95%** ** Congratulations to RF, 2W, 3W and 4W for achieving the highest attendance. Well Done!**.... Top

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https://www.productinfo.schneider-electric.com/pm5300/viewer?docidentity=TotalPowerCalcuationForAccuracyVeri-96B384E4&lang=en&extension=xml&manualidentity=PowerLogicPM5300series-AABF9A47

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EAV15107-EN11 Total power calculation for accuracy verification testing Accuracy verification testing supplies the same test signal (total power) to both the energy reference/standard and the meter under test. Total power is calculated as follows, where: • Ptot = total instantaneous power in kilowatts (kW) • VLN = test point line-to-neutral voltage in volts (V) • I = test point current in amps (A) • PF = power factor The result of the calculation is rounded up to the nearest integer. For a balanced 3–phase Wye system: Ptot = 3 x VLN x I x PF x 1 kW/1000 W for the kW/W conversion, would it not be simpler just to multiply by 0.001? The units are specified in the list below so the unit conversion aspect is covered already. NOTE: A balanced 3–phase system assumes that the voltage, current and power factor values are the same for all phases. For a single-phase system: Ptot = VLN x I x PF x 1 kW/1000W

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# Yearly Archives: 2017 ## A more natural Disjunction Elimination rule? We work in a natural deduction setting, and choose a Gentzen-style layout rather than a Fitch-style presentation (this choice is quite irrelevant to the point at issue). The standard Gentzen-style disjunction elimination rule encodes the uncontroversially valid mode of reasoning, … Continue reading Posted in Logic | 6 Comments ## MA Scholarship in Logic/Phil Math (Montreal) Ulf Hlobil writes: “At Concordia University (Montreal), we want to do something about the gender imbalance in philosophy.  We offer specialized scholarships for female international students who are working ancient philosophy or logic and philosophy of mathematics.  Each scholarship is … Continue reading ## The Great Formal Machinery Works I’d like to have had the time now to carefully read Jan von Plato’s new book and comment on it here, as the bits I’ve dipped into are very interesting. But, after a holiday break, I must get my nose … Continue reading ## Postcard from the Lake District After a week in the Lakes, here’s a photo taken walking back from Howtown to Pooley Bridge above Ullswater. Beautiful. Worries about Trump, Brexit, and even Begriffsschrift seem happily remote. ## Begriffsschrift and absolutely unrestricted quantification We owe to Frege in Begriffsschrift our modern practice of taking unrestricted quantification (in one sense)  as basic. I mean, he taught us how to rephrase restricted quantifications by using unrestricted quantifiers plus connectives in the now familiar way, so that … Continue reading Posted in Logic | 9 Comments ## Jeanne Moreau, 23.i.1928 – 31.vii.2017 Posted in This and that | 1 Comment ## Which is the quantifier? A note on another of those bits of really elementary logic you don’t (re)think about from one year to the next – except when you are (re)writing an introductory text! This time, the question is which is the quantifier, ‘’ or ‘’, ‘’ or ‘’? Really exciting, … Continue reading Posted in Logic | 4 Comments ## Ivana Gavrić, Chopin I’ve very much admired Ivana Gavrić previous rightly praised discs (I wrote about the first two here in an earlier post, and you can find more about  them here). So I was really  looking forward to hearing her play in the intimate surroundings of the Fitzwilliam Museum in … Continue reading Posted in Music | 1 Comment ## Why mandatory reiteration in Fitch-style proofs? Digressing from issues about the choice of language(s), another post about principles for selecting among natural deduction systems — another choice point, and (though I suppose relatively minor) one not considered by Pelletier and Hazen. Take the most trite of examples. It’s … Continue reading Posted in IFL, Logic | 7 Comments ## The language(s) of first-order logic #3 Back to those choice-points noted in the first of these three posts: one formal language for FOL or many? Tarski or quasi-substitutional semantics? use of symbols as parameters as opposed to names or variables to be syntactically marked? In the second … Continue reading

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http://at.metamath.org/ileuni/sniota.html

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crawl-data/CC-MAIN-2020-05/segments/1579250606872.19/warc/CC-MAIN-20200122071919-20200122100919-00028.warc.gz

Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  sniota Structured version   GIF version Theorem sniota 4821 Description: A class abstraction with a unique member can be expressed as a singleton. (Contributed by Mario Carneiro, 23-Dec-2016.) Assertion Ref Expression sniota (∃!xφ → {xφ} = {(℩xφ)}) Proof of Theorem sniota StepHypRef Expression 1 nfeu1 1893 . . 3 x∃!xφ 2 iota1 4808 . . . . 5 (∃!xφ → (φ ↔ (℩xφ) = x)) 3 eqcom 2024 . . . . 5 ((℩xφ) = xx = (℩xφ)) 42, 3syl6bb 185 . . . 4 (∃!xφ → (φx = (℩xφ))) 5 abid 2010 . . . 4 (x {xφ} ↔ φ) 6 vex 2538 . . . . 5 x V 76elsnc 3373 . . . 4 (x {(℩xφ)} ↔ x = (℩xφ)) 84, 5, 73bitr4g 212 . . 3 (∃!xφ → (x {xφ} ↔ x {(℩xφ)})) 91, 8alrimi 1396 . 2 (∃!xφx(x {xφ} ↔ x {(℩xφ)})) 10 nfab1 2162 . . 3 x{xφ} 11 nfiota1 4796 . . . 4 x(℩xφ) 1211nfsn 3404 . . 3 x{(℩xφ)} 1310, 12cleqf 2183 . 2 ({xφ} = {(℩xφ)} ↔ x(x {xφ} ↔ x {(℩xφ)})) 149, 13sylibr 137 1 (∃!xφ → {xφ} = {(℩xφ)}) Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 98  ∀wal 1226   = wceq 1228   ∈ wcel 1374  ∃!weu 1882  {cab 2008  {csn 3350  ℩cio 4792 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004 This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-eu 1885  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-rex 2290  df-v 2537  df-sbc 2742  df-un 2899  df-sn 3356  df-pr 3357  df-uni 3555  df-iota 4794 This theorem is referenced by:  snriota  5421 Copyright terms: Public domain W3C validator

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http://math.stackexchange.com/questions/227602/creating-a-3d-surface-from-2d-graphs

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# Creating a 3D surface from 2D graphs So I have two sets of equations: $\mathcal{A}$ = $$\{ f(y_{0},x), \, f(y_{1},x) , \;... \;, f(y_{n},x) \}$$ $\mathcal{B}$ = $$\{ g(y,x_{0}), \, g(y,x_{1}) , \;... \;, g(y,x_{n}) \}$$ And I created a surface out of these equations in a plot. I know I can find an equation for this surface by fitting the plot data to known surfaces, but that is not what I want. I want to be able to directly derive an equation for the surface from just these equations. Is this possible? How can I do this? - Just a fleeting though, perhaps this could be considered as the (possibly overdetermined) method of lines solution of a PDE, and then one could run an inverse method approach to reconstruct the original surface. – Emily Nov 2 '12 at 16:03 The equations in the sets are determined experimentally themselves and don't represent differential equations, if that helps. – The Dude Nov 2 '12 at 16:09 You are not given "equations", but $2n+2$ curves in three-space, namely the curves $$\gamma_j:\quad x\mapsto\bigl(x,y_j,f(x,y_j)\bigr)\qquad(0\leq j\leq n)$$ in the vertical planes $y=y_j$, and the curves $$\gamma_k'\quad y\mapsto\bigl(x_,y,g(x_k,y)\bigr)\qquad(0\leq k\leq n)$$ in the vertical planes $x=x_k$. These $2n+2$ curves form a wire mesh over the $(x,y)$-plane which from above looks like an orthogonal grid. Now you are in search of a function $$\phi: \ (x,y)\mapsto z=\phi(x,y)\ ,$$ such that the graph of $\phi$ (a surface over the $(x,y)$-plane) contains all these wires $\gamma_j$ and $\gamma_k'$. In the first place such a $\phi$ is not uniquely determined at all. There are various principles to choose an "optimal" $\phi$ corresponding to the given data. Which of these principles suits best in your situation has to be judged by an "expert". In any case the problem formulated here is a problem of utmost interest in practical applications (e.g., sculpting of car fenders), and there is a large variety of numerical techniques (and software) available to deal with it. @The Dude: If the given input consists only of the values $z_{kj}=\phi(x_k,y_j)$ then the method of choice is called spline interpolation. Look it up in a suitable text book, e.g., Gerald Farin: Curves and surfaces for computer aided geometric design; Academic press 1988. I'm sure there are newer books on this topic available, but that's the book on my shelf. – Christian Blatter Nov 2 '12 at 20:51

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http://oeis.org/A279927

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crawl-data/CC-MAIN-2018-51/segments/1544376830305.92/warc/CC-MAIN-20181219005231-20181219031231-00131.warc.gz

