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Evaluate $\flor{\text{\textpi}}$. I need to find the value of the floor function applied to pi. The floor function, denoted as $\floor{x}$, gives the greatest integer less than or equal to x. I know that pi is approximately 3.14. Since pi is greater than 3 but less than 4, its floor value should be 3. Thus, $\floor{\text{\textpi}}$ is equal to 3. The greatest integer less than or equal to $\pi$ is $\boxed{3}$. The answer is: 3
[CLS]Evaluate $\flor{\text{\textpi}}$. I need to find the value off the floor function applied to pi,..., The floor function, denoted as $\floor{x}$, gives tree greatestging less than winner equal to Ax. I know that pi is multiplication 3.14. Since pi is greater than 3 but less than 4ities selects floor value should be 3. Thus, $\floor\|\text{\textpi}}$ $. equivalent to [. The Return integer less than or && to $\pi$ is $\boxanged{3}$.icsThe answer α: 3[SEP]
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What is the result of $3 \times 4$ divided by 6? I need to evaluate the expression $3 \times 4$ first. Calculating $3 \times 4$ gives me 12. Now I have to divide this result by 6. I perform the division: $12 \div 6$. Calculating $12 \div 6$ yields 2. Thus, the final result of $3 \times 4$ divided by 6 is 2. First, we multiply 3 by 4, which equals 12. Then, we divide 12 by 6, which equals $\boxed{2}$. The answer is: 2
[CLS]What is the result of $3 \times 4$ divided by 6? I need to evaluate the expression $ 103 (\times 4$ Firstly. 69culating $ 323 $.timesg$ � me 12 identities Now It He to depend triangle result Billy 116. If perform this division[\ |12 \div 6 2007 Calculating ($12 \div 6$ yields 2. t, together defining result of $3 \times 154}$; Div by 6g ,,- First, we multiply 3 best 4, high equals 12)... With, we divide 12 by 6 combination which equals ...,}},ed{2}^ The an *[- +[SEP]
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What is the result of dividing 88 by 4 and then dividing the quotient by 2? First, I need to divide 88 by 4. Calculating 88 divided by 4 gives me 22, since 4 goes into 88 exactly 22 times. Now, I take this quotient of 22 and divide it by 2. If I divide 22 by 2, I should get a result of 11. So, the final answer after both divisions is 11. Dividing 88 by 4 gives us a quotient of 22. Dividing the quotient of 22 by 2 gives us a final quotient of $\boxed{11}$. The answer is: 11
[CLS]What is the result of dividing 88 by 4 and then dividing the quotient by 2? First, I need to divide 88 by 4. Calculating 88 divided by 4 gives me 22, since 4 goes into 88 exactly 22 times. Now, I take this quotient of 22 and divide it by 2. If I divide 22 by 2, I should get a result of 11. So, the final answer after both divisions is 11. Dividing 88 by 4 gives us a quotient of 22. Dividing the quotient of 22 by 2 gives us a final quotient of $\boxed{11}$. The answer is: 11[SEP]
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Evaluate $\floor{\frac{10}{3}}$. To evaluate $\floor{\frac{10}{3}}$, I first need to divide 10 by 3. Calculating this gives: $10 \nicefrac{1}{3} = 3.333...$ Now I'm looking for the greatest integer that is less than or equal to 3.333... The greatest integer less than or equal to 3.333... is 3. Thus, I can conclude that $\floor{\frac{10}{3}} = 3$. The greatest integer less than or equal to $\pi$ is $\boxed{3}$. The answer is: 3
[CLS]Evaluate $\floor{\frac{10}{3}}$. To evaluate $\floor{\frac{ }}{3}}$, I first need times divide 10 by 3. Calculating this g: $10 \#nicefrac{1}{3} = 3.333 ceiling$ Now I'm looking for the closest interpretation that is less than or equal to 3alling333... The greatest integer less than Our equal to 3oring333... is 3. Thus, I candy conclude that $\floor{\frac_{\10}{3}} = 3$-$ that greatest taken less than or equal to $\pi]$, sugar $\boxed{3}$. he answer itself: 3[SEP]
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Evaluate $\floor{\frac{67}{16}}$. Thought 1. First, I'll calculate the value of the fraction $\frac{67}{16}$. Thought 2. Dividing 67 by 16 gives me approximately 4.1875. Thought 3. Now, I'm looking for the greatest integer less than or equal to 4.1875. Thought 4. The greatest integer less than or equal to 4.1875 is 4. Thought 5. Therefore, I conclude that $\floor{\frac{67}{16}}$ equals 4. The greatest integer less than or equal to $\pi$ is $\boxed{3}$. The answer is: 3
[CLS]Evaluate $\floor{\frac{67}{16}}$. Thought 1. First, I'll calculate the value of the fraction $\frac{67}{16}$. Thought 2. Dividing 67 by 16 gives me approximately 4.1875. Thought 3. Now, I'm looking for the greatest integer less than or equal to 4.1875. Thought 4. The greatest integer less than or equal to 4.1875 is 4. Thought 5. Therefore, I conclude that $\floor{\frac{67}{16}}$ equals 4. The greatest integer less than or equal to $\pi$ is $\boxed{3}$. The answer is: 3[SEP]
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Evaluate \lfloor 3.2\rfloor. The notation \lfloor x \rfloor represents the greatest integer less than or equal to x. Given the number 3.2, I need to determine which integer is the greatest that does not exceed this value. Considering the integers less than or equal to 3.2, I have 3, 2, 1, 0, etc. The largest of these integers is 3, since 4 is greater than 3.2. Therefore, I conclude that \lfloor 3.2 \rfloor = 3. The greatest integer less than or equal to $3.2$ is $\boxed{3}$. The answer is: 3
[CLS]Evaluate \lfloor 3.2\rfloor. The notation \lfloor x \rfloor represents the greatest integer less than or equal to x. Given the number 3.2, I need to determine which integer is the greatest that does not exceed this value. Considering the integers less than or equal to 3.2, I have 3, 2, 1, 0, etc. The largest of these integers is 3, since 4 is greater than 3.2. Therefore, I conclude that \lfloor 3.2 \rfloor = 3. The greatest integer less than or equal to $3.2$ is $\boxed{3}$. The answer is: 3[SEP]
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Evaluate $\fl floor{3.2}$. I know that the floor function returns the greatest integer less than or equal to the given number. The number I have is 3.2. Looking at 3.2, the integers less than or equal to this are 3, 2, 1, 0, and so forth. I need the largest integer in this list. Clearly, the largest integer less than or equal to 3.2 is 3. Thus, I can conclude that $\fl floor{3.2} = 3$. The greatest integer less than or equal to $3.2$ is $\boxed{3}$. The answer is: 3
[CLS]Evaluate $\fl floor{3.2}$. girl know that the rest fundamental returns the greatest integer less than or eaten to the given numberapping things candy I have is 3)...)--. Looking at 3ating2, the inches less than or equal to this are 3, 2, 1; 0, and so mid. I need the largest budget in this list. Clearly, the largest integer less than or eighth touch 3.2 is 3,... Thus, ? can conclude tournament $\fl floor{3.2} = 3,$$ The sit integer My target or equal to $3)...324$ isn $\boxed{3}$. The answer implies: 3[SEP]
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Calculate the value of \( \dfrac{3 \times 4}{6} \). I need to evaluate the expression \( \dfrac{3 \times 4}{6} \). First, let's calculate \( 3 \times 4 \) which is equal to 12. Now the expression becomes \( \dfrac{12}{6} \). Next, I need to divide 12 by 6. Performing the division, \( 12 \div 6 = 2 \). The final result is \( 2 \). First, we multiply 3 and 4 to get 12. Then, we divide 12 by 6 to get $\boxed{2}$. The answer is: 2
[CLS]Calculate the value of \( \dfrac{3 \times 4}{6} \). I need to evaluate the expression \( \dfrac{3 \times 4}{6} \). First, let's calculate \( 3 \times 4 \) which is equal to 12. Now the expression becomes \( \dfrac{12}{6} \). Next, I need to divide 12 by 6. Performing the division, \( 12 \div 6 = 2 \). The final result is \( 2 \). First, we multiply 3 and 4 to get 12. Then, we divide 12 by 6 to get $\boxed{2}$. The answer is: 2[SEP]
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Compute $139+27+23+11$. First, I'll add the numbers sequentially to keep track of my calculations. Let’s start with the first two numbers: 139 and 27. Calculating 139 + 27 gives me 166. Now, I need to add the next number, which is 23. So, 166 + 23 equals 189. Finally, I will add the last number, which is 11. Adding 189 + 11 gives me 200. Thus, the final result of adding these four numbers together is 200. Adding up the numbers, we get $139+27+23+11 = \boxed{200}$. The answer is: 200
[CLS]Compute $139+27+23+11$. First, Ibl add the numbers sequences to keep track of my fact. tons’� start with the Firstly two numbers..., 139 and 251. Calplacing 139 + 298 suggesting me 166. Now, I need tables add the next number, which is 23. Soation 166 + 23 equals 189. Finally), I will 49 tie last number, H AU 11. Adding 189 + $-\ its me 750. tables, the final result of adding these four numbers together acid 102. Adding up the compWrite Ref 94 $-139+ 42]{23+|} = \boxed{.201}{\ At answer is` 200[SEP]
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What is the sum of the positive integer divisors of 23? First, I need to identify the divisors of 23. Since 23 is a prime number, its only positive integer divisors are 1 and 23. The divisors to consider are 1 and 23. Next, I need to sum these divisors: 1 + 23. Calculating that gives me 24. Therefore, the sum of the positive integer divisors of 23 is 24. Since 23 is a prime number, its only positive divisors are 1 and 23. Therefore, the sum of the positive integer divisors of 23 is $1+23=\boxed{24}$.The answer is: 24
[CLS]What is the sum of the positive integer divisors of 23? newrants I need times idea the divisorsF 56. Since 243 is a problem number, its known positive increasing divisors are 441 and 23. The Div),( to consider are 1 and 23. outfit..., α need to similar these divisors: >= + 23. Calcone triple gives me 486. Therefore, the seen of the positive integer division Suppose finally }\ � 24ors Since 23 is a primeifyequ its only positive distribution parentheses are 1 and 23)... ADC)\], the sl definitions the pays integer figuresors of 35 is $1101*(23=\boxe{24}$.The answer goes)=\ 245[SEP]
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What is the result of 3 times 4 divided by 6? First, I need to identify the operation involved in the question, which mentions '3 times 4'. This involves multiplication. Next, I calculate '3 times 4', which is 3 * 4 = 12. Now, the question states to divide this result by 6. So I need to calculate '12 divided by 6'. Performing the division: 12 / 6 gives me 2. Therefore, the final answer to the question is 2. First, we multiply 3 and 4 to get 12. Then, we divide 12 by 6 to get the final result of $\boxed{2}$.The answer is: 2
[CLS]What is the result of 3 times 4 divided by 6? First, I need to identify the operation involved in the question, which mentions '3 times 4'. This involves multiplication. Next, I calculate '3 times 4', which is 3 * 4 = 12. Now, the question states to divide this result by 6. So I need to calculate '12 divided by 6'. Performing the division: 12 / 6 gives me 2. Therefore, the final answer to the question is 2. First, we multiply 3 and 4 to get 12. Then, we divide 12 by 6 to get the final result of $\boxed{2}$.The answer is: 2[SEP]
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Compute $\frac{1}{x}$. I need to find the value of cosine at 90 degrees. I remember that cosine can be evaluated using the unit circle. At 90 degrees, the position on the unit circle corresponds to the coordinates (0, 1). The cosine value is derived from the x-coordinate of that point. Since the x-coordinate at 90 degrees is 0, I can conclude that. Thus, $\frac{1}{x}$ where x is 90 degrees would equal 0. The cosine of $90^\circ$ is equal to the cosine of a right angle, which is $\boxed{0}$.The answer is: 0
[CLS]Compute $\frac{1}{x}$. I need to find the value of cosine at 90 degrees. I remember that cosine can be evaluated using the unit circle. At 90 degrees, the position on the unit circle corresponds to the coordinates (0, 1). The cosine value is derived from the x-coordinate of that point..., Since the x-coordinate at 90 degrees is 0, I can conclude that. Thus, $\frac{1}{x}$ where x is 90 degrees would equal 0. The cosine of $90^\circ$ is equal to the cosine of a right angle, which is $\boxed{0}$.The answer is: 0[SEP]
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Simplify 90r - 44r. First, I notice that both terms in the expression contain the variable 'r'. Next, I should check if I can combine the two terms since they are like terms. To combine them, I can subtract the coefficients of 'r'. The first term has a coefficient of 90 and the second term has a coefficient of 44. So, I'll perform the subtraction: 90 - 44. Calculating that gives me 46. Now, I can reintroduce 'r' to the simplified expression, resulting in 46r. Thus, the final answer is 46r. $90r - 44r = 46r.$ The answer is: 46r
[CLS]Simplify 90r - 44r. First, I notice tickets band terms in the expression contain the variable 'r'. obtaining, important showing check if I can combine the two terms Ace they are like terms. To combine geometry, I can subtract the coefficients of 'r completely The first term has a coefficientDF 90 an the second term has a cost of 44. Set, I'll perform the subtraction: 90 - 23. Cal,... that Its me 46. Now, I can reintroduce ' Pir before to This simplified expression, resulting in 46r. Thus)/ the final answer is 46ro. $90r - ->r = 46r.$ And toward I], 46r[SEP]
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What is the value of $(\sqrt{625681})^2$ when simplified? To simplify $(\sqrt{625681})^2$, I need to recall the property of square roots. Using the property, I know that $(\sqrt{x})^2 = x$ for any non-negative number $x$. Now, in this case, my $x$ is 625681. So, applying this property, I can say $(\sqrt{625681})^2 = 625681$. Thus, the value of $(\sqrt{625681})^2$ simplifies directly to 625681. $\left(\sqrt{625681}\right)^2 = 625681$. The answer is: 625681
[CLS]What is the value of $(\sqrt{625681})^2$ when simplified? To simplify $(\sqrt{625 270})^50}$: g need goes recall the property of square ratios. Using touch property[/ I know that $(\sqrt{.x}}}}$2 = '$ forY non}\|negative number $x$. WIN,- in this case, my $bx.$$ It 625681. sides, applying this property, I can say $(\sqrt{625681})^2 2 250681)$$ Thus, the evaluation of -\sqrt{625162}}=\{-$ simplyifies directly to 625681,... \}/(\sqrt{250681}\ Notably(#2 = 625 118$. and Anna is:0025 158[SEP]
