claim: (Multiplying .95 by itself 15 times yields 46.3 percent.)”
evidences.evidence_id: Dimensional analysis:69
evidences.article: Dimensional analysis
evidences.evidence: 1000   g   NO x 1 kg   NO x × 46   kg   NO x 1   kmol   NO x × 1   kmol   NO x 22.414   m 3   NO x × 10   m 3   NO x 10 6   m 3   gas × 20   m 3   gas 1   minute × 60   minute 1   hour = 24.63   g   NO x hour {\displaystyle {\frac {1000\ {\ce {g\ NO}}_{x}}{1{\cancel {{\ce {kg\ NO}}_{x}}}}}\times {\frac {46\ {\cancel {{\ce {kg\ NO}}_{x}}}}{1\ {\cancel {{\ce {kmol\ NO}}_{x}}}}}\times {\frac {1\ {\cancel {{\ce {kmol\ NO}}_{x}}}}{22.414\ {\cancel {{\ce {m}}^{3}\ {\ce {NO}}_{x}}}}}\times {\frac {10\ {\cancel {{\ce {m}}^{3}\ {\ce {NO}}_{x}}}}{10^{6}\ {\cancel {{\ce {m}}^{3}\ {\ce {gas}}}}}}\times {\frac {20\ {\cancel {{\ce {m}}^{3}\ {\ce {gas}}}}}{1\ {\cancel {\ce {minute}}}}}\times {\frac {60\ {\cancel {\ce {minute}}}}{1\ {\ce {hour}}}}=24.63\ {\frac {{\ce {g\ NO}}_{x}}{\ce {hour}}}} After canceling out any dimensional units that appear both in the numerators and denominators of the fractions in the above equation, the NOx concentration of 10 ppmv converts to mass flow rate of 24.63 grams per hour.
evidences.votes: NOT_ENOUGH_INFO NOT_ENOUGH_INFO
evidences.evidence_id: Rate of return:33
evidences.article: Rate of return
evidences.evidence: This is a return of 20,000 USD divided by 100,000 USD, which equals 20 percent.
evidences.votes: NOT_ENOUGH_INFO NOT_ENOUGH_INFO
evidences.evidence_id: Rate of return:46
evidences.article: Rate of return
evidences.evidence: Assuming returns are reinvested, if the returns over n {\displaystyle n} successive time sub-periods are R 1 , R 2 , R 3 , ⋯ , R n {\displaystyle R_{1},R_{2},R_{3},\cdots ,R_{n}} , then the cumulative return or overall return over the overall time period is the result of compounding the returns together: ( 1 + R 1 ) ( 1 + R 2 ) ⋯ ( 1 + R n ) − 1 {\displaystyle (1+R_{1})(1+R_{2})\cdots (1+R_{n})-1} If the returns are logarithmic returns however, the logarithmic return over the overall time period is: ∑ i = 1 n R l o g , i = R l o g , 1 + R l o g , 2 + R l o g , 3 + ⋯ + R l o g , n {\displaystyle \sum _{i=1}^{n}R_{\mathrm {log} ,i}=R_{\mathrm {log} ,1}+R_{\mathrm {log} ,2}+R_{\mathrm {log} ,3}+\cdots +R_{\mathrm {log} ,n}} This formula applies with an assumption of reinvestment of returns and it means that successive logarithmic returns can be summed, i.e.
evidences.votes: NOT_ENOUGH_INFO NOT_ENOUGH_INFO
evidences.evidence_id: Rate of return:53
evidences.article: Rate of return
evidences.evidence: For example, assuming reinvestment, the cumulative return for annual returns: 50%, -20%, 30% and -40% is: ( 1 + 0.50 ) ( 1 − 0.20 ) ( 1 + 0.30 ) ( 1 − 0.40 ) − 1 = − 0.0640 = − 6.40 % {\displaystyle (1+0.50)(1-0.20)(1+0.30)(1-0.40)-1=-0.0640=-6.40\%} and the geometric average is: ( 1 + 0.50 ) ( 1 − 0.20 ) ( 1 + 0.30 ) ( 1 − 0.40 ) 4 − 1 = − 0.0164 = − 1.64 % {\displaystyle {\sqrt[{4}]{(1+0.50)(1-0.20)(1+0.30)(1-0.40)}}-1=-0.0164=-1.64\%} which is equal to the annualized cumulative return: 1 − 0.0640 4 − 1 = − 0.0164 {\displaystyle {\sqrt[{4}]{1-0.0640}}-1=-0.0164} In the presence of external flows, such as cash or securities moving into or out of the portfolio, the return should be calculated by compensating for these movements.
evidences.votes: NOT_ENOUGH_INFO NOT_ENOUGH_INFO
evidences.evidence_id: Rate of return:72
evidences.article: Rate of return
evidences.evidence: The value of an investment is doubled if the return r {\displaystyle r} = +100%, that is, if r l o g {\displaystyle r_{\mathrm {log} }} = ln($200 / $100) = ln(2) = 69.3%.
evidences.votes: NOT_ENOUGH_INFO NOT_ENOUGH_INFO