This site is supported by donations to The OEIS Foundation. Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A279927 Expansion of e.g.f. arctan(x)*exp(x). 4 0, 1, 2, 1, -4, 9, 110, -279, -4520, 17265, 322618, -1638031, -35226860, 223578809, 5463436134, -41639195623, -1142009233872, 10162622387809, 309463272791538, -3149754003442847, -105510576441518164, 1208991988527548137, 44200537412519181278, -563099647603189449783 (list; graph; refs; listen; history; text; internal format) OFFSET 0,3 LINKS Stanislav Sykora, Table of n, a(n) for n = 0..199 FORMULA From Emanuele Munarini, Dec 16 2017: (Start) a(n) = Sum_{k=0..n/2} binomial(n+1,2*k+1)*(-1)^k*((n-2*k)/(n+1))*(2k)!. a(n+3) - a(n+2) + (n+1)*(n+2)*a(n+1) - (n+1)*(n+2)*a(n) = 1. a(n+4) - 2*a(n+3) + (n^2+5*n+7)*a(n+2) - 2*(n+2)^2*a(n+1) + (n+1)*(n+2)*a(n) = 0. (End) a(n) ~ (n-1)! * sin(Pi*n/2-1). - Vaclav Kotesovec, Dec 17 2017 EXAMPLE atan(x)*exp(x) = x + 2*x^2/2! + x^3/3! - 4*x^4/4! + 9*x^5/5! + ... MATHEMATICA CoefficientList[Series[Exp[x] ArcTan[x], {x, 0, 12}], x] Range[0, 12]! Table[Sum[Binomial[n+1, 2k+1] (-1)^k (n-2k)/(n+1) (2k)!, {k, 0, n/2}], {n, 0, 12}] (* Emanuele Munarini, Dec 16 2017 *) PROG (PARI) x='x+O('x^33); concat([0], Vec(serlaplace(atan(x)*exp(x) ) ) ) \\ Joerg Arndt, Jan 06 2017 (Maxima) makelist(sum((-1)^k*binomial(n+1, 2*k+1)*(n-2*k)/(n+1)*(2*k)!, k, 0, floor(n/2)), n, 0, 12); /* Emanuele Munarini, Dec 16 2017 */ CROSSREFS E.g.f. of exp(x) A000012, -arctan(x) A186246. Sequence in context: A097949 A268572 A117338 * A137634 A100229 A071949 Adjacent sequences:  A279924 A279925 A279926 * A279928 A279929 A279930 KEYWORD sign AUTHOR Stanislav Sykora, Jan 06 2017 STATUS approved Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent The OEIS Community | Maintained by The OEIS Foundation Inc. Last modified December 18 20:06 EST 2018. Contains 318245 sequences. (Running on oeis4.)

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CC-MAIN-2018-51

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https://sudonull.com/post/25964-Compilation-of-a-rating-of-territories-by-the-method-of-thermal-potentials-using-open-data

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crawl-data/CC-MAIN-2023-50/segments/1700679100525.55/warc/CC-MAIN-20231204052342-20231204082342-00819.warc.gz