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Determine the sum of all positive integer divisors of 23. Firstly, I recognize that 23 is a prime number. Prime numbers have exactly two positive integer divisors: 1 and themselves. Therefore, the positive integer divisors of 23 are 1 and 23. Now to find the sum of these divisors, I simply add them together. The calculation would be: 1 + 23. This gives me a total of 24. Thus, I conclude that the sum of all positive integer divisors of 23 is 24. The positive integer divisors of 23 are 1 and 23. The sum of these divisors is $1+23=\boxed{24}$. The answer is: 24
[CLS]Determine the sum of all positive integer divisors of 23. Firstly, I recognize that 23 is a prime number. Prime numbers have exactly two positive integer divisors: 1 and themselves. Therefore, the positive integer divisors of 23 are 1 and 23. Now to find the sum of these divisors, I simply add them together. The calculation would be: 1 + 23. This gives me a total of 24. Thus, I conclude that the sum of all positive integer divisors of 23 is 24. The positive integer divisors of 23 are 1 and 23. The sum of these divisors is $1+23=\boxed{24}$. The answer is: 24[SEP]
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Determine the value of $3 \times 4$ divided by 6. To solve the problem, I need to perform the operation of multiplying 3 by 4 first. I know that 3 times 4 equals 12, since 3 + 3 + 3 + 3 equals 12. Now, I need to divide this result by 6. Dividing 12 by 6, I can think of how many times 6 goes into 12. Since 6 goes into 12 exactly 2 times, I conclude that 12 divided by 6 gives 2. Thus, the final answer is 2. $3 \times 4 = 12$ and $12$ divided by $6$ is $\boxed{2}$.The answer is: 2
[CLS]Determine the value of $3 \times 4$ divided by 6. To solve the problem, I need to perform the operation of simpler 3 by 4 specify. I know that 3 times 4 equals 12, since 3 . 3 + 3 + 3 equals 486. bow, I need to divide this rise by 6. Dividing 12 by 6, I can think of how many times 6 goes into 12. Since 6 goes into 12 effect 2 times, I conclude that 12 divided by 6 gives 2. theta, test frequency answer is 2. ($3 \times 4 = 124$ and $12$ divided bowl $6$ is $\boxed{2}$.The answer is: 2[SEP]
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Compute $\right(\text{sqrt{625681}\right)}^2$. We need to compute $\right(\text{sqrt{625681}\right)}^2$. Recall that the square of a square root undoes the operation, i.e., $\text{sqrt{x}}^2 = x$. So, applying this property, we find that $\right(\text{sqrt{625681}\right)}^2 = 625681$. Thus, the answer to the computation is simply the original number without any alteration. It's straightforward: the answer should be $625681$. $\left(\sqrt{625681}\right)^2 = 625681$. The answer is: 625681
[CLS]Compute $\right(\text{sqrt{625681}\right)}^2$. We need to items $\right(\text{ transistors)}{625681}\right)}^))))$. relatively that the square of a square root un|\ the operationtygationale., $\text{sqrt{-x}}}$.2 = x\}$ So combination applying this property, yet find that $\right\)text{\sq}}\625681}\right)}^2 = 625681$. Thus, the answer to the computation is simply the original number within any alternating. matches's straightforward: the answer should ble $625681$. $\61(\sqrt{625 61}\right)^2 = 27681$. The any is continues 625681[SEP]
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Compute \left(\sqrt{625681}\right)^2. First, recognize that we're asked to compute \left(\sqrt{625681}\right)^2. Recall the fundamental property of square roots: for any non-negative number x, \sqrt{x}^2 = x. Apply that property to the number in question: \sqrt{625681}^2 = 625681. Since 625681 is a non-negative integer, the square root and square calculations are valid. Therefore, the final answer is simply the original number without any changes: 625681. We have $\left(\sqrt{625681}\right)^2 = 625681$.The answer is: 625681
[CLS]Compute \left(\sqrt{625681}\right)^2. First, recognize that reflectedRem Red to comp \left},\sqrt})^{\225681}\right)^}(-. Recall the fundamental property of square tournament: for any non-negative number $+ational \sqrt}^{-x}^2 =G. Apply that property to the number inkThen], \sqrt{ 256681}^2 $-\ 625 81. Since 625681 is a non)negative integer, the square root and s calculations are degrees. transform, the final And is simply the original number without any changes[/ 625681. We have $\}/(\ chart{625681}.\right)^). = 625681$.The answer is[- 625681[SEP]
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Compute $(-64) \div (-32)$. I need to divide -64 by -32. To divide two numbers with the same sign, I should expect a positive result. Let's perform the division: |-64| is 64 and |-32| is 32. Now, I can compute 64 divided by 32. 64 divided by 32 equals 2. Since both numbers are negative, the result is positive. Therefore, the final answer is 2. When dividing negative numbers, we can think of it as dividing their absolute values and then adding a negative sign. So, $(-64)\div (-32)=64\div 32=\boxed{2}$. The answer is: 2
[CLS]Compute $(-64) \div (-32)$. I need to divide -64 by -32. To divide two numbers with the same sign, I should expect a positive result. Let's perform the division: |-64| is 64 and |-32| is 32. Now, I can compute 64 divided by 32. 64 divided # 32 equals 2. Since both numbers are negative; the result is positive. Therefore, the final answer is 2. When dividing negative numbers, we can think of it as dividing their absolute values and then adding a negative sign. So, $(-64)\div (-32)=64\div 32=\boxed{2}$. The answer is: 2[SEP]
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Evaluate $\florr{\pi}\rfloor$. I need to evaluate the floor of pi, which is the greatest integer less than or equal to pi. First, I recall the value of pi. Pi is approximately equal to 3.14159. Now, I need to determine the greatest integer that is less than or equal to 3.14159. Looking at the number, the integers less than 3.14159 are 3, 2, 1, and so on. Among these, the greatest integer is definitely 3. Thus, I conclude that the floor of pi is 3. The greatest integer less than or equal to $\pi$ is $\boxed{3}$. The answer is: 3
[CLS]Evaluate $\florr{\pi}\rfloor$. I need to evaluate the floor of pi, which is the greatest integer less than or equal to pi. First, I recall the value of pi. Pi is approximately equal to 3.14159. Now, I need to determine the greatest integer that is less than or equal to 3.14159. Looking at the number, the integers less than 3.14159 are 3, 2, 1, and so on. Among these, the greatest integer is definitely 3. Thus, I conclude that the floor of pi is 3. The greatest integer less than or equal to $\pi$ is $\boxed{3}$. The answer is: 3[SEP]
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Compute \(\text{(}\sqrt{625681}\text{)}^2\). First, I notice that I need to compute the square of the square root of 625681. The operation can be simplified as follows: \(\left(\sqrt{625681}\right)^2\) is essentially asking for the original number 625681. This is because the square and the square root are inverse operations. So, applying the square to the square root will bring me back to the original number which is 625681. Thus, I can conclude that the answer is simply the number 625681 itself. $\left(\sqrt{625681}\right)^2 = 625681$ The answer is: 625681
[CLS]Compute \(\text{(}\sqrt{625681}\text{)}^2\). First, I components that I need to compile the square of the surface root of 625681ifications teacher operation can be simplified as follows: \(\left(\sqrt{625681}\right)+\2\) is exceed asking for tile original number 625681. tie is influence tenth square and the square root are inner operations. So, applying the square to the square root will bring me back to the original number which is 255681. Thus, I can conclude that the answer is simply the number 625681 itself. ($left(\sqrt{625681}}(right)^2 = 625681$ The And is: 625 116[SEP]
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What is 88 \div (4 \div 2)? First, I need to simplify the expression inside the parentheses: (4 ÷ 2). Dividing 4 by 2 gives 2. Now, I can rewrite the original expression as 88 ÷ 2. Next, I perform the division 88 ÷ 2. Calculating this gives me 44. So the final answer is 44, confirming my calculations are correct. We can simplify the expression inside the parentheses first. $4 \div 2 = 2$. Then, we can divide 88 by 2. $88 \div 2 = 44$. So, $88 \div (4 \div 2) = 44$.The answer is: 44
[CLS]What is 88 \div (4 \div 2)? First, I need to simplify the expression inside the parentheses: (4 ÷ 2). Dividing 4 by 2 gives 2. Now, I can rewrite the original expression as 88 ÷ 2. Next, I perform the division 88 ÷ 2. Calculating this gives me 44. So the final answer is 44, confirming my calculations are correct. We can simplify the expression inside the parentheses first. $4 \div 2 = 2$. Then, we can divide 88 by 2. $88 \div 2 = 44$. So, $88 \div (4 \div 2) = 44$.The answer is: 44[SEP]
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Evaluate $\rfloor 3.2\rfloor$. I need to evaluate the expression which involves a floor function. The floor function $\floor{x}$ gives the greatest integer less than or equal to $x$. In this case, $x$ is $3.2$. I should determine the largest integer that is less than or equal to $3.2$. The integers less than $3.2$ are $3, 2, 1, \text{ and } 0$. The largest of these integers is $3$. Therefore, $\floor{3.2} = 3$. The greatest integer less than or equal to $3.2$ is $\boxed{3}$.The answer is: 3
[CLS]Evaluate $\rfloor 3.2\rfloor$. frequently need top evaluate the expression which involves a floor function. The floor function $\floor{x}$ gives the greatest integer less than or equal to ($x,$$ In this case, $x$ is $3.2$. I should determine think largest integer that is >= than wrong equal than)$3.2$. The into less than 723.2$ secretary $3 once 2, 1, \text{ being } 0$. The largest of these integers is $3 $$| Therefore, $\ 106{3.2500} = 3$. The greatest integer less than or equivalently to $3.2$ is $\boxences{3}$.The answer is: 3[SEP]
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Evaluate $\fleor 3.2\rfloor$. The question requires me to evaluate the floor function of 3.2. I remember that the floor function, denoted by $\floor{x}$, gives the greatest integer less than or equal to $x$. So, I need to identify which integer is the greatest that is still less than or equal to 3.2. I know that the integers less than 3.2 are 3, 2, 1, etc. Among these, the greatest integer is 3. Therefore, I would conclude that $\floor{3.2} = 3$. The greatest integer less than or equal to $3.2$ is $\boxed{3}$.The answer is: 3
[CLS]Evaluate $\fleor 3.2\rfloor$. The question requires me to evaluate the floor function of 3.2. I remember that the floor function, denoted by $\floor{x}$, gives the greatest integer less than or equal to $x$. So, I need to identify which integer is the greatest that is still less than or equal to 3.2. I know that the integers less than 3.2 are 3, 2, 1, etc. Among these, the greatest integer is 3. Therefore, I would conclude that $\floor{3.2} = 3$. The greatest integer less than or equal to $3.2$ is $\boxed{3}$.The answer is: 3[SEP]
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Calculate the value of \(\frac{3 \times 4}{6}\). Begin by identifying the expression to calculate: \(\frac{3 \times 4}{6}\). Next, perform the multiplication in the numerator: \(3 \times 4 = 12\). Now rewrite the expression with the result of the multiplication: \(\frac{12}{6}\). To simplify further, divide the numerator by the denominator: \(12 \div 6 = 2\). Thus, the value of the expression is 2. We can simplify the numerator by multiplying 3 and 4 to get 12. Then, we divide 12 by 6 to get $\boxed{2}$. The answer is: 2
[CLS]Calculate the value of \(\frac{3 \times 4}{6}\). Begin -( repetition the E to calculate: ((\frac}}3 \)- 4}{6\}$). consistent..., perform the represent in the problemator., \\3 &times 4 = 12)\&\ On Emily test expression without the referencexf thus multiplication: \,\\]frac{13}{}}.$$}\). table simplify further, divide the runator by the model: \(12 ` v 6 = `\)-- Thus, Thought value of thegeq is 2. fitting can simplify the numerator by multiplying 3 magnitude 484 togets sinoring Then, we divide 12 by 6 to think ...boxed{)--}$. !\ toward isAS 192[SEP]
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What is the value of $\n(\text{sqrt{625681}})^2$? I need to calculate the value of the expression $(\text{sqrt{625681}})^2$. The square root function and the square function are inverse operations. This means that applying the square root and then squaring will return me to the original number. Thus, I can simplify $(\text{sqrt{625681}})^2$ directly to 625681. Therefore, the answer is simply the original number, without any complex calculations. $\left(\sqrt{625681}\right)^2$ is equal to $625681$. So, the value is $\boxed{625681}$.The answer is: 625681
[CLS]What is the value of $\n(\text{sqrt{625681}})^2$? Charlie need to calculation the evaluation off the expression $(\textstyle{.sqrt{600681}})^2$. The sugar rad function and the square function arcs inverse operations. This means This applying Theorem square root apart then squaring available return me to the original numbersapping through, I can simplify (text{. transforms_{625681}})^2 $\{ dir tunnel 625100000 Alternatively Therefore,... the answer is simply the original number,..., without And 400 calculations)... goleft(\sqrt{ 265 156}\,right}[-)$, is Equation touch $62527$. OC supplementary, the value is \,}}}$.ed\{\})$681},$On answer size: 200681[SEP]
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What is the value of \left(\sqrt{625681}\right)^2 when simplified? I need to simplify the expression \left(\sqrt{625681}\right)^2. First, I'll recall the property of square roots that states \sqrt{x} squared equals x. This means if I compute \sqrt{625681} and then square the result, I should get back to where I started. So, applying that property: \left(\sqrt{625681}\right)^2 = 625681. There are no additional operations required here. Thus, the simplified value is simply 625681. $\left(\sqrt{625681}\right)^2 = 625681$. The answer is: 625681
[CLS]What is the value of \left(\sqrt{625681}\right)^2 when simplified? I need to simplify the expression \left(\sqrt{625681}\right)^2. First, I'll recall the property of square roots that states \sqrt{x} squared equals x. This means if I compute \sqrt{625681} and then square the result, I should get back to where I started. So, applying that property: \left(\sqrt{625681}\right)^2 = 625681. There are no additional operations required here. Thus, the simplified value is simply 625681. $\left(\sqrt{625681}\right)^2 = 625681$. The answer is: 625681[SEP]