# Compilation of a rating of territories by the method of thermal potentials using open data In this article, we consider the algorithm and the results of the analysis of large areas without any restrictions on their borders, using the method of thermal potentials and the method of principal components . As initial information, preference was given to open data, primarily with OSM. The study was conducted on the territory of 40 subjects of the European part of the Russian Federation, as a whole with a total area of ​​1.8 million sq. Km. Some tasks solved by the potential method: • The definition of a set of point estimates at each point of the territory, giving an idea of ​​the level of development of the territory in general, and in some subject area in particular. For example, trade, industry, services, etc. • Finding homogeneous zones (clusters) of the analyzed territory and their exact boundaries. • Calculation of recommendations for the placement of a new facility , including a composite facility, including other facilities. • Finding cost or territory value models for each cluster. • Comparison of territories, i.e. compilation of ratings of territories (which will be discussed in this article). Scope of the study The mentioned problems are solved for the level of cities (several hundred sq. Km with spatial accuracy of 25 meters) and the level of regions (several hundred thousand sq. Km with spatial accuracy of 250 meters). The article describes the methods of analyzing the territory on a new scale - the unification of cities, regions, districts into a single space. The main research methods: • It uses open spatial information, primarily OSM, and methods of processing it. • To take into account the degree of influence of objects of different nature on the territory, the method of potentials is used . • To reduce the dimension of the problem and improve the quality of the models, the principal component method is used . • To calculate linear models, the least squares method is used . • For analysis, clustering methods are used to determine homogeneous regions. Each cluster has its own model; models are stitched together at the boundaries of the clusters. The study was conducted at the level of constituent entities of the Russian Federation and large cities, with their subsequent unification. First of all, we present the algorithm and results of the study of homogeneous territories of the constituent entities of the Russian Federation - the Volga Federal District, the Central Federal District, the Southern Federal District, the North-Western Federal District and part of the Ural Federal District, so the total research area was approximately 1.8 million square kilometers. Description of research technology: 1. Collection of source information from open data sources (our preference is OpenStreetMap) in the context of each subject of the Russian Federation. The initial information is downloaded with the maximum radius of influence Rmax for all factors (for example, in our case the maximum radius of influence was 50 km, i.e. we will download the information with a buffer of 50 km). 2. The meshing is carried out clearly within the boundaries of the subject of the Russian Federation (the mesh step for this study is 1 kilometer), and the procedure for splitting the factors of influence into fragments for further calculation of potentials is carried out taking into account the constructed buffer in order to take into account the influence of factors at the border of the subject. 3. The calculation of potential values and filling in the calculation results in grid nodes is carried out within the boundaries of the subject of the Russian Federation. 4. The union of the constituent entities of the Russian Federation into a “single project”. That is, at this stage, we combine all the grids built for each subject earlier into one. Thus, we get a grid covering an area of ​​1.8 million square kilometers. and containing 1.8 million nodes (points of analysis) and 88 influence factors (in our opinion, the most influential OSM factors are point and extended objects (highways, forests, rivers, infrastructure objects)). 5. Calculation of integral indicators using the principal component method. 6. Search for homogeneous areas. The studied territories are united in homogeneous areas according to factors describing any side of the territory's development, for example, the social sphere, trade, industry. The image below shows images of homogeneous areas of the “single project” in the context of: industry, trade, services. Homogeneous territories of the European part of the Russian Federation by factor "industry" Homogeneous territories of the European part of the Russian Federation by factor "industry" (fragment Moscow) Homogeneous territories of the European part of the Russian Federation by factor "trade" Homogeneous territories of the European part of the Russian Federation by factor "trade" (fragment of Moscow) Homogeneous territories of the European part of the Russian Federation by the factor of “service” Homogeneous territories of the European part of the Russian Federation by the factor of “services” (fragment of Moscow) The presented centers clearly dominate the subjects of the Russian Federation, but it can also be noted that some homogeneous areas (areas highlighted in the same color) are found in almost every subject. In other words, these homogeneous (in importance) territories in different entities are the most attractive, both in investment and in other plans. The next stage of the study was the compilation of ratings of the subjects of the European part of the Russian Federation, which are given in the tables below. Compiled ratings show the best square kilometer, the best 100 square meters. km and the best 20,000 sq. km. It should be noted that this is not a specific fragment of a territory of 1, 100 or 20,000 sq. Km, but a set of grid nodes (analysis points) built on a subject that have the best integral characteristics, i.e. these nodes can be located randomly on the territory of the subject of the Russian Federation. Table 1. Rating of constituent entities of the Russian Federation (the best 1 sq. Km.) Table 2. Rating of constituent entities of the Russian Federation (the best 100 sq. Km.) Table 3. Rating of constituent entities of the Russian Federation (the best 20 sq. Km.) The first positions in the ranking are held by Moscow and the Moscow Region, St. Petersburg and the Leningrad Region, Sverdlovsk Region, Chelyabinsk Region, Nizhny Novgorod Region, and Tatarstan. However, it is worth paying attention that the rating is “floating” depending on the scale of research (the subjects of the Russian Federation change places), that is, the set of the best nodes is affected by the fact that we consider -1 sq. Km, or 100 sq. Km, or 20 000 sq km Solving a similar problem for the centers of the constituent entities of the Russian Federation (we selected 40 largest and largest centers), we set the step of building a grid of 100 meters and obtain the following results. Table 4. Rating of centers of constituent entities of the Russian Federation (best 0.01 sq. Km. - the best point in the territory) Table 5. Rating of centers of constituent entities of the Russian Federation (best 10 sq. Km) Table 6. Rating of centers of constituent entities of the Russian Federation (best 200 sq. Km) Thus, as in the task at the level of the constituent entities of the Russian Federation, the rating turned out to be dependent on the studied scale. This is because the number of grid nodes (analysis points) with the best integral indicators varies depending on the selected scale. In conclusion, it is worth noting that any rating is a thing that is conducive to discussion, however, we conducted research on open data using new methods of analyzing the territory, allowing us to transfer existing methods to a smaller scale - the level of the constituent entities of the Russian Federation, federal districts and beyond. The variable scale and new methods allow us to analyze objects distant from each other as a whole, taking into account the mutual influence of territories on each other.

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http://www.gregthatcher.com/Stocks/StockFourierAnalysisDetails.aspx?ticker=HQH

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Back to list of Stocks    See Also: Seasonal Analysis of HQHGenetic Algorithms Stock Portfolio Generator, and Best Months to Buy/Sell Stocks # Fourier Analysis of HQH (Tekla Healthcare Investors) HQH (Tekla Healthcare Investors) appears to have interesting cyclic behaviour every 68 weeks (.653*sine), 73 weeks (.5197*sine), and 96 weeks (.3806*cosine). HQH (Tekla Healthcare Investors) has an average price of 10.55 (topmost row, frequency = 0). Click on the checkboxes shown on the right to see how the various frequencies contribute to the graph. Look for large magnitude coefficients (sine or cosine), as these are associated with frequencies which contribute most to the associated stock plot. If you find a large magnitude coefficient which dramatically changes the graph, look at the associated "Period" in weeks, as you may have found a significant recurring cycle for the stock of interest. ## Fourier Analysis Using data from 1/3/2000 to 4/16/2018 for HQH (Tekla Healthcare Investors), this program was able to calculate the following Fourier Series: Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod 010.55196   0 14.42784 -6.26128 (1*2π)/955955 weeks 2-.68122 -5.05863 (2*2π)/955478 weeks 3-.73095 -1.32057 (3*2π)/955318 weeks 4-.11371 -.60617 (4*2π)/955239 weeks 5.56885 -.50849 (5*2π)/955191 weeks 6.19796 -1.06489 (6*2π)/955159 weeks 7.22821 -1.15185 (7*2π)/955136 weeks 8-.11986 -1.29996 (8*2π)/955119 weeks 9-.20071 -.93272 (9*2π)/955106 weeks 10-.38055 -.30588 (10*2π)/95596 weeks 11-.14127 -.1363 (11*2π)/95587 weeks 12.03224 -.24309 (12*2π)/95580 weeks 13.1552 -.51975 (13*2π)/95573 weeks 14-.30847 -.653 (14*2π)/95568 weeks 15-.21957 -.37008 (15*2π)/95564 weeks 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(879*2π)/9551 weeks 880.01186 .08605 (880*2π)/9551 weeks 881-.05341 .08783 (881*2π)/9551 weeks 882-.06891 .04457 (882*2π)/9551 weeks 883-.09832 .08251 (883*2π)/9551 weeks 884-.02473 .1428 (884*2π)/9551 weeks 885.02362 .09195 (885*2π)/9551 weeks 886-.01692 .03744 (886*2π)/9551 weeks 887-.04575 .08705 (887*2π)/9551 weeks 888-.02693 .15765 (888*2π)/9551 weeks 889.03089 .12068 (889*2π)/9551 weeks 890.02119 .05778 (890*2π)/9551 weeks 891-.03225 .05798 (891*2π)/9551 weeks 892-.03868 .08386 (892*2π)/9551 weeks 893-.01921 .08276 (893*2π)/9551 weeks 894-.03013 .05692 (894*2π)/9551 weeks 895-.06655 .02513 (895*2π)/9551 weeks 896-.03037 .01243 (896*2π)/9551 weeks 897-.1081 .03915 (897*2π)/9551 weeks 898-.08745 .07196 (898*2π)/9551 weeks 899-.09123 .11406 (899*2π)/9551 weeks 900-.00338 .06673 (900*2π)/9551 weeks 901.00507 .12962 (901*2π)/9551 weeks 902.01725 .02385 (902*2π)/9551 weeks 903-.05117 -.00581 (903*2π)/9551 weeks 904-.10057 -.01504 (904*2π)/9551 weeks 905-.13759 .06049 (905*2π)/9551 weeks 906-.11013 .13037 (906*2π)/9551 weeks 907-.04377 .19142 (907*2π)/9551 weeks 908.0019 .11737 (908*2π)/9551 weeks 909-.00417 .16321 (909*2π)/9551 weeks 910-.02413 .04252 (910*2π)/9551 weeks 911-.0868 .08431 (911*2π)/9551 weeks 912-.09619 .04761 (912*2π)/9551 weeks 913-.14025 .10115 (913*2π)/9551 weeks 914-.17324 .12697 (914*2π)/9551 weeks 915-.05416 .20516 (915*2π)/9551 weeks 916.0296 .09608 (916*2π)/9551 weeks 917.04557 .08247 (917*2π)/9551 weeks 918-.0816 .08291 (918*2π)/9551 weeks 919-.06595 .16946 (919*2π)/9551 weeks 920-.08422 .2038 (920*2π)/9551 weeks 921-.04081 .19534 (921*2π)/9551 weeks 922-.05384 .18708 (922*2π)/9551 weeks 923.03646 .21093 (923*2π)/9551 weeks 924.00282 .13143 (924*2π)/9551 weeks 925.12243 .12054 (925*2π)/9551 weeks 926-.02076 .08118 (926*2π)/9551 weeks 927-.12261 .0971 (927*2π)/9551 weeks 928.0108 .1413 (928*2π)/9551 weeks 929.06069 .11759 (929*2π)/9551 weeks 930-.07915 .28788 (930*2π)/9551 weeks 931-.08646 .3244 (931*2π)/9551 weeks 932.07959 .42281 (932*2π)/9551 weeks 933.12993 .30964 (933*2π)/9551 weeks 934.15889 .28493 (934*2π)/9551 weeks 935-.00571 .17378 (935*2π)/9551 weeks 936.02752 .25469 (936*2π)/9551 weeks 937.06394 .12819 (937*2π)/9551 weeks 938-.12052 .20008 (938*2π)/9551 weeks 939-.2306 .33427 (939*2π)/9551 weeks 940-.21957 .37008 (940*2π)/9551 weeks 941-.30847 .653 (941*2π)/9551 weeks 942.1552 .51975 (942*2π)/9551 weeks 943.03224 .24309 (943*2π)/9551 weeks 944-.14127 .1363 (944*2π)/9551 weeks 945-.38055 .30588 (945*2π)/9551 weeks 946-.20071 .93272 (946*2π)/9551 weeks 947-.11986 1.29996 (947*2π)/9551 weeks 948.22821 1.15185 (948*2π)/9551 weeks 949.19796 1.06489 (949*2π)/9551 weeks 950.56885 .50849 (950*2π)/9551 weeks 951-.11371 .60617 (951*2π)/9551 weeks 952-.73095 1.32057 (952*2π)/9551 weeks 953-.68122 5.05863 (953*2π)/9551 weeks

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CC-MAIN-2018-17

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https://www.fmaths.com/interesting-about-math/quick-answer-what-is-multiplication-in-math.html