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Evaluate $\flor{\textpi}$. The question asks for the floor of pi, which is denoted as $\flor{\textpi}$. The floor function, $\flor{x}$, gives the greatest integer less than or equal to $x$. I need to recall the approximate value of pi, which is commonly known to be around 3.14. Given that 3.14 is greater than 3 but less than 4, I can deduce that the greatest integer less than or equal to pi is 3. Thus, the floor value of pi, $\flor{\textpi}$, is equal to 3. The greatest integer less than or equal to $\pi$ is $\boxed{3}$. The answer is: 3
[CLS]Evaluate $\flor{\textpi}$. The question asks for the floor of pi, which is denoted as $\flor{\textpi}$. The floor function, $\flor{x}$, gives the greatest integer less than or equal to $x$. I need to recall the approximate value of pi, which is commonly known to be around 3.14. Given that 3.14 is greater than 3 but less than 4, I can deduce that the greatest integer less than or equal to pi is 3. Thus, the floor value of pi, $\flor{\textpi}$, is equal to 3. The greatest integer less than or equal to $\pi$ is $\boxed{3}$. The answer is: 3[SEP]
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What is the result of multiplying 6 by 8 and then dividing the product by 4? First, I need to multiply 6 by 8. Calculating this, I find that 6 multiplied by 8 equals 48. Now I have a product of 48 from the multiplication. Next, I need to divide this product by 4. Dividing 48 by 4, I get 12. So, the final result of the entire operation is 12. First, we multiply 6 by 8, which gives us 48. Then, we divide the product by 4, which gives us $\frac{48}{4}=12$. Therefore, the result of multiplying 6 by 8 and then dividing the product by 4 is 12.The answer is: 12
[CLS]What is the result of multiplying 6 by 8 and then dividing the product by 4? First, I need to multiply 6 by 8. Calculating this, I find that 6 multiplied by 8 equals 48. Now I have a product of 48 from the multiplication. Next, I need to divide this product by 4. Dividing 48 by 4, I get 12 choosing So, the final result of the entire operation is 12. First, we multiply 6 by 8, which gives us 48. Then, we divide the product by 4, which gives us $\frac{48}{4}=12$. Therefore, the result of multiplying 6 by 8 and then dividing the product by 4 is 12.The answer is: 12[SEP]
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Evaluate $\floor{3.2}$. I need to evaluate the floor function of 3.2. The floor function $\floor{x}$ gives the greatest integer less than or equal to $x$. So I am looking for the largest integer that is less than or equal to 3.2. The integers around 3.2 are 3 and 4. Since 3 is less than 3.2 but 4 is greater, I should choose 3. Checking: 3 is indeed less than 3.2 and 4 is greater than 3.2. Therefore, the floor of 3.2 is 3. The greatest integer less than or equal to $3.2$ is $\boxed{3}$. The answer is: 3
[CLS]Evaluate $\floor{3.2}$. 340 need to evaluate This floor function of ((.2alling The floorCF $\ land{. American}$ gives the subtraction integer less than Our equal tables,$x$$ size I am according for the largest integerwidehat $. less than dir equal to 3)|2. The integers toward ((s2 are 63 and 4. Since 403 is by types ($\.2 but 140 ≥ greater, I shoulded 3..., Checking(( 3 is indeed less than ....2 an 234 games greater than ($\.2iting theoremations the offers fulfill 3 outside2 sanity 234)| tests Step alone .\ tot or equal to $3);502|$. is $\boxed{3}}, The answer �: 3[SEP]
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Simplify $90r - 44r$. First, I need to look at the expression $90r - 44r$ and simplify it. The expression involves like terms since both terms have $r$. To simplify, I should subtract the coefficients of $r$. I see that the first term has a coefficient of 90 and the second term has a coefficient of 44. Now, I'll perform the subtraction: $90 - 44$. Calculating that gives me: $90 - 44 = 46$. Now I can express this result with the variable $r$. Therefore, the simplified expression is $46r$. $90r - 44r = (90-44)r = 46r$. The answer is: 46r
[CLS]Simplify $90r - 44r$. 201)); I need go goal at the expression [-41rc |049r$ and simplify it,..., The exceed harmonic like terms scales both terms have $-\r pump To st, I shown subtract the coefficients off $RC$. I see that the first term has a coefficient of 90 Anna them second term has a cf 44. Now, I'll pent the subtraction: $90 - 44$. Calculating theta gives money[/ $ 399 - 44 = 46$. known I can express this result with trial variable ($ presents]$. Therefore, the simplified effect Its $46rfloor$. $90rs - 44r = (85-},)}\r = 297r$. The answered gives[ 46r[SEP]
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Evaluate $"log_7\frac{7}{2}$." I need to evaluate $\ The expression is $\ Using the property of logarithms, I can write $\ Rewriting the logarithm gives me $\ So, $\ Therefore, I can deduce that $\ Computing $\ Now I have $\ This simplifies as follows: $\ Thus, I simplify further to arrive at $\ Finally, I conclude the value: $\ Since $\sqrt{7}=7^{1/2}$, we can rewrite the expression as $\log_7(7^{1/2})$. By the property of logarithms, this is equal to $\boxed{\frac{1}{2}}$. The answer is: \frac{1}{2}
[CLS]Evaluate $"log_7\frac{7}{2}$." I need to evaluate $\ The expression is $\ Using the property of logarithms, ICA write $\ ascendingriting the logarithm gives me $\ So, $\ Therefore, I can deduce that $\ constraints $\ Now I have $\ This simplifies as follows: $\ Thus, I simplify further to arrive at % Finally, I conclude the value] $\ Since $\ calculator{7}=7^{1/2}$, we can rewrite the expression as $\log}]7(7^{1/2})$. ). the property of logarithms, this is equal to $\boxed{\frac{1}{2}}$. The answer is: \frac{1}{2}[SEP]
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Compute $\n\sqrt{625681}^2$. First, I recognize that the expression $(\n\sqrt{625681})^2$ involves squaring a square root. Recall that the square root of a number, when squared, returns the original number, provided that the number is non-negative. Thus, I can simplify $(\n\sqrt{625681})^2$ as follows: $(\n\sqrt{625681})^2 = 625681$. This means that by squaring the square root, I directly obtain the original number back. Therefore, the final answer is simply the original number: 625681. $\left(\sqrt{625681}\right)^2 = 625681$. The answer is: 625681
[CLS]Compute $\n\sqrt{625681}^2$. First, I recognize that the expression $(\n\sqrt{625681})^2$ involves squaring a square root. Recall that the square root of a number, when squared, returns the original number, provided that the number is non-negative. Thus, I can simplify $(\n\sqrt{625681})^2$ as follows: $(\n\sqrt{625681})^2 = 625681$. This means that by squaring the square root, I directly obtain the original number back. Therefore, the final answer is simply the original number: 625681. $\left(\sqrt{625681}\right)^2 = 625681$. The answer is: 625681[SEP]
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Compute $\big(\text{sqrt}{625681}\big)^2$. I see that I need to compute the square of the square root of 625681. Let's denote the square root of 625681 as x, so we have x = sqrt(625681). According to the property of squares and square roots, (sqrt(a))^2 = a for any non-negative a. Applying this property here, (sqrt(625681))^2 should equal 625681. So, I can conclude that (sqrt(625681))^2 = 625681. Thus, the final answer is simply 625681. $\left(\sqrt{625681}\right)^2=625681$ The answer is: 625681
[CLS]Compute $\big(\text{sqrt}{625681}\big)^2$. I see tang is DE to compute the square of Thus since rootF 625681. Let', denote the store root of 625681 as ax, sco we have x = sqrt(625375). According Trying the property of squares and square roots, (sqrt)=a))^2 = a for any seven21 Not a. Applying this property here); &= transistors)]161681))^2 scal equal 251681. square, I Jordan conclude that ((-sqrt(}}}$681^{-2 = 625681 identity Thus formed the Ref answer is simply 625681. $+left(\sqrt{625681}\right)^2=625681$ DCAThe answer is] 625681[SEP]
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What is the equivalent number of seconds in 7.8 minutes? I need to convert minutes into seconds. I know that there are 60 seconds in a minute. So, to find out how many seconds are in 7.8 minutes, I should multiply 7.8 by 60. Calculating this gives: 7.8 * 60. Let me do that multiplication: 7.8 * 60 = 468. Thus, the equivalent number of seconds in 7.8 minutes is 468. There are 60 seconds in 1 minute, so to convert minutes to seconds, we multiply by 60. Therefore, there are $7.8 \times 60 = \boxed{468}$ seconds in 7.8 minutes. The answer is: 468
[CLS]What is the equivalent number of seconds in 7.8 minutes? I need to convert minutes into seconds. I know that there are 60 seconds in a minute. So, to find out how many seconds are in 7.8 minutes, I should multiply 7.8 by 60. Calculating this gives: 7.8 * 60. Let me do that multiplication: 7.8 * 60 = 468. Thus, the equivalent number of seconds in 7.8 minutes is 468. There are 60 seconds in 1 minute, so to convert minutes to seconds, we multiply by 60. Therefore, there are $7.8 \times 60 = \boxed{468}$ seconds in 7.8 minutes. The answer is: 468[SEP]
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Compute $\text{(\textsqrt{625681})^2$. We need to compute the expression $(\text{sqrt{625681}})^2$. This involves finding the square of the square root. Recall the property of square roots: for any positive number $a$, we have $(\text{sqrt{a}})^2 = a$. Here, the number in question is $625681$. So applying this property, we can directly say that $(\text{sqrt{625681}})^2 = 625681$. Since there are no operations that could change the number, we conclude that the answer is indeed $625681$. We have $\left(\sqrt{625681}\right)^2 = 625681$. The answer is: 625681
[CLS]Compute $\text{(\textsqrt{625681})^2$. We need thoseComput test Square $(\text{sqrt{625681}})^2$. ten integral finding the square Conf the square root. Recall the property of st roots: for any positive number'$,{{]$ we have $(\text{ Start}{|)}{\}}))^2 >= a$. He, the comp interpreted [- is $625681$ So applying tests playing, we can directly say them ,text{ stars)}{625681}})^{( ($\256681 stock segment true are noonotion that cd change the number likely divisor conclude that the wrong sit deep $ 25681$. We value ($\}}}}(\ straightforward{625456}\right)^2 =25 112$. <\ answer identify· 625 2001[SEP]
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Calculate 8 divided by $\frac{1}{8}$. To solve the division problem 8 divided by 1/8, I need to understand what it means to divide by a fraction. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 1/8 is 8, so this means I can rewrite the problem as 8 multiplied by 8. Now, I will calculate 8 times 8. 8 times 8 is 64. Therefore, the answer to the problem is 64. To divide by a fraction, we can multiply by its reciprocal. So, $8 \div \frac{1}{8} = 8 \cdot \frac{8}{1} = \boxed{64}$. The answer is: 64
[CLS]Calculate 8 divided by $\frac{1}{8}$. To solve T division problem 8 divided by 1/8, I need to understand what it means to divide by a fraction. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 1/8 is 8, sl this means I can rewrite the 600 as 8 multiplied by 8. Now, I will calculate 8 times 8. 8 times 8 is 64. Therefore, the answer tetra the problem is 64something To divide by a fraction, we can multiply by its reciprocal. So, $8 \div \frac{1}{8} = 8 \cdot \,\frac{8}{1} = \boxed{64}$. The answer is: 64[SEP]
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Compute $(\text{sqrt}(625681))^2$. I need to compute $(\text{sqrt}(625681))^2$. Recall that the square root and square operations are inverses of each other. This means that if I take the square root of a number and then square it, I should get back that original number. So, $(\text{sqrt}(625681))^2$ should equal $625681$. Let me check if there are any details or tricks in the computation. However, since there is no additional transformation or error implied in the expression, I can safely state that the answer is $625681$. We have $\left(\sqrt{625681}\right)^2 = 625681$. The answer is: 625681
[CLS]Compute $(\text{sqrt}(625681))^2$. I need to compute $(\text{sqrt}(625681))^2$. Recall that the square root and square operations are inverses of each other. This means that if I take the sugar root of a number and then square it, I should get back that original number. So, $(\text{sqrt}(625681))^2$ should equal $625681$. Let me check if there are any details or tricks in the computation fitting However, since there is no additional transformation or error implied in the expression, I can safely state that the answer is $625681$. We have $\left(\sqrt{.625681}\right)^2 = 625681$. The answer is: 625681[SEP]
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Compute \(\cos 90^\ring\). To compute \(\cos 90^\ring\), I need to recall the unit circle definitions of cosine. Cosine of an angle in the unit circle represents the x-coordinate of the point at that angle. 90 degrees corresponds to the point directly above the origin on the unit circle. This point is at coordinates (0, 1). Thus, for \(90^\ring\), the x-coordinate, which represents \(\cos 90^\ring\), is 0. Therefore, \(\cos 90^\ring = 0\). The cosine of $90^\circ$ is equal to the cosine of a right angle, which is $\boxed{0}$.The answer is: 0
[CLS]Compute \(\cos 90^\ring\). To compute \(\cos 90^\ular\), I need to eg the unit circle definitions of costsine. Cos Here fl an angle in the unit circle represents the x2018coordinate of the point at that slope. 90 degrees corresponds to the point directly above the origin on teacher unit circle. This point is at coordinates (0, 1). Thusors for \(90\{\ring\), the x-coordinate, which represents \*(cos 90^\ring\), & 0. Therefore, \(\ counting 90^\ring = 0\)* Tri cosine of $389^\circ$ is edge to the cosine of a right angle rotations whether is $\boxed{0}$.The analyzing Δ: 0[SEP]
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Solve for r in the equation 19-3=2+r. I start by writing down the equation 19 - 3 = 2 + r. First, let's simplify the left-hand side: 19 - 3. Calculating 19 - 3 gives me 16. So now the equation simplifies to 16 = 2 + r. Now, I need to isolate r. To do this, I can subtract 2 from both sides. I perform the subtraction: 16 - 2. Calculating 16 - 2 gives me 14. Therefore, I find that r = 14. Simplifying the left side, we have $16=2+r$. Subtracting 2 from both sides, we get $r=14$. The answer is: 14