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# Quick Answer: What Is Multiplication In Math? ## How do you explain multiplication? Essentially, to multiply numbers is to add groups of a number. Multiplying means repeated addition of a number. (The number must all be the same before we can use it to multiply.) When you think of it this way, learning the Times Tables makes sense. ## What is multiplication and division? In multiplication, the numbers being multiplied are called factors; the result of the multiplication is called the product. In division, the number being divided is the dividend, the number that divides it is the divisor, and the result of the division is the quotient. ## Where do we use multiplication in real life? You have to multiply to find out the total. The third way you can use multiplication in your life is to help you bake. For example, the cookbook says 10 cups of flour. How much is a cup? ## What is multiplication in simple words? Multiplication, one of the four basic operations of arithmetic, gives the result of combining groups of equal sizes. In other words, multiplication is repeated addition. Multiplication is represented by the signs cross ‘×’, asterisk ‘*’ or dot ‘·’. When we multiply two numbers, the answer we get is called ‘product’. You might be interested:  What Is Extrema In Math? ## How do I teach my child multiplication tables? Here are our eight highly effective tips on how to teach times tables the easy way. 1. Hang up a times table sheet. 2. Make sure they can walk before they can run. 3. Teach your kids some tricks. 4. Listen to some fun songs. 5. Stage a multiplication war. 6. Draw a Waldorf multiplication flower. 7. Quiz them regularly, but not incessantly. ## What is a multiplication sign called? The multiplication sign, also known as the times sign or the dimension sign, is the symbol ×, used in mathematics to denote the multiplication operation and its resulting product. While similar to a lowercase X (x), the form is properly a four-fold rotationally symmetric saltire. ## What is the trick to learning multiplication tables? Tricks by Number 1. add the number to itself (in other words, double it) Example 2×9 = 9+9 = 18. 2. double, then double again. 3. Cut in half, then times 10. 4. when you multiply 6 by an even number, they both end in the same digit. 5. 7×8. 6. Double, double, double! 7. is 10× the number minus the number. 8. put a zero after it. ## How is maths used in daily life? People use math knowledge when cooking. For example, it is very common to use a half or double of a recipe. In this case, people use proportions and ratios to make correct calculations for each ingredient. If a recipe calls for 2/3 of a cup of flour, the cook has to calculate how much is half or double of 2/3 of a cup. ## Why do we need math in our daily life? Mathematics makes our life orderly and prevents chaos. Certain qualities that are nurtured by mathematics are power of reasoning, creativity, abstract or spatial thinking, critical thinking, problem-solving ability and even effective communication skills. You might be interested:  Where To Study Math Online? ## What is the importance of multiplication in our daily life? By learning multiplication and memorizing the times tables you provide yourself with essential building blocks to do higher learning math, like division, fractions and even algebra.

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http://tiao.io/posts/project-euler/problem-45-triangular-pentagonal-and-hexagonal/

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# Project Euler Problem 45: Triangular, pentagonal, and hexagonal Triangle, pentagonal, and hexagonal numbers are generated by the following formulae: Triangle $$T_n = \frac{n(n+1)}{2} \\ 1, 3, 6, 10, 15, \dotsc$$ Pentagonal $$P_n = \frac{n(3n−1)}{2} \\ 1, 5, 12, 22, 35, \dotsc$$ Hexagonal $$H_n = n(2n−1) \\ 1, 6, 15, 28, 45, \dotsc$$ It can be verified that $T_{285} = P_{165} = H_{143} = 40755$. Find the next triangle number that is also pentagonal and hexagonal. #### Version 1: Brute force¶ In [1]: from six.moves import map, range from itertools import islice In [2]: def argmin(iterable): argmin_ = 0 for i, n in enumerate(iterable): if n < iterable[argmin_]: argmin_ = i return argmin_ In [3]: from random import randint In [4]: a = [randint(1, 100) for _ in range(15)]; a Out[4]: [78, 25, 88, 84, 50, 62, 83, 30, 80, 90, 38, 52, 26, 43, 82] In [5]: argmin(a) Out[5]: 1 In [6]: def polygonal(s): c = s - 2 a = b = 1 while True: yield a b += c a += b In [7]: list(islice(polygonal(2), 10)) Out[7]: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] In [8]: list(islice(polygonal(3), 10)) Out[8]: [1, 3, 6, 10, 15, 21, 28, 36, 45, 55] In [9]: list(islice(polygonal(4), 10)) Out[9]: [1, 4, 9, 16, 25, 36, 49, 64, 81, 100] In [10]: s = [3, 5, 6] In [11]: polygonal_iters = list(map(polygonal, s)) In [12]: list(islice(polygonal(7), 10)) Out[12]: [1, 7, 18, 34, 55, 81, 112, 148, 189, 235] In [13]: polygonal_iters = list(map(polygonal, s)) In [14]: values = list(map(next, polygonal_iters)) In [15]: next(polygonal_iters[argmin(values)]) Out[15]: 3 In [16]: all_equals = lambda lst: lst[1:] == lst[:-1] In [17]: def polygonal_combinations(s_lst): iters = list(map(polygonal, s_lst)) values = list(map(next, iters)) while True: if all_equals(values): yield values[0] amin = argmin(values) values[amin] = next(iters[amin]) In [18]: list(islice(polygonal_combinations([3, 5, 6]), 4)) Out[18]: [1, 40755, 1533776805, 57722156241751] In [19]: it = polygonal_combinations([3, 4, 6, 29, 60, 124]) In [20]: next(it) Out[20]: 1 In [21]: next(it) Out[21]: 1225 The number 1225 is hecticositetragonal ($s=124$), hexacontagonal ($s=60$), icosienneagonal ($s=29$), hexagonal, square, and triangular. In [22]: from operator import itemgetter In [23]: def polygonal_combinations(s_lst): values = [1 for _ in s_lst] increm = [1 for _ in s_lst] while True: if all_equals(values): yield values[0] amin = argmin(values) increm[amin] += s_lst[amin] - 2 values[amin] += increm[amin] In [24]: it = polygonal_combinations([3, 5, 6]) In [25]: next(it) Out[25]: 1 In [26]: next(it) Out[26]: 40755 In [27]: next(it) Out[27]: 1533776805