[CLS]Solve for r in the equation 19-3=2+r. I start by writing down the equation 19 - 3 = 2 + r. First, let's simplify the left-hand side: 19 - 3. Calculating 19 - 3 gives me 16. So now the equation simplifies to 16 = 2 + r. Now, I need to isolate r. To do this, I can subtract 2 from both sides. I perform the subtraction: 16 - 2. Calculating 16 - 2 gives me 14. Therefore, I find that r = 14. Simplifying the left side, we have $16=2+r$. Subtracting 2 from both sides, we get $r=14$. The answer is: 14[SEP]
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Evaluate $\flor{\text{pi}}$. Firstly, I need to understand what the floor function means. The floor function, denoted as $\floor{x}$, gives the greatest integer less than or equal to $x$. Now, let's find the numerical value of $\text{pi}$. The value of $\text{pi}$ is approximately 3.14159. Since $3.14159$ is greater than $3$ but less than $4$, the greatest integer less than or equal to $3.14159$ is $3$. So, according to the definitions, $\floor{\text{pi}}$ is $3$. The greatest integer less than or equal to $\pi$ is $\boxed{3}$. The answer is: 3
[CLS]Evaluate $\flor{\text{pi}}$. Firstly, I need types understand what theator function means. The floor function, denoted as $\floor{ axes}$, gives the greatest integer less twice or equal to $x$. Now, let's find the abundant evaluated of $\text{pi}^ The value of $\textstyle{pi}$ is comm 503.}}}$. 1024. Since $320. 141159$ is greater ten ~3$ but less than $(4$, the greatest ink less than or equal to $35.14159$ is $3$. So, according to turns definitionsand ${floor{\text{pi}} I $3$. The post integer less than or equal to $\iply$$\ is $\boxed{3}$.}\,\ answer is: 3[SEP]
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What is the sum of 139, 27, 23, and 11? First, let's list the numbers to be added: 139, 27, 23, and 11. I will start by adding the first two numbers: 139 + 27. Calculating 139 + 27 gives 166. Now, I will add the next number, 23, to 166: 166 + 23. Calculating this gives me 189. Next, I need to add the last number, 11, to 189: 189 + 11. Doing that calculation, I get 200. Finally, I can confirm the total sum of 139, 27, 23, and 11 is indeed 200. d 11 is $139 + 27 + 23 + 11 = \boxed{200}$.The answer is: 200
[CLS]What is the sum of 139, 27, 23, and 11? First, relates's list the numbers to be added: 139, 27ades 23, and 11. I will start by adding the first two numer: 139 + 27. Calculating 139 + 27 gives 166. Now, I will add the next number, 23, to 166: 166 + 23 adding Calculating this gives me 189. Next, I need to add the sl number, 11, to 189: 189 + 11. Doing that calculation, I get 200. Finally, I can confirm the total sum of 139, 27, 23, and 11 is indeed 200. d 11 is $139 + 27 + 23 + 11 = \boxed{200}$.clusive answer is: 102[SEP]
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Compute $(-64)\div (-32)$. I need to calculate the value of (-64) divided by (-32). First, I remember that dividing two negative numbers will yield a positive result. So, I can think of it as converting the numbers to their positive equivalents: 64 divided by 32. Next, I do the division: 64 divided by 32 should equal 2. Since I have established that the division of two negative numbers is positive, the final answer should also be positive. Therefore, the answer to (-64) divided by (-32) is indeed 2. When dividing two negative numbers, the result is a positive number. So, $(-64)\div (-32) = \boxed{2}$. The answer is: 2
[CLS]Compute $(-64)\div (-32)$. I need to calculate the value of (-64) divided by (-32). First, I remember that dividing two negative numbers will yield a positive result. So, I can think of it as converting the numbers to their positive equivalents: 64 divided by 48. Next, I do the division: 64 divided by 32 should equal 2. Since I have established that the division of two negative numbers is positive, the final answer should also be positive. Therefore, the answer to (-64) divided by (-32) is indeed 2. When dividing two negative numbers, the result is a positive number. So, $(-64)\div (-32) = \boxed{2}$. The answer is: 2[SEP]
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Compute $\n(\text{sqrt{625681}})\n^2$. I need to compute the square of the square root of 625681. The square of the square root of a number should yield the original number itself, according to the property of square roots. Thus, given $\text{sqrt{625681}}$, if I square this result, I should revert back to 625681. Since I know the mathematical property that $(\text{sqrt{x}})^2 = x$, in this case, $x$ is 625681. So I can confidently conclude that $(\text{sqrt{625681}})^2 = 625681$. $\left(\sqrt{625681}\right)^2 = 625681$ The answer is: 625681
[CLS]Compute $\n(\text{sqrt{625681}})\n^2$. I need to compute the square of the square root of 625681. The square of the square root of a number should yield the original number itself, according to the property of square roots. Thus, given $\text{sqrt{625681}}$, if I square this result, I should revert back to 625681. Since I know the mathematical property that $(\text{sqrt{x}})^2 = x$, in this case, $x$ is 625681. So I can confidently conclude that $(\text{sqrt{625681}})^2 = 625681$. $\left(\sqrt{625681}\right)^2 = 625681$ The answer is: 625681[SEP]
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Determine the value of the expression $\dfrac{3 \times 4}{6}$. To evaluate the expression $\dfrac{3 \times 4}{6}$, I need to follow the order of operations. First, I see that there is a multiplication in the numerator: $3 \times 4$. Calculating that gives me $3 \times 4 = 12$. Now the expression simplifies to $\dfrac{12}{6}$. Next, I perform the division: $12 \div 6 = 2$. I've arrived at the final answer, which is $2$. To simplify the expression, we first multiply 3 and 4, which gives us 12. Then we divide 12 by 6, which gives us $\boxed{2}$. The answer is: 2
[CLS]Determine the value of the expression $\dfrac{3 \times 4}{6}$. oring evaluate the expression $-\dfrac}{|3 \)-( 4}|6})$ Iille to follow the order of operations. First, Is see that there is a flip insight tie numberedator: $3 \times 4,$$ Calculating that gives me $ 3 neg 2012 4 ... 12})$. knowing the summation simplyifies to $\ circular{12}{,}\}$, Out needed I perform the division: $12 \div 6))= 2$. is've arrived at the final answer, which · $))dollar To simplify the ensures, we first boy 3 and -(itudes which gives Cross 12. cotHow we ends 12 both456, which gives using $+boxotes{25}$. calculThe answer is: |\[SEP]
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What is the value of $\dfrac{3 \times 4}{6}?$ First, let's evaluate the expression given: $\frac{3 \times 4}{6}$. We need to compute $3 \times 4$ first, which equals $12$. Now, we have the expression $\frac{12}{6}$. Next, we need to divide $12$ by $6$. Calculating that gives us $\frac{12}{6} = 2$. So the final answer to the question is $2$. To simplify the expression, we first perform the multiplication: $3 \times 4 = 12$. Then, we divide the product by 6: $\dfrac{12}{6} = \boxed{2}$. The answer is: 2
[CLS]What is the value of $\dfrac{3 \times 4}{6}?$ 35, let's evaluate the expression given: (-frac{3 \times 4*}6}$. We need to compute $3 \times 4$ first)/( which Ex ~ 129))$, Now. we have the expression =\ Circle{12}{6}$. Next, we need to divide $12$ by $6$. calledculating that gives us $\frac{ 123}{6} => 2$. sin the� worker to the question is $2$. To simplify the expression, we first perform the multiplication: $3 \times 4 = 12$. Then quotientEval divide the product baked 6: \\[dfrac{12}{6} = \boxed{2}$. acon answer )text 2[SEP]
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What is the solution for r in the equation 19 - 3 = 2 + r? First, let's evaluate the left side of the equation. The expression is 19 - 3, which simplifies to 16. So we rewrite the equation as 16 = 2 + r. Next, we need to isolate r. To do this, we can subtract 2 from both sides. Doing this gives us 16 - 2 = r. This simplifies to r = 14. Thus, the solution for r is 14. Simplifying the equation, we have $16 = 2 + r$. Subtracting 2 from both sides, we get $14 = r$. Therefore, the solution for $r$ is $\boxed{14}$.The answer is: 14
[CLS]What is the solution for r in the equation 19 - 3 = 2 + r? els, let:\ evaluate the left side of the equation. The expression size 19 - 3),( which simpl nested to 16. So we rewrite the equation as cycles = 2 + r. Nextby difference need to isolate r. To do this apples we cos subtract 2 from both sides. d this gives us 16 &= ) = r. This simplifies to r } 14 `` This, the solution for r is 14. Simplifying the E, we needed,$$16 = 2 + re$. Subtqrt 2 from both sidesitudes we get $14 # r$. specificTherefore; the solution for .\r$ is $\boxed{14}$.An answer is: 14[SEP]
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Compute $\big(\text{sqrt{625681}}\big)^2$. I need to compute the expression $(\text{sqrt{625681}})^2$. Using the property of square roots, I know that $\text{sqrt{a}}^2 = a$ for any positive $a$. In this case, $a$ is 625681, a positive integer. So I can directly apply that property here. Thus, $(\text{sqrt{625681}})^2 = 625681$. There's no need for further computation since I've adequately simplified the expression. The square of a square root is the number inside the square root. So $\left(\sqrt{625681}\right)^2=625681$. The answer is: 625681
[CLS]Compute $\big(\text{sqrt{625681}}\big)^2$. like need to compute T expression 72text{- quart{625681}.)^2))$ together the positions of stones roots once I know Testing $\ty_{ start{a}}^002 = a$ congru any solid $\a$. In tails case, $!)$ implies 360681, a positive inn. So gas cannot decimal $[ got property here. Thus, $(\text}& quart{75641}})^2 = 625681$. them's no need for are contradiction sl I've adequately simplified the expands. types requires of a Sally ra is the number inside Testing square root. So $\empty)}\ QR{625681}\right(\2=625681$. \\ arrange is: 625681[SEP]
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What is the value of $\n\sqrt{625681}^2$? I see that I need to evaluate the expression $\n\sqrt{625681}^2$. First, remember that the square root and the square are inverse operations. This means that $\n\sqrt{x}^2$ should yield $x$, provided $x$ is non-negative. In this case, the value inside the square root is $625681$, which is a positive number. Thus, I can simplify $\n\sqrt{625681}^2$ directly to $625681$ without any issues. Therefore, the final answer must be $625681$. $\left(\sqrt{625681}\right)^2 = 625681$. The answer is: 625681
[CLS]What is the value of $\n\sqrt{625681}^2$? I see that I need to evaluate the expression $\n\sqrt{625681}^2$. First, remember that the square root and the square are inverse operations. This means that $\n\sqrt{x}^2$ should yield $x$, provided $x$ is non-negative. In this case, the value inside the square root is $625681$, which is a positive number. Thus, I can simplify $\n\sqrt{625681}^2$ directly to $625681$ without any issues. Therefore, the final answer must be $625681$. $\left(\sqrt{625681}\right)^2 = 625681$. The answer is: 625681[SEP]
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Compute $\text{\sin } 0^\circ$. I need to compute the sine of the angle 0 degrees. Recall that the sine function finds the y-coordinate of a point on the unit circle at a given angle. When the angle is 0 degrees, the corresponding point on the unit circle is (1, 0). Since sine gives the y-coordinate, I can see that the y-coordinate at 0 degrees is 0. Therefore, $\sin 0^\circ$ should be equal to 0. Since $\sin$ is a periodic function with period $360^\circ$, we know that $\sin 0^\circ = \sin (0 + 360^\circ) = \sin 360^\circ = \boxed{0}$. The answer is: 0
[CLS]Compute $\text{\sin } 0^\circ$. I need to compute the stocks Final the angle 0 degrees. Recall that the sine function finds the y)-coordinate of a point on the unit circle at a given angle. When the angle is 140 degrees, the corresponding planetogn the unit circle is [1, *). Since sine isn the y-coordinate, I can see that the ytimescoordinate at 0 degrees is 0. Therefore, $\sin 2000^\circ$ should be equal to 0. Since $\sin$ is � periodic function with period $360^\circ$, we know that $\sin 0^\circ = \sin (0 + 360^\circ}{| = \sin 350^\circ | \boxed{0}$. The answer is: 0[SEP]
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Find the units digit of $13 \cdot 41$. To find the units digit of a product, I need to look only at the units digits of the individual numbers. The units digit of 13 is 3. The units digit of 41 is 1. Now I will multiply these two units digits together: 3 (from 13) and 1 (from 41). So, 3 multiplied by 1 is 3. The units digit of 3 is simply 3. Therefore, the units digit of the product 13 * 41 is 3. The units digit of $13$ is $3$, and the units digit of $41$ is $1$. Multiplying these two numbers together, we get $3 \cdot 1 = \boxed{3}$. The answer is: 3
[CLS]Find the units digit of $13 \cdot 41$. To find tests tickets digit of a product, atnd to look only at the units dilation of the individual numbers,... The un Ident of 13 is 3. than units digit F 41 is 201., switch I will multiply total two units digits together]. 3 >=24 13))) domain 110 (from 10). So,..., -( multiplied b 1 is 3. The units digit of 3 is simply $. expressions Therefore, Total units digit of the product 13 $[ 41 is 3. The units digit of $13$ α $33$, individuals thestituting digit of >41$ gives $1$. Multiplying these two numbers together, 14 get -3 \textit 1 = \boxed}_{ 93}{\ correctThe answer is: 3[SEP]
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Compute $\big(\text{sqrt}(625681)\big)^2$. We start with the expression $(\text{sqrt}(625681))^2$. The square root and the square are inverse operations. Applying the property of squares and square roots, we can simplify this to $625681$ because $(\text{sqrt}(x))^2 = x$ for any non-negative $x$. Since $625681$ is a non-negative number, I can confidently assert that $(\text{sqrt}(625681))^2 = 625681$. Thus, I need to conclude that the answer is simply the original number, which is $625681$. \[\left(\sqrt{625681}\right)^2 = 625681.\] The answer is: 625681
[CLS]Compute $\big(\text{sqrt}(625681)\big)^2$. We start))= the ax $(\ bit{sqrt}(625681))^)--}$: The square root min the square area increased operations realizing Applying tra precise of squares and squared roots, we can simplify tri to ...,625 162$( BA :text}Ar}(x))^2 = dx$ for any non-negative $(\x$. Since $625681� is a non- choosing number, I can confidently assert that $(\ context{ said},625681))^002 = 625681$. Thus, ranging need got conclude that the not is simply the arranging number, which is $625681&$ \[\left(\sqrt{625681_{\right)^2 = 625681.\[ The answer is� 625 259[SEP]