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https://www.michaeljamesonmoney.com/2009/12/modifying-4-rule.html?showComment=1260815597646

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## Monday, December 14, 2009 ### Modifying the 4% Rule What amount can an investor, Ian, withdraw safely each year from a portfolio 50% in stocks and 50% in bonds? Suppose that Ian wants to fix some dollar amount and bump it up by inflation each year, and wants a high probability of not outliving the money. According to a 1994 paper by William Bengen, the answer if Ian is between 60 and 65 years old is about 4% of his starting portfolio size. This has come to be called the 4% rule. So, starting with \$750,000, Ian should be able to withdraw \$30,000 the first year, and then bump up the withdrawal amount by inflation each year. With reasonable probability, Ian won’t run out of money during his remaining lifetime, according to Bengen. Patrick at A Loonie Saved noted a logical inconsistency with this 4% rule. Two investors in exactly the same situation might receive different advice. Let’s illustrate this with an example. Suppose that in the first year of Ian’s retirement stocks performed very poorly. Between the \$30,000 worth of withdrawals and the portfolio losses, Ian has \$600,000 left today. Assuming inflation is 3%, Ian plans to continue with the 4% of starting portfolio rule and bump up his withdrawal amount to \$30,900 for the upcoming year. A second investor, Sam, is the same age as Ian, but is just retiring today. Sam’s portfolio is also worth \$600,000. However, when Sam follows the 4% rule starting now, he will only withdraw \$24,000 during the upcoming year. How can it make any sense that Ian and Sam are the same age and have the same amount of money, but should withdraw very different amounts during the upcoming year? This inconsistency caused me to modify the 4% rule for my own use. When I get to full retirement, I plan to target withdrawing 4% of whatever my portfolio is worth each year. So, if my portfolio drops in value from one year to the next, my income for the next year will drop as well. This kind of uncertainty may not be for everyone. I’m quite comfortable making lifestyle changes to increase or decrease spending. Many people can’t do this well. On the positive side, I won’t ever run out of money this way. If my portfolio happens to perform well, I will get to enjoy rising income. The approach I plan to use may be forced upon some investors even if they planned to follow the original 4% rule. The poor performance of Ian’s portfolio in his first year of retirement greatly increases the risk that he will outlast his money if he doesn’t cut back on withdrawals. If he sticks to the original 4% rule for 5 or 10 years, it may become very obvious that he is running out of money fast. 1. On the one extreme Ian could invest all his money in stocks and withdraw say 4% of the balance every year, indexed to inflation. The pro of this approach is he'll likely see his retirement income grow more than inflation. The con is there is a risk his income might not keep pace with inflation - this would occur if returns were poor in the first years of his retirement. On another extreme, Ian could use all of his savings to purchase say a bond ladder of government inflation-indexed bonds. His withdrawal rate will depend on interest rates and how long he wants the money to last. Say he wants the money to last until age 96, around 10 years after his life expectancy, and inflation-indexed interest rates are averaging 1.5%. Then he will be able to secure an inflation adjusted income stream of around 4% of his initial retirement savings. The pro of this approach is the certainty of his income, assuming he doesn't outlive it. The con is he is giving up the pro from the all-stock scenario, where he would likely see his retirement income grow more than inflation. I don't think either approach is wrong, it depends on your priorities and risk tolerance. For me, I would probably want some blend of stocks and bonds in retirement (maybe 50/50 or 40/60), noting that I might need to adjust my retirement income either up or down, depending on how the markets perform. 2. Blitzer68: I agree that different portfolio allocations can suit different people. It all depends on how much you value extra income and how painful an income reduction is. However, where I think people can go wrong is in doggedly basing withdrawals on the initial portfolio value instead of adjusting income down in the face of poor portfolio performance. 3. Yes, I agree. Thanks for bringing up the topic, it's an important one. 4. Very useful analysis. I wish more were written about these types of calculations. I think the number of variables (asset allocation, inflation, interest rates, stock market performance) can scare a lot of us away from even looking at the numbers. But look at them we must for all of us will reach retirement some day. 5. Thanks for the link Michael. Your remarks about lifestyle changes reminded me that I have made exactly these kinds of lifestyle changes in the past. (eg. I once left a well-paying job to finish my degree.) I've taken it for granted that a reliable income stream is a must, but perhaps not everyone needs that level of certainty enough to pay the price for it. 6. I think of the 4% rule as more of a planning tool instead of an actual plan. I would find it difficult to sit back and watch things go up and down without making some adjustments to my withdrawals. My tendency would be to squirrel away some of the excess in the good years so I would have more to spend in the lean years. 7. 2 Cents: Not to be too much of a downer, but some of us won't reach retirement, either because we choose to work late in life or we die young. However, the vast majority of us need to plan based on the assumption that we will retire one day. Hazy: I agree that I would probably tend to spend less than 4% in good years to save up for poor years. Trying to pin down an exact spending and investment strategy in retirement is a surprisingly slippery business. 8. I also find it difficult to pin down an exact spending strategy in retirement. One idea which has some appeal me is to breakdown my spending into minimum and discretionary spending. Minimum spending are things like food, shelter, clothing, etc. and discretionary spending are things like traveling. Say a 1/4 of my ideal retirement spending is in this descretionary category that I could do without. Others will no doubt have their own breakdown. So then what scheme will provide reasonable certainty for the 3/4 of minimum spending with reasonable but less certainty for the 1/4 of discretionary spending? One scheme would be to set my withdrawal rate at 3% of the initial retirement savings, and only spend on discretionary when the retirement savings grows beyond the 3% + inflation. Of course, there is still the problem of deciding what to do if the market tanks in the first years of retirement. I can't imagine cutting my minimum spending back too much. One way to eliminate this risk is with inflation indexed bonds to cover off the minimum spending, and then put the remainder in stocks for the discretionary spending.