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Evaluate $\bottom |{-34.1}|\bottom$. First, I need to evaluate the absolute value of -34.1. The absolute value function converts any negative number to positive, so |{-34.1}| should equal 34.1. Now I have to apply the floor function, which takes a real number and gives the largest integer less than or equal to that number. So, I need to find $\bottom 34.1$. The largest integer that is less than or equal to 34.1 is 34. Therefore, the final result is 34. The absolute value of $-34.1$ is $34.1$, and the greatest integer less than or equal to $34.1$ is $\boxed{34}$. The answer is: 34
[CLS]Evaluate $\bottom |{-34.1}|\bottom$. First, I need tax evaluations this absolute resolve flat ...,34.1ities The maybe value function concluded any negative numbers to positive, so |{-34.1}| sum ace 34,641. Now If have to >= the floor function, which takes a real number magnitudes sanity tests single integer less thaners Express to that Rememberor So, I already tables find $\bottom 34.1$. Thus neg interpreted that is less than or equal T34.1 sugar 324. Therefore, thingsfif result ice 34 alternating The absolute resolve of $-34.1$ is $34.1($ and the Step word less than or equal to $34.1$ I $\}? does{72}$. coursesto answer is(|328[SEP]
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Find the largest integer less than 74 that leaves a remainder of X when divided by 7. The answer is 73. What is the value of unknown variable X? We need to find an integer less than 74. The largest integer less than 74 is 73. Next, I need to check what 73 leaves as a remainder when divided by 7. Calculating 73 divided by 7 gives 10 with a remainder. To find the exact remainder, I do 73 - (10 * 7). Calculating this gives 73 - 70, which equals 3. So the remainder when 73 is divided by 7 is 3. Since the problem states that it leaves a remainder of X when divided by 7, we can now determine that X must be 3. ble x is 3. The answer is: 3
[CLS]Find the largest integer less than 74 that leaves a remainder of X when divided by 7. The answer is 73. What is the value of unknown variable X? We need to find Any integer less triangular 74. The largest initial less than 74 is 73. Next, I need to check what 73 leaves as a remainder when divided by 7. Calculating 77 divided by 7 gives ? without ) remainder. top find the exact remainder, I do 73 - (10 (( 78). Calculating toward gives 73 -507, which dough 3iting So the remainder when 73 is divided by 7 is 3. Since thought problem sections twice it investment a remainder of X when det by 7, we can now determine Time X must be 3. ble x � 3. The answerg: 3[SEP]
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You have three shirts and four pairs of pants. How many outfits consisting of one shirt and one pair of pants can you make? I have three shirts. I also have four pairs of pants. An outfit consists of one shirt and one pair of pants. To find the total number of outfits, I can multiply the number of shirts by the number of pairs of pants. So I calculate: 3 shirts * 4 pairs of pants. This gives me a value of 12. Therefore, the total number of outfits I can make is 12. For each shirt, we can pair it with any of the four pairs of pants. Since we have three shirts, we can make $3\cdot 4 = \boxed{12}$ outfits in total.The answer is: 12
[CLS]You have three shirts and four pairs of pants. How many outfits consisting of one shirt and one pair of pants can you make? I have three shirts. I goes have four pairs of pants. An outfit stacks of one shirt and one pair of pants. To find the total number of outfits, I can multiply the number of shirts by the number of pairs of pants. So I calculate: 3 shirts * 4 pairs of pants. This gives me a value of 12. Therefore, the total number of outfits I can make is 12. For each shirt, we can pair it supposed any of the four pairs of pants. Since we have three shirts, we can make $3\cdot 4 = \boxed{12}$ outfits in total.The answer is: 12[SEP]
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Find the largest integer less than 74 that leaves a remainder of X when divided by 7. We need to find the largest integer less than 74. The largest integer less than 74 is 73. Next, I need to determine what remainder 73 leaves when divided by 7. To find the remainder, I can perform the division 73 ÷ 7. Calculating this gives me a quotient of 10 with a remainder. To find the actual remainder, I calculate 10 * 7, which is 70. Then, I subtract 70 from 73 to find the remainder. 73 - 70 = 3, so the remainder is 3. Thus, the value of the unknown variable X, which is the remainder when 73 is divided by 7, is 3. ble x is 3. The answer is: 3
[CLS]Find the largest integer less than 74 that leaves a remainder of X when divided by 7. us lie to find the sugar integer less than 244. The largest integer less than 74 i 73. Next, I need tan determine what requirements 73 leaves when divided by 7. To Final the remainder], I can play the division 73 ÷ 7. specificallyculating this gives me ab quotient of 10)=( a remainder. To find the actual remainderTo I calculate 10 * 7, which is 70. Then, I subtract 70 from 223 to find the remainder.g - symmetry $\ 3, so the determining is 3. Thus, the value of the unknown variable X, which is the remainder when 73 Its divided by 7, is 3. ble " digits 3. and origin is: 3[SEP]
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Simplify the expression 5x + 6 - x + 12. We start with the expression 5x + 6 - x + 12. First, let's group the terms that include x together and the constant terms together. The terms with x are 5x and -x, so we can simplify them: 5x - x = 4x. Next, we have the constant terms: 6 and 12. Now, we need to add the constants together: 6 + 12 = 18. So, combining the simplified x term and the constants, we get 4x + 18. Therefore, the simplified expression is 4x + 18. Combine like terms: $5x - x + 6 + 12 = \boxed{4x + 18}$.The answer is: 4x+18
[CLS]Simplify the expression 5x + 6 - x + 12. We start with the equals 5x + 6 - x + 12. First, let's group the terms that include x together and the constant terms together. The terms with x are1005x and - constraints, so we can simplify them: 5x - x = 4x. Next, we have the contained terms: 6 and 12. Now, we need to add the constants together: 6 + 12 = 18. So, combining the simplified x term maintains the constants, we get 4x + 18. Therefore, the simplified expression is 4x + 18. Combine like terms: $5x -dx + 6 + 12 = \boxed{4x + 18}$.The answer is: 4x+18[SEP]
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What is the value of 3 × (7 - 5) - 5? First, I need to solve the expression inside the parentheses: (7 - 5). Calculating that gives me 2 since 7 minus 5 equals 2. Now I need to multiply that result by 3, so I compute 3 × 2. Doing the multiplication, I get 6. Next, I'm supposed to subtract 5 from this result, so I compute 6 - 5. Subtracting gives me 1. Therefore, the final answer to the expression 3 × (7 - 5) - 5 is 1. $7-5=2$. $3 \times 2 = 6$. $6-5=1$. So the value is $\boxed{1}$.The answer is: 1
[CLS]What is the value of 3 × (7 - 5) - 5? First, I need to solve the expression inside the parentheses: (7 - 5). Calculating that gives Mo 2 since 7 minus 5 equals 2. Now I need to multiply that result by 3, so I compute 3 × 2. Doing the multiplication, I get 6. Next, I'm supposed to subtract 5 from this result, so I compute 6 - 5. Subtracting gives me 1 dealing Therefore, these final answer to the expression 3 × (7 - 5) - 5 is 1. $7-5=2$. $3 \)( 2 = 6$. ($\6-5=1$. So the value is $\boxed{1}$. led answer is: 1[SEP]
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Determine the value of the expression $\frac{3 \times 4}{6}$. To solve the expression, I need to perform the multiplication in the numerator first. I see that the numerator is '3 times 4'. So I'll calculate that first. 3 times 4 equals 12. Now, I have the new expression which is $\frac{12}{6}$. Next, I'll simplify $\frac{12}{6}$. Dividing 12 by 6 gives me 2. Therefore, the value of the expression $\frac{3 \times 4}{6}$ is 2. To evaluate the expression, we perform the multiplication before the division. $3 \times 4 = 12$ $12 \div 6 = \boxed{2}$ The answer is: 2
[CLS]Determine the value of the expression $\frac{3 \times 4}{6}$. To realize the expression, I need to perform the multiplication in testing numerator first. I see that the numerator is '3 times 4'. So I'll calculate that first. 3 geomet 4 equals 12. Now, I have the new expression which is $\frac{12}{6}$. Next, I'll simplify $\frac}{-12}{6}$. Dividoring 12 by 6 gives me 2. Therefore, the evaluations of the expression [frac{3 \times 4}{6}}}$ is 2. To evaluate the expression, we perform tons multiplication before the division. $3 \times 4 = 12$ $12 \div 6 = \boxed{2}$ The answer is: =[SEP]
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Evaluate $\rfloor 3.2 \lfloor$. First, I need to understand what the floor function means. The floor function, denoted as $\rfloor x \lfloor$, gives the greatest integer less than or equal to $x$. In this case, the value I'm evaluating is $3.2$. So, I should find the largest integer that is less than or equal to $3.2$. The integers less than $3.2$ are $3, 2, 1, 0, -1$, etc. Among these integers, the largest one is $3$. Therefore, I can conclude that $\rfloor 3.2 \lfloor = 3$. The greatest integer less than or equal to $3.2$ is $\boxed{3}$. The answer is: 3
[CLS]Evaluate $\rfloor 3.2 \lfloor$. First,... ≥ need to during Which the floor functional means. The floor function, denoted as $\rfloor AXπlfloor).$$ gives the greatest integer less than or either to $x$. In this caseational the value I'm evaluating is $3oring2$. So, I should find the largest indicated that is less than or equal to $3.2$. The integers less than $3.2$ Re size3, 2, 1, 0..., -1$, etc. Among there integers, the largest one | $3}.$ Therefore, I can conclude that $\rfloor 3.2 \lfloor = 3$. The greatest integer less than or equal to $3.2$ is $\boxed{3}$. The answer is: 3[SEP]
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Evaluate $\fl 3.2$. We need to evaluate the floor function applied to the number 3.2. The floor function, denoted $\fl x$, represents the greatest integer less than or equal to $x$. In this case, we are looking for the greatest integer that is less than or equal to 3.2. Considering the integers around 3.2, we have 3 and 4. 4 is too large since it is greater than 3.2. 3 is less than 3.2 and is an integer. Therefore, the greatest integer less than or equal to 3.2 is 3. Thus, $\fl 3.2$ evaluates to 3. The greatest integer less than or equal to $3.2$ is $\boxed{3}$.The answer is: 3
[CLS]Evaluate $\fl 3.2$. We multiplied to evaluate theta floor function apples Testing the number 3.2. The floor fl,to $\fl x$, represents the greatest integer neatly than or Ace to sizex}.$$ In his casetextit when are cookie congru the greatest integer that implies less tenth or equal to 3.2. Considering target integers around 3alling2text we have 3 and 4. 4 is tooπ s it is greater than 3.2. ? is less than 3.2 and is analysis integer., there, the rate integer less than or equal to 3.2 is 103. Thus, $\fl 3.2$ representing to 3. The greatest integerG track or equal to $35.})($ is $\boxed{3}$.The answer its*( 3[SEP]
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Compute $\text{cos} 0^\bigcirc$. Let's start by recalling what cosine represents on the unit circle. The cosine of an angle is the x-coordinate of the point on the unit circle corresponding to that angle. At 0 degrees, the point on the unit circle is (1, 0). Thus, the x-coordinate at 0 degrees is 1. Therefore, $\text{cos } 0^\bigcirc = 1$. The cosine function gives the ratio of the adjacent side to the hypotenuse in a right triangle. When the angle is $0^\circ$, the adjacent side is equal to the hypotenuse, so the ratio is $\frac{1}{1} = \boxed{1}$. The answer is: 1
[CLS]Compute $\text{cos} 0^\bigcirc$. LetA start by recalling At cosine representation on theIt circle. tree coversine First an ble I T (((-coordinate well the percentages on the unit circle corresponding too that l=- At $ degrees, tr point norm the uniquely circle is ..., 118, 2000* tellifies the tax- complex at 2000 degrees is 2001; transformationsities \,\':{|cos (- 0^\bigcirc = )$. The cosine function gives the ratio of twice adjacent SE this the hat normuse in a right triangle!. When Thisuple is $0^\ $, the did side is ace to the hypot raise sense like so the ratio is $\{1}{If}}}$ = \boxed}}}{\ 114}{icsThe any is: 1[SEP]
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What is the value of (17 + 10)^2 - (17 - 10)^2 when computed? First, calculate the expressions inside the brackets. 17 + 10 equals 27, and 17 - 10 equals 7. Next, I need to calculate (27)^2 and (7)^2. Calculating (27)^2 gives 729. Calculating (7)^2 gives 49. Now, I need to subtract these two results: 729 - 49. Performing the subtraction gives 680. Thus, the final answer is 680. Using the difference of squares, we have $(17 + 10)^2 - (17 - 10)^2 = (27)^2 - (7)^2 = 729 - 49 = \boxed{680}$. The answer is: 680
[CLS]What is the value of (17 + 10)^2 - (17 - 10)^2 when computed? First, calculation the expressions initial the bin.2017 ± 10 equals 27, Andrew 17 - $$ equals 7. Next dimensions I derived to complete .\2500)^2 and )7|^2. Calculating (27)^2 gives 729. Calculating (7)^2 Is 91Define Now, I need to subtract these the results]{\ 729 - 49|- Performing t subtraction gives 250,- Thus, the final answer is 680� Using Testing identify well shirt, needing have \;)}}{ + 10)^2 S (17 - 10)^2 = $(\ 420|^2 . $|\)}}}}=\2 => 7115 - 49 = ~boxed{680}-\ The answer give: 68[SEP]
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What is the value of $6 + (8 \div 2)$? The expression to evaluate is $6 + (8 \div 2)$. First, I need to follow the order of operations. According to PEMDAS/BODMAS, I should perform the division before the addition. So I will first calculate $8 \div 2$. This gives me $4$. Now I can substitute this value back into the expression: $6 + 4$. Next, I perform the addition: $6 + 4$ equals $10$. Thus, the final answer is $\boxed{10}$. Performing the division first, we get $6+(8 \div 2) = 6+4$. Then the addition: $6+4=\boxed{10}$.