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CC-MAIN-2021-21

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https://manifold.markets/KevinChen95b9/will-i-get-hm-on-the-2024-jmo

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Will I get HM on the 2024 JMO? 25 236 653 Apr 21 21% chance Coord bashed #1, misread #4 but provided a full rigorous solution with a right answer which the grading committee will consider confirmed by Evan Chen, did #5 with a unique method but assumed f(x) was a polynomial. Expected distrib is 700?500 Get Ṁ200 play money Sort by: bought Ṁ40 NO if you had the right answer for 5, likely 1 point but if wrong answer likely 0. Assuming f(x) is a polynomial is worth <=1 point

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https://socratic.org/questions/what-is-the-cartesian-form-of-16-pi-12#321453

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# What is the Cartesian form of ( 16,(pi )/12? $\left(16 \cos \left(\frac{\pi}{12}\right) , 16 \sin \left(\frac{\pi}{12}\right)\right)$

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https://www.studypool.com/services/50630/perimeter-circumference-and-area

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# Perimeter, Circumference and Area May 20th, 2015 Studypool Tutor Price: \$5 USD Tutor description Geometry Word Count: 375 Showing Page: 1/3 Perimeter, Circumference and Area of shapesPerimeter is the sum of all sides of a polygon.Area is the quantity the extent of a two-dimensional figure.Circumference is the measure of the closed curve around the circle.SquareRectangleCircleTriangle Square is 4-sided polygon with all sides are equal, parallel and angle equal to 90 degrees..The Perimeter is given by P = 4s where s is the side lengthArea is given by A = s^2Rectangle is 4-sided polygon with opposite sides that are equal, parallel and angle equal to 90 degrees.The Perimeter is given by P = 2L + 2W where L is the length and W is the WidthArea is given by A = LWA circle is a conical figure that all of its points are equidistant around the centerDiameter is the distance from the two end-points of the circle.Radius is the measure of the diameter it is commonly used to find the area o ## Review from student Studypool Student " Thank you, Thank you, for top quality work, this is your guy!! " 1823 tutors are online ### Other Documents 05/20/2015 05/20/2015 05/20/2015 05/20/2015 05/20/2015 05/20/2015 05/20/2015 05/20/2015 Brown University 1271 Tutors California Institute of Technology 2131 Tutors Carnegie Mellon University 982 Tutors Columbia University 1256 Tutors Dartmouth University 2113 Tutors Emory University 2279 Tutors Harvard University 599 Tutors Massachusetts Institute of Technology 2319 Tutors New York University 1645 Tutors Notre Dam University 1911 Tutors Oklahoma University 2122 Tutors Pennsylvania State University 932 Tutors Princeton University 1211 Tutors Stanford University 983 Tutors University of California 1282 Tutors Oxford University 123 Tutors Yale University 2325 Tutors

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