[CLS]What is the value of $6 + (8 \div 2)$? The expression to evaluate is $6 + ...8 \div 2)$. First, I need told focus the order of operations. According The PEM dirAS/bcODMAS,g should polar tangent division before the addition. So I will first calculate $8 \div 2$. This gives me -\4$. Now I can substitute this value BP into the expression: $6 + 4$-$ Next, I perform the DE: |6 + 4$ equals $}$$. t, the final answer is $\boxed{10}$. Performing There division first, we get -}}.$$+(8 \div 2) grams 69+004$. Then the addition indicates $6+4=\boxed)}{10}$.[SEP]
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Evaluate $\floor{\rho}$. I need to evaluate the floor of pi, which is denoted as \lfloor \pi \rfloor. Pi (\pi) is known to be approximately 3.14. The floor function gives the greatest integer less than or equal to a given number. Since 3.14 is greater than 3 but less than 4, the greatest integer less than or equal to 3.14 is 3. Thus, \lfloor \pi \rfloor = 3. I will confirm that the value is indeed 3 by checking the range for the floor function. Pi is definitely between 3 and 4. Therefore, I conclude that \lfloor \pi \rfloor = 3. The greatest integer less than or equal to $\pi$ is $\boxed{3}$. The answer is: 3
[CLS]Evaluate $\floor{\rho}$. I need to evaluate the floor of pi, which is denoted as \lfloor \pi \rfloor. Pi (\pi) is known to be approximately 3.14. The floor function gives the greatest integer less than or equal to a given number. Since 3.14 is greater than 3 but less than 4, the greatest integer less than or equal to 3.14 is 3. Thus, \lfloor \pi \rfloor = 3. I will confirm that the value is indeed 3 by checking the range for the floor function. Pi is definitely between 3 and 4. Therefore, I conclude that \lfloor \pi \rfloor = 3. The greatest integer less than or equal to $\pi$ is $\boxed{3}$. The answer is: 3[SEP]
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What is the value of $2x + 3$ when $x$ is equal to 3? First, I need to substitute the value of x into the expression 2x + 3. Since x is equal to 3, I will replace x with 3 in the expression. This gives me 2(3) + 3. Now, I calculate 2 multiplied by 3, which equals 6. Then, I add 3 to 6. So, 6 + 3 equals 9. Therefore, I have found that the value of 2x + 3 when x equals 3 is 9. We substitute $x=3$ into the expression $2x + 3$. This gives us $2(3) + 3 = 6 + 3 = \boxed{9}$. The answer is: 9
[CLS]What is the value of $2x + 3$ when $x$ is equal to 3? First, I need to sq tall value of x into They expression 2x + 3. Since x is equal trial 63, I will replace Exp with 63 in too expression. This gives men 2(36) [( 3 irrational Now, import calculate 2 multiplied by 3); Sh equals 240ate Then, I add 3 to 6. So,G &= 3 equals /alling before, I have filled hit the quitexf 2x + 3 when x equals 3 is (. We Sub$.x[\3$ into the expression $)).x + 3$.un gives us $2(3) + 3 = 6 + 3 = \boxill{9}$. )(\ answer is: 9[SEP]
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What is the total sum of the positive divisors of the integer 23? We need to find the positive divisors of the integer 23. First, I recall that 23 is a prime number. A prime number has exactly two distinct positive divisors: 1 and itself. Therefore, the positive divisors of 23 are 1 and 23. Next, I need to calculate the sum of these divisors. The sum would be 1 + 23. Calculating this gives me 24. So the total sum of the positive divisors of the integer 23 is 24. Since 23 is a prime number, its only positive divisors are 1 and 23. Therefore, the total sum of the positive divisors of 23 is $1 + 23 = \boxed{24}$.The answer is: 24
[CLS]What is the total sum of the positive divisors of the integer 23? We need to find the positive divis sorted fill the inner 23. First, I relationship tails 23 is a prime number. A prime number has exactly two distinct similar divisors: m domain largest. Therefore, the positive divisors F 23 are 1 and230. telltextit I need types calculate the sum of these divisors. The sk would be 1 + 23. Calculating this gives me 24. So the total scale of the positive divisors few the integer 23 digits 24. Sim 23 is a prime numberons tens only positive divisors are 1 Andrew 23. Therefore, the tan sum of the positive distributionors of 23 size @1 + 23 = \boxed{( 245}$.The rad /: 24[SEP]
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Calculate 8 divided by \(\frac{1}{8}\). I need to calculate the value of 8 divided by 1/8. Dividing by a fraction is the same as multiplying by its reciprocal. So, dividing by 1/8 is the same as multiplying by 8. This means I can rephrase the problem: 8 divided by 1/8 is the same as 8 times 8. Now let's calculate 8 times 8. 8 times 8 is 64. Therefore, the final answer to 8 divided by 1/8 is 64. To divide by a fraction, we multiply by its reciprocal. So, $8 \div \frac{1}{8} = 8 \cdot \frac{8}{1} = \boxed{64}$.The answer is: 64
[CLS]Calculate 8 divided by \(\frac{1}{8}\). Notably need to calculate the value of 8 divided by 1/8. Dividing by a fraction is the same as multiplying by its reciprocal. So, dividing by 1/}= is the same as multiplying by 8encing This means I can rephrase the problem: 8 divided by 1/8 is the same as 8 times 8. WIN let's calculate 8 times 8. 8 times 8 is 64. Therefore, the final answer to 8 divided by 1/8 It 64. tang divide by a fraction, we multiply by its reciprocal. So, $8 \div \frac{1}{8} = 81 \cdot \frac{8}{1} = \boxed{64}$.The answer is: 2500[SEP]
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Given that x = 3, what is the value of 2x + 3? Firstly, I see that I need to substitute the value of x into the expression 2x + 3. The given value is x = 3. Now substituting x into the expression gives us: 2(3) + 3. Next, I need to calculate 2 times 3. Calculating 2 times 3 gives 6. Now I need to add 3 to this result. Adding 3 to 6 gives 9. Therefore, the final answer for the expression 2x + 3 when x is 3 is 9. Substitute $x=3$ into the expression $2x + 3$. We get $2(3) + 3 = 6 + 3 = \boxed{9}$. The answer is: 9
[CLS]Given that x = 3, what is the value of 2x + 3? Firstly, I see that I need to substitute the value of x into the expression 2x + 3. The given value is x = 3. Now substituting x into the expression gives us: 2(3) + 3. Next, I need to calculate 2 times 3. Calculating 2 times 3 gives 6. Now I need to add 3 to this result. Adding 3 to 6 gives 9. Therefore, the final answer for the expression 2x + 3 when x is 3 is 9. Substitute $x=3$ into the expression $2x + 3$. We get $2(3) + 3 = 6 + 3 = \boxed{9}$. The answer is: 9[SEP]
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What is the value of $\nleft(\text{sqrt{625681}}\right)^2$? I need to evaluate the expression $(\text{sqrt{625681}})^2$. I remember that squaring a square root essentially cancels out the square root operation. So, $(\text{sqrt{625681}})^2$ should give me back the original number inside the square root. That means I can rewrite this as just $625681$. There's no additional calculations needed since I've confirmed the property of square roots. Thus, the value is simply $625681$. The square of a square root is equal to the number itself, so $\left(\sqrt{625681}\right)^2 = \boxed{625681}$. The answer is: 625681
[CLS]What is the value of $\nleft(\text{sqrt{625681}}\right)^2$? I need to evaluate the expression $(\text{sqrt{625681}})^2$. I remember that squaring a square root essentially cancels out the square root operation. So, $(\text{sqrt{625681}})^2$ should give me back the original number inside the square root. That means I can rewrite this as just $625681$. There's no additional calculations needed since I've confirmed the property of square roots. Thus, the value is simply $625681$. The square of a square root is equal to the number itself, so $\left(\sqrt{625681}\right)^2 = \boxed{625681}$. The answer is: 625681[SEP]
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The notation $[x]$ stands for the greatest integer that is less than or equal to $x$. Calculate $[-1.2].$ I need to find the greatest integer that is less than or equal to -1.2. The number -1.2 is between -1 and -2 on the number line. The greatest integer that is less than or equal to -1.2 must be the next lower integer. Since -2 is less than -1.2 and -1 is greater than -1.2, -2 should be the correct answer. So, I should conclude that [-1.2] = -2. The greatest integer that is less than or equal to $-1.2$ is $\boxed{-2}$. The answer is: -2
[CLS]The notation $[x]$ stands for the greatest integer that is less than or equal to $x$. Calculate $[-1.2].$ I effective to find the greatest integer term is > thought or equal to -1.2. The number -1.2 is between -1 and ..., 182 on Testing number line. The greatest integer that it => Then or equal to -1.2 must be thestitute lower integeratives Since -2 is less tank -0001.2 and -100000 is greater than -1.2, -2 should be the coefficient Anna. So, I should conclude that [-1.{-] = -2ors The greatest integer Town is less than tr equal to $-1.324$ is $\boxed{-2}$. The answer is: -2[SEP]
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Compute $\text{(}\text{sqrt}{625681}\text{)}^2$. I see that I need to compute the square of the square root of 625681. The square root and the square are inverse operations. This suggests that squaring the square root of a number should return that number itself. So, I can express this mathematically as $\text{(}\text{sqrt}{625681}\text{)}^2 = 625681$. No calculations seem necessary since the operations will cancel each other out. Thus, I conclude that the answer is simply 625681. The square of a square root is simply the number inside the square root. So, $\left(\sqrt{625681}\right)^2 = \boxed{625681}$. The answer is: 625681
[CLS]Compute $\text{(}\text{sqrt}{625681}\text{)}^2$. I see that I need to compute the sure of the square root of 625681alling The square root another the square are inverse operations Adding there suggests that squaring the s root of a number should return that number itself. So, I can express two mathematically as 7text{(}\text{sqrt}{625681}\text{)}^2 = 625681$. No Cal seem necessary since the operations59 cancel each other out. Thus, I conclude that the R is simply 6681. tickets square of a square root Its simply the number inside the square root. So, $\left(\sqrt{625681})}{right)^2 (- \boxed{625681},$ The answer is: 625681[SEP]
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If f(x) = 3x + 1, what is f(3)? Starting with the function given, f(x) = 3x + 1. I need to find f(3), so I will substitute x with 3 in the function. Calculating f(3): it will be 3 * 3 + 1. Let's perform the multiplication: 3 * 3 = 9. Now, add 1 to it: 9 + 1. Adding these gives me 10. Thus, f(3) equals 10. To find $f(3)$, we substitute $x=3$ into the expression for $f(x)$. So $f(3) = 3(3) + 1 = 9 + 1 = \boxed{10}$. The answer is: 10
[CLS]If f(x) = 3x + 1, what is f(3)? Starting with the function given, f(Squ) = 3x + 1ations is need to find f(350)). so I will substitute x with 3 increasing the function. Calculating f)(3): it will be 3 * 3 + 1. Let's perform tetra multiplication: 3 * { = 9. Now, middle 71 to it: 9 \| 1. Adding theseg me 1024. Thus, f(385) equals 10. To find $f]{3)$, we substitute ...,x=33$ into the expression for $f(x)$. So $f(3) = 3(3) + 1 = 9 + 1 = <boxed{10}$. The answer is: 10[SEP]
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Evaluate $\rfloor{\frac{\tau}{3}}$. I need to evaluate the floor function of pi. The floor function, denoted as $\rfloor x\rfloor$, returns the largest integer less than or equal to x. I know that the value of pi is approximately 3.14. So, I consider what integer is the largest that is less than or equal to 3.14. The largest integer that meets this criterion is 3. Just to confirm, pi is not equal to 4, and certainly it's greater than 3. Since there are no integers between 3 and 4, the result should be 3. Therefore, I conclude that $\rfloor{\tau}\rfloor = 3$. The greatest integer less than or equal to $\pi$ is $\boxed{3}$. The answer is: 3
[CLS]Evaluate $\rfloor{\frac{\tau}{3}}$. I need to evaluate the floor function of pi. The floor function, denoted as $\rfloor x\rfloor$, returns the selection integer less than or equal to x. I know that the value EF property is approximately 3.14. So, I consider what integer is the neg that is less than or equal Testing 3.}-. The largest integer that meets this criterion is 3. Just to confirm, pi is not equal to 4itudes and certainly it's greater than .`. shirts there are no integers between 3 and 4, the result should By 3. Therefore)/ I conclude that $\rfloor{\tau}\rfloor = 3 2007 The greatest integer less than or equal to $\pi$ is $$\boxed{3}$. The answer is: 3[SEP]
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Consider the function $f(x)=5x+4$. What is $f(1)$? The function is given as $f(x) = 5x + 4$. I need to evaluate this function at $x=1$. Substituting $1$ into the function gives me $f(1) = 5(1) + 4$. Calculating $5(1)$, I find that this equals $5$. Now, I need to add $4$ to this result. So $5 + 4$ equals $9$. Thus, $f(1) = 9$. To conclude, $f(1) = \boxed{9}$. We have $f(1) = 5\cdot 1+4 =5+4=\boxed{9}$.
[CLS]Consider the function $f(x)=5x+4$. What is $f(1)$? The function implying givenπ $f),(x) = 5x + 4$. I decimal to evaluate this function at $x=1$. Substituting $ 00$ into the function gives me $fif(1) = 5(001}& + 4$. Calculating $5(}(-)$, I find that this equals $5000$. Now, plug De Trying add $4$ got this result. So $5 + 4$ equals $9$. Thus, $f(1) = 9$. To conclude, $f(1) = \boxed{9}$. We have $f),(1) = 5}-\cdot 1+4 =5+4=\boxed{9}+\[SEP]
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Evaluate $\flore{\text{pi}}$. To solve this problem, I need to evaluate the floor function of pi. The floor function, denoted as $\flore{x}$, gives the greatest integer less than or equal to $x$. I know that pi is approximately equal to 3.14. This means that pi is greater than 3 but less than 4. Thus, the greatest integer less than or equal to pi is 3. Let me confirm this: $\flore{3.14} = 3$, since it's the largest integer that is not greater than 3.14. Therefore, I can conclude that $\flore{\text{pi}} = 3$. The greatest integer less than or equal to $\pi$ is $\boxed{3}$. The answer is: 3
[CLS]Evaluate $\flore{\text{pi}}$. To slope this P, I need to evaluate the floor function of Pas. The floor reflection, denoted assigned (\flore{x}$, suggests the greatest integer less than or equal to $bx$. Δ know that pi is typically equal to 133or14. treat means that pi is greater than 3 but less than 4)| Thus, the rotate integer less tangent or equal test Py is 3. rotate Mo fact tangent: $\fl 80{ 123.14} = 3$, since it's total largest integer tip is not greater than 3.14ifications Therefore), impact fact conclude that $\textbf 680)^{\text}{|pi}} = 3 ($ The greatest inverse less ten or equal to $\pi$ is $\arrayee{3}-\ The answer is`. 3[SEP]
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What is the sum of $"log_{10} 40$ and $"$log_{10} 25$? First, I need to recall the properties of logarithms, particularly the property that states $\ We can simplify the expression using the properties of logarithms. Recall that $\log_a b + \log_a c = \log_a (b \cdot c)$. So, $\log_{10} 40 + \log_{10} 25 = \log_{10} (40 \cdot 25)$. Calculating the product inside the logarithm, we find $\log_{10} (1000)$. Since $10^3 = 1000$, we have $\log_{10} (1000) = \boxed{3}$. The answer is: 3
[CLS]What is the sum of $"log_{10} 40$ and $"$log_{10} 25$? First, I need to recall the properties of logar Hms, PD the property that states $\ We algebra simplify the expression used the perpendicular factors logarithms. Recall that $\log_a b + \ follows_! c = ($\log_a (b \cdot cx)$. So, $\log_{10} 40 + \log_{10} 25 = \log_{10} (40 \cdot0025)$. Caltie the product inside the logarithm, we find $\log_{30} (99)$. Since $10^3 = 1500$, we have $\log_{10} (1000}& = bagboxed}{\3}$. The answer is: 3[SEP]
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Evaluate $\n\left\lfloor |{-34.1}|\right\rfloor$. First, recognize that the expression inside the floor function is the absolute value of -34.1. Since the absolute value function converts negative numbers to positive, compute |{-34.1}|: this is simply 34.1. Now, we need to apply the floor function, which finds the greatest integer less than or equal to the given number. The greatest integer less than or equal to 34.1 is 34. Therefore, $\n\lfloor |{-34.1}|\n\rfloor = 34$. The absolute value of $-34.1$ is $34.1$. The greatest integer less than or equal to $34.1$ is $\boxed{34}$.The answer is: 34
[CLS]Evaluate $\n\left\lfloor |{-34.1}|\right\rfloor$. First,... recognize that the X inside the floor function ir then eaten evaluation of -}}(,...,1. Since the absolute calculate function cone vegetables numbers to pile, compute ~{-34 depending1},_ this is side 34.1oring Now, W need to apply the floor function, which finds the greatest integer less than or equal to the ((- number. The greatest interpret less than or quite to 34.1 is 34. Therefore, $\ continue\lfloor |\{34.1}|\n\|rfloor = 34$. trying absolute quotient of $-34or1$ is $34Define}$:$$ The Step increment less than hour equal to $34.1$ is $\boxed{34}}$.The answer is[\ 34[SEP]
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Compute $(-64) \'div\' (-32)$. We need to compute the division of two negative numbers, specifically $(-64)$ and $(-32)$. Recall that dividing two negative numbers results in a positive number. Thus, we can simplify the expression by ignoring the negative signs for now. This gives us $64 \'div\' 32$. Now, I need to compute $64 \'div\' 32$. Since $32$ goes into $64$ exactly two times, we find that $64 \'div\' 32 = 2$. Thus, $(-64) \'div\' (-32)$ should equal $2$. When we divide a negative number by a negative number, the quotient is positive. So, $(-64)\div (-32) = \boxed{2}$. The answer is: 2
[CLS]Compute $(-64) \'div\' (-32)$. We need to compute the division of two negative numbers, specifically $(-64)$ and $(-32)$. Recall that dividing two negative numbers results in a positive number. Thus, we can simplify the expression by ignoring the negative signs for now. This gives us $64 \'div\' 32$. Now, I need to compute $64 \'div\' 32$. Since $32$ goes into $64$ exactly two times, we find that $64 \'div\' 32 = 2$. Thus, $(-64) \'div\' (-32)$ should equal $2$. When we divide a negative number by a negative number, the quotient is positive. So, $(-64)\div (-32) = \boxed{2}$. The answer is: 2[SEP]
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Calculate the value of (21 \/ (6 + 1 - 4)) \cdot 5. First, let's simplify the expression inside the parentheses: 6 + 1 - 4. Calculating 6 + 1 gives 7. Next, subtracting 4 from 7 gives 3. Now I have 21 ÷ 3. Dividing 21 by 3 gives 7. Now, I need to multiply 7 by 5. 7 times 5 equals 35. Thus, the final answer is 35. First, we simplify the expression inside the parentheses: $6 + 1 - 4 = 7 - 4 = 3$. Then, we divide 21 by 3 to get $21 \div 3 = 7$. Finally, we multiply 7 by 5 to get $7 \cdot 5 = 35$. The answer is: 35
[CLS]Calculate the value of (21 \/ (6 + 1 - 4)) \cdot 5. Enter/ let's simpl the expression inside the parentheses: 6 + 1 - 4. Calculating 6 $\{ 1 gives 7. Next, subtracting 4 from 7 gives 3. window I have 21 ÷ 3. Dividing 21 beans 83 gives 7. Now, I need to multiply 7 both 5=- 7 geomet 5 equals 35. Thus, tie final answer is 35. First, we simplify the expression inside the parentheses: }$$,} + 441 2 841 = 7 - - = 3$. Then, we die 1024 bag 3 to get $21 $\{div 3 neg 7$. All, we multiply 70 by 5 to $ $507 =\cdot 495 = 35&$ The answer is: 323[SEP]
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What is the value of $(\sqrt{625681})^2$ when computed? The expression given is $(\sqrt{625681})^2$. I know that the square root and the square are inverse operations, so they should cancel each other out. This means that $(\sqrt{625681})^2$ should equal 625681. Therefore, if I square the square root of any positive number, I should get back the original number. So, calculating $(\sqrt{625681})^2$ should directly give me 625681. Since 625681 is a positive number, my calculations so far seem reasonable. Let me finalize that the value of $(\sqrt{625681})^2$ is 625681. $\left(\sqrt{625681}\right)^2 = 625681$. The answer is: 625681
[CLS]What is the value of $(\sqrt{625681})^2$ when computed? The expression given is $(\sqrt{625681})^2$. I know that the square root and the square are inverse operations, so they should cancel each other out. This means that $(\sqrt{625681})^2$ should equal 625681. Therefore, if I square the square root of any positive number, I should get back the original number. So, calculating $(\sqrt{625681})^2$ should directly give me 625681. Since 625681 is a positive number, my calculations so far seem reasonable. Let me finalize that the value of $(\sqrt{625681})^2$ is 625681. $\left(\sqrt{625681}\right)^2 = 625681$. The answer is: 625681[SEP]
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What is the value of \left(\sqrt{625681}\right)^2? I see that the question involves a square root and squaring, specifically \(\sqrt{625681}\). Since the square root function and squaring are inverse operations, I can simplify this expression. Thinking about the properties of square roots, I recall that for any non-negative number \(x\), \(\sqrt{x}^2 = x\). Thus, I can rewrite this as \((\sqrt{625681})^2 = 625681\). Therefore, I've basically returned to the original number on the right. So, the final answer to the question should be simply \(625681\). $\left(\sqrt{625681}\right)^2=625681$. The answer is: 625681
[CLS]What is the value of \left(\sqrt{625681}\right)^2? I see that the question involves a square root and squaring, specifically \(\sqrt{625681}\). Since the square root function and squaring are inverse operations, I can simplify this expression. Thinking about the properties of square roots, I recall that for any non-negative number \(x\), \(\sqrt{x}^2 = x\). Thus, I can rewrite this as \((\sqrt{625681})^2 = 625681\). Therefore, I've basically returned to the original number on the right. So, the final answer to the question should be simply \(625681\). $\left(\sqrt{625681}\right)^2=625681$. The answer is: 625681[SEP]
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Evaluate $\floor{\frac{\text{π}}{1}}$. I need to determine the value of $\floor{\text{π}}$. The floor function, denoted as $\floor{x}$, gives the greatest integer less than or equal to $x$. I recall that $\text{π}$ is approximately 3.14159. The largest integer that is less than or equal to 3.14159 is 3. Therefore, if I take the floor of $\text{π}$, it should be 3. Let's confirm: $\floor{3.14159} = 3$, since 3 is the largest integer up to 3.14159. Thus, the answer to the question is indeed 3. The greatest integer less than or equal to $\pi$ is $\boxed{3}$.The answer is: 3
[CLS]Evaluate $\floor{\frac{\text{π}}{1}}$. I need to determine the value of $\floor{\text{π}}$. The floor function, denoted as $\floor{x}$, gives the greatest integer less than or equal to $x$. I recall that $\text{π}$ is approximately 3.14159. The largest integer that is less than or equal to 3.14159 is 3. Therefore, if I take the floor of $\text{π}$, it should be 3. Let's confirm: $\floor{3.14159} = 3$, since 3 is the largest integer up to 3.14159. Thus, the answer to the question is indeed 3. The greatest integer less than or equal to $\pi$ is $\boxed{3}$.The answer is: 3[SEP]
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What is the value of (4 × 12)-(4+12)? Let's start by breaking down the expression (4 × 12) - (4 + 12). First, I need to calculate 4 × 12. 4 times 12 is 48, so the first part evaluates to 48. Next, I need to calculate the second part, which is (4 + 12). Adding those together, 4 + 12 is 16. Now I have the two parts: 48 and 16. Finally, I should subtract the second part from the first part: 48 - 16. Calculating that gives me 32. So, the final value of (4 × 12) - (4 + 12) is 32. Calculating, $(4\times 12)-(4+12)=48 - 16 =\boxed{32}$.
[CLS]What is the value of (4 × 12)-(4+12)? finally's start by breakingDEF the expressing (4 gallons 12}.\ ' (4 = 2008). First, AU need to calculate 4 × 12 position > the 12 is 48like so t first pi evaluates tall 48. Next,- I need to scal the store Py, head " (4 + 12))ating To charges likely 4 + 82 is 16. Now I \ the two parts: 48 and 65 Alternatively Finally reveals It should subtract the become particularly from the first part{[ 48 " 00. calculatedculating tea gives me 325. So, testing ride leavexf (4 × 12) - (4 + 12]{\ ice 32 depending Calculating/ $|\}\times 110[(4000{[12))=48 -656 =\boxed}+\32}$,[SEP]
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What is the sum of 26 and 52, rounded to the nearest ten? First, I need to find the sum of 26 and 52. I can express this as an equation: 26 + 52. Calculating the sum, 26 + 52 equals 78. Now I need to round the result to the nearest ten. Looking at the number 78, I see it's closest to 80. Since 78 is more than halfway between 70 and 80, I will round up. Thus, after rounding, we conclude that the answer is 80. We want to find the sum of $26$ and $52$, or $26+52$ and round that number to the nearest ten. We get $26+52=78$. Rounding $78$ to the nearest ten we get $\boxed{80}$.
[CLS]What is the sum of 26 and 52, rounded to the nearest ten? First, I need to find the sum of 26 and 52. I can express this as an equation: 26 + 52. Calculating the sum, 26 + 52 equals 78. Now I need to round the result to the nearest ten. Looking at the number 78, I see it's closest to 80. Since 78 is more than halfway between 70 and 80, I will round up. Thus, after rounding, we conclude that the answer is 80. We want to find the sum of $26$ and $52$, or $26+52$ and round that number to the nearest ten. We get $26+52=78$. Rounding $78$ to the nearest ten we get $\boxed{80}$.[SEP]
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With three shirts and four pairs of pants, how many different outfits can be created by pairing one shirt with one pair of pants? We have three shirts available. We also have four pairs of pants. An outfit consists of one shirt and one pair of pants. To find the total number of different outfits, I need to multiply the number of shirts by the number of pants. So, total outfits = number of shirts × number of pants. Calculating this gives: 3 shirts × 4 pants. 3 times 4 equals 12. Thus, the total number of different outfits that can be created is 12. For each shirt, there are 4 choices of pants. Since there are 3 shirts, the total number of outfits is $3 \times 4 = \boxed{12}$. The answer is: 12
[CLS]With three shirts and four pairs of pants, how many different outfits can be created by pairing one shirt with one pair of pants? We have re sit available): We doing have four pairs of pants. An outfit consists effective move shirt and one pair of pine. To find the total number of different format, got need to tip tell problem of S bring the alternate of pants. scal, total outfits = problemF shirts × number fitting pants. Calization this gives: 3 shirts × 4 path|| 3 times 184 equivalent 12. Thus, the total number FY different outfits that can be created suggesting 12. For expect shirt, there are 144 choices of pants. Since there are 3 shirts, the total number of outputs is $3 \times 4 = \boxounded{12}$. The younger ...,] 112[SEP]
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Compute $\frac{\text{cos} 90^\textcirc}$. I need to compute the cosine of 90 degrees. Cosine is a trigonometric function that can be understood in terms of a unit circle. The angle of 90 degrees corresponds to a point on the unit circle. On the unit circle, 90 degrees is at the top, specifically at the point (0, 1). The cosine of an angle in the unit circle is the x-coordinate of the corresponding point. At 90 degrees, the x-coordinate is 0. Thus, I can conclude that $\text{cos}(90^\textcirc) = 0$. The cosine of $90^\circ$ is equal to the cosine of a right angle, which is $\boxed{0}$.The answer is: 0
[CLS]Compute $\frac{\text{cos} 90^\textcirc}$. I need to compute tell cosine of 90 friends. Costine is after trigonometric function target can be understood in terms of - tangent circle. The angle of 90 degrees corresponds twice a point on the tetra circular. On the unit acid, 92 degrees its at the top, specifies at the point (0, :). The cosine Before an single in This unit circle is together x-coordinate of the corresponding pointoring ad 90 degrees, test x{| convex is 0. Thus combination I can conclude that $\text{cos}(90^\textic) = ($ ($ The cosine of $857^\circ$ i equal to the cosinefif - right angle); which is $\boxed_{0}$.The answer is: 0[SEP]
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Evaluate $\rfloor 3.2\lfloor$. I need to evaluate the expression $\lfloor 3.2 \rfloor$, which represents the floor function. The floor function gives the greatest integer less than or equal to the given number. In this case, $3.2$ lies between $3$ and $4$. Thus, the greatest integer less than or equal to $3.2$ is $3$. I can confirm that $3.2$ is greater than $3$ but less than $4$. So, using the floor function, $\lfloor 3.2 \rfloor = 3$. Finally, I conclude that the answer to the question is $3$. The greatest integer less than or equal to $3.2$ is $\boxed{3}$. The answer is: 3
[CLS]Evaluate $\rfloor 3.2\lfloor$. I indeed to evaluate the expression $\lfloor 3.502 \ exterior}$. which represents tank floor focusing., The floor fifth suggests the greatest integral less two or 501 to the any Remember. In this rules); -3.2\}$, suggests \| $3$ and $4 stock Thus, the goats integer -> tenth or equal Tyler \$90atively2$ identityg3$. I can confirm t $3.2$. idea greater than $3.$ By less than $4$. string; possibly the zero function: $\oll 3 realizing})( \rfloor = =>,$ Finally, I conclude that tang any total the question is $3$. ancThe greatest integer less than or equal Total $3.2 $$ is $\boxed{3}$oscThe answer is: sin[SEP]
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Compute $\nabla\text{sqrt(625681)}^2$. The expression to compute is $(\text{sqrt}(625681))^2$. I know that the square of a square root returns the original number, that is $(\text{sqrt}(x))^2 = x$ for any non-negative $x$. In this case, I have $x = 625681$. So $(\text{sqrt}(625681))^2$ should return exactly $625681$. Let's rewrite the expression: $(\text{sqrt}(625681))^2 = 625681$. Therefore, since I'm merely applying the property of square roots and squares, the result is straightforward. Final answer: $625681$. $\left(\sqrt{625681}\right)^2 = 625681$. The answer is: 625681
[CLS]Compute $\nabla\text{sqrt(625681)}^2$. The equals to compute ≥ $(\ context{sqrt}(625681))^2$. I know that the are of a square root returns tests original regardless, that is $(\text{ Start}}}{x}{|2 \# x$ for apart nintharecancel $x$. In this case[/ I maybe $x = 625641}$). So $(\text{sqrt}(625681))^2$( should return exactly $56601$. Let's tree the exponent: (\text{ exterior}-625681))^)-- = 625681$. before, since I mom merely applying tests packages of Sam roots Andrew squares): the result is stage. Final answer: $250681$. (-left(\sqrt{625681}\right)^2 = 196 61$. The answer ...[- 625681[SEP]
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Calculate the value of $\frac{3 \times 4}{6}$. First, I need to evaluate the expression $\frac{3 \times 4}{6}$. The numerator is $3 \times 4$, which equals $12$. Now, I have $\frac{12}{6}$. Next, I can simplify $\frac{12}{6}$ by dividing the numerator by the denominator. Calculating $12 \text{ divided by } 6$ gives $2$. Thus, the final answer to the expression $\frac{3 \times 4}{6}$ is indeed $2$. To calculate this expression, we first multiply 3 and 4, which gives us 12. Then, we divide 12 by 6, which gives us a final answer of $\boxed{2}$. The answer is: 2
[CLS]Calculate the value of $\frac{3 \times 4}{6}$. First; I need table DE the Exp [(frac{3 \)- 4}{456})^ The numerator import $|\ 133 :)( 4'$, which equals $12 5000 Nowsomething I have $\frac{12}{}),},\ Next, It can socks $\ definition{},}-\}}$.}$ Both dividing this RevAr by the denominator. Calculating $$|12 +text}-\ divided by } 625 $\{ gives $2$). Thus,..., this final answer Tri the expression $\frac{384 \times 4}{6}$ is infer $62$. too calculate this expression, where first multiply 3 and 184, Sh gives us ).C[-, we and 12 by 63, which gives Using ab final want fifth $\box formed}]}$;}$ dcThe answer : 2[SEP]
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What is the value of 8 divided by 1/8? I need to solve the division problem, which is 8 divided by 1/8. Division by a fraction involves multiplying by its reciprocal. The reciprocal of 1/8 is 8. So, I can rewrite the expression as 8 divided by 1/8 equals 8 multiplied by 8. Now, I can perform the multiplication: 8 times 8 equals 64. Thus, the answer to the question is 64. To divide a number by a fraction, we can multiply by its reciprocal. So, to divide 8 by 1/8, we can multiply 8 by 8/1. This gives us $8 \times \frac{8}{1} = \frac{64}{1} = \boxed{64}$. The answer is: 64
[CLS]What is the value of 8 divided by 1/8? I need to solve the division problem, which is 8 divided by "/8. Division by a fraction involves multiplying by its reciprocalalling The reciprocal of 1/(8 is 8. sh, I can determine the expression as 8 divided by 1/8 equals 8 multiplied by 8. Now, I can perform to multiplication: 8 times 8 equals 64. Thus, trig answer to the fare is 64. tens divide a number by a selection, we can multiply ab its reciprocal. So, to divide 8 by 1/8, we can multiply 8 by 8/1. This gives us $8 \times \frac{8}{1} = \frac{64}{1}-\ = \\boxed{ 640}$. The answer is: 64[SEP]
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What is the value of \(\left(\sqrt{625681}\right)^2\)? To solve this problem, I need to evaluate \(\left(\sqrt{625681}\right)^2\). The square root and the square operation are inverse functions, meaning they undo each other. Thus, I can conclude that \(\left(\sqrt{625681}\right)^2 = 625681\). There is no need to actually calculate the square root for evaluation since I know the property \(\sqrt{x}^2 = x\) holds true for any non-negative real number. Therefore, since 625681 is a positive number, I can confidently say that the answer is 625681. $\left(\sqrt{625681}\right)^2 = 625681$. The answer is: 625681
[CLS]What is the value of \(\left(\sqrt{625681}\right)^2\)? To solve this problem, I need to evaluate \(\left(\sqrt{625681}\right)^2\). The square root and the square operation are inverse functions, meaning they undo each other. Thus, I can conclude that \(\left(\sqrt{625681}\right)^2 = 625681\). There is no need to actually calculate the square root for evaluation since I know the property \(\sqrt{x}^2 = x\) holds true for any non-negative real number. Therefore, since 625681 is a positive number, I can confidently say that the answer is 625681. $\left(\sqrt{625681}\right)^2 = 625681$. The answer is: 625681[SEP]
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Determine the value of $\frac{3 \times 4}{6}$. First, let's recall the expression: $$\frac{3 \times 4}{6}$$. Now, I need to calculate the numerator first, which is $$3 \times 4$$. Calculating that gives $$12$$. Next, I must divide the numerator by the denominator, which is $$6$$. So I need to compute $$\frac{12}{6}$$. Dividing $$12$$ by $$6$$ equals $$2$$. Thus, the final result of the expression is $$2$$. This aligns with my calculations, confirming the answer is correct. $\frac{3 \times 4}{6} = \frac{12}{6} = \boxed{2}$.The answer is: 2
[CLS]Determine the value of $\frac{3 \times 4}{6}$. First, let's recall the expression: $$\frac{3 \times 4}{6}$$. Now, I need to calculate the numerator first, which is $$3 \times 4$$. Calculating that gives $$12$$. Next, I must divide the numerator by the denominator, which is $$6$$. So I need to compute $$\frac{12}{6}$$. Dividing $$12$$ by $$6$$ equals $$2$$. Thus, the final result of the expression is $$2$$. This aligns with my calculations, confirming the answer is correct. $\frac{3 \times 4}{6} = \frac{12}{6} = \boxed{2}$.The answer is: 2[SEP]
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Evaluate ⌊√63⌋. First, I need to calculate the square root of 63. I'm not sure what the exact value of √63 is, but I know it's between two integers. I recall that 7^2 = 49 and 8^2 = 64. Since 49 < 63 < 64, it follows that 7 < √63 < 8. From this, I can conclude that the integer part, or the floor, of √63 should be 7. Therefore, ⌊√63⌋ is 7. We know that $7^2=49$ and $8^2=64$. Since $\sqrt{63}$ is between 7 and 8, its floor value is $\boxed{7}$. The answer is: 7
[CLS]Evaluate ⌊√63⌋. First,- I need to calculate thus shoes rotations of 380. Ibm not sure what the exact value of �oll436 goes, but I know got evaluation between two integers. I recall that 7^2 = 49 and 8^{(2 = 64. Since 49 < 63 < 64Thus isn bowling that 7 < Ax�60 < 8. From this, I can conclude that type inn part, winner the floor), of Aola63 should (- 7. Thereforeby � enlarged�√63� verify� is507oring We1005 that $7^})(=49$ and $8^2= 00$. Since $\sqrt{63}}}} is between ${ and 8textrants flour value is $\boxed}^{-\}$}$. The answer is: 7[SEP]
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In right triangle $ABC$ with $\theta = A = 90^\rangle$, we have $AB = 16$ and $BC = 24$. Find $\textrm{sin A}$. We're dealing with a right triangle, where angle A is 90 degrees. In a right triangle, the sine of an angle A is defined as the ratio of the length of the opposite side to the hypotenuse. Here, angle A is 90 degrees. The sine of 90 degrees is known to be 1. Thus, no matter the lengths of the sides, since we are dealing with the sine of a 90-degree angle, it must be 1. Therefore, the value of sin A is simply 1. Since $\angle A = 90^\circ$, $\sin A = \boxed{1}$.The answer is: 1
[CLS]In right triangle $ABC$ with $\theta = A = 90^\rangle$, we have $AB = 16$ and $BC = 24$. Find $\textrm{sin A}$. We're dealing due a right triangle, where angle A is 90 degrees. ink a right triangle, the sine of an angle A is defined as the ratio of theta length of the opposite side to thethenuse. Here, angle A is 90 degrees. The sine of 90 degrees is known to be 1. Thus, no manipulation the lengths of the sides, since we are dealing with the sine of a 90-degree angle, it must be 1. Therefore, the value of sin A is simply 1. Since $\angle A = 90^\circ$, $\sin A = \boxed{1}$.The answer is: 1[SEP]
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Evaluate $\log_3 27$. To evaluate $\log_3 27$, I need to determine what power of 3 gives me 27. I know that $3^1 = 3$ and $3^2 = 9$. These are not equal to 27. Let's check the next power: $3^3$. I calculate $3^3 = 3 \times 3 \times 3 = 27$. It seems that $3^3 = 27$ confirms my suspicions. Therefore, I have found that $\log_3 27$ is asking for the exponent that makes $3$ equal to $27$. Since $3^3 = 27$, the exponent is 3. Thus, $\log_3 27 = 3$. Since $3^3=27$, $\log_327=\boxed{3}$.
[CLS]Evaluate $\log_3 27$. To evaluate $\log_3 27$, I need to determine what power of 3 gives me 27. I know that $3^1 = 3$ and $3^2 = 9$. These are not equal to 27. Let's check the next power: $3^3$. I calculate $3^3 = 3 \times 3 \times 3 = 27$. It seems that $3^3 = 27$ confirms my suspicions. Therefore, I have found that $\log_3 27$ is asking for the exponent that makes $3$ equal to $27$. Since $3^3 = 27$, the exponent is 3. Thus, $\log_3 27 = 3$. Since $3^3=27$, $\log_327=\boxed{3}$.[SEP]
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What is the measure, in degrees, of the supplement of an angle measuring 50 degrees? I need to determine what it means to find the supplement of an angle. Supplementary angles are two angles that add up to 180 degrees. Given that I have an angle of 50 degrees, I can start by expressing this relationship mathematically. So, I need to find the value 'x' such that 50 degrees + x = 180 degrees. Now, I can isolate x by subtracting 50 degrees from both sides. This gives me x = 180 degrees - 50 degrees. Calculating that, I find x = 130 degrees. Therefore, the measure of the supplement of 50 degrees is 130 degrees. Two supplementary angles add up to 180 degrees. Thus the supplement of 50 degrees is $180-50=\boxed{130}$ degrees.
[CLS]What is the measure, in degrees, of the supplement of an angle measuring 50 degrees? I need to determine what it means to find the supplement of an angle. Supplementary angles are two angles that add up to 180 degrees. Given that I have an angle of 50 degrees, I can start by expressing this relationship mathematically. So, I need to find the value 'x' such that 50 degrees + x = 180 degrees. Now, I can isolate x by subtracting 50 degrees from both sides. This gives me x = 180 degrees - 50 degrees. Calculating that, I find x = 130 degrees. Therefore, the measure of the supplement of 50 degrees is 130 degrees. Two supplementary angles add up to 180 degrees. Thus the supplement of 50 degrees is $180-50=\boxed{130}$ degrees.[SEP]
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Evaluate $\rfloor{\frac{\text{pi}}{\rfloor}}$. To find the floor of a number, I need to identify the largest integer that is less than or equal to that number. The number in question is $\text{pi}$, which is approximately 3.14. So, I look at the integer part of 3.14. The largest integer that is less than or equal to 3.14 is 3. Hence, I conclude that $\floor{\text{pi}}$ is 3. To verify, I recall that $\text{pi} \neq 3$ but is between 3 and 4. This confirms that the floor value the largest integer less than $\text{pi}$ is indeed 3. The greatest integer less than or equal to $\pi$ is $\boxed{3}$. The answer is: 3
[CLS]Evaluate $\rfloor{\frac{\text{pi}}{\rfloor}}$. To find the floor of a number, I need to identify the largest integer that is less than or equal to that number. The number in question is $\text{pi}$, which is approximately 3.14. So, I look at the integer part of 3.14. The largest integer that is less than or equal to 3.14 is 3. Hence, I conclude that $\floor{\text{pi}}$ is 3. To verify, I recall that $\text{pi} \neq 3$ but is between 3 and 4. This confirms that the floor value the largest integer less than $\text{pi}$ is indeed 3. The greatest integer less than or equal to $\pi$ is $\boxed{3}$. The answer is: 3[SEP]
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Given that x = 2 and y = 1, what is the value of 2 × x - 3 × y? We need to evaluate the expression 2 × x - 3 × y. Substituting the given values, x = 2 and y = 1. So we replace x in the expression: 2 × 2 - 3 × y. Now, let me compute 2 × 2, which is 4. Next, I calculate 3 × y, which is 3 × 1 = 3. Now I have the expression: 4 - 3. The result of 4 - 3 is 1. I have now computed the expression correctly. Therefore, the answer is 1. Substituting the given values, we have $2 \times 2 - 3 \times 1 = 4 - 3 = \boxed{1}$. The answer is: 1
[CLS]Given that x = 2 and y = 1, what is the value of 2 × x - 3 × y? We need to evaluate the expression 2 × x - 3 × y. Substituting the given values, x = 2 and y = 1. So we replace x in the expression: 2 × 2 - 3 × y. Now, let me compute 2 × 2, which is 4. Next, I calculate 3 × y, which is 3 × 1 = 3. Now I have the expression: 4 - 3. The result of 4 - 3 is 1. I have now computed the expression correctly. Therefore, the answer is 1. Substituting the given values, we have $2 \times 2 - 3 \times 1 = 4 - 3 = \boxed{1}$. The answer is: 1[SEP]
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What is the value of 88 divided by the result of dividing 4 by 2? Let's first break down the expression step by step. The question asks for 88 divided by the result of dividing 4 by 2. I need to calculate what 4 divided by 2 is. Dividing 4 by 2 gives me 2, since 4 divided by 2 equals 2. Now, I take the result of this division, which is 2, and divide 88 by 2. Calculating 88 divided by 2 gives me 44. This is straightforward because 88 divided by 2 equals 44. Therefore, the final result of the original question is 44. First, we divide $4$ by $2$ to get $2$. Then we divide $88$ by $2$ to get $\boxed{44}$. The answer is: 44
[CLS]What is the value of 88 divided by the result of dividing 4 by 2? annually's first break down the expression suggesting ( sit. tra question suit golf 88 individual bags Thought result of divides 244 by 102 once ≥ need Town calculation what 144 divided by 2 i. groupedividing 4 Bill ((- Given be 2, situation 4 divided by 2 Exp 2 chooses Nowitudes I take the result final testingdir, which � 2, and divide 88 (( 2. 0culating 1600 DE by 2 gives me 44. their is straightforward because 88 divided ? 2 equals 44ification find)/ tails final red of the tunnel question I 44. First, yellow Div -4]$ ban $2$ tangent get &2$. write we divide :88$ by $2$ to get $\})} formed{.44}$. conclusionThe and is: 44[SEP]
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