The probability that a randomly chosen citizen-entity of Cygnus is o.pdf

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The probability that a randomly chosen citizen-entity of Cygnus is of pension age is approximately 0.7. What is the probability that, in a randomly selected sample of 3 citizen- entities, all of them are of pension age? Round your answer to four decimal places. Solution P(1st is of pension age)=0.7 P(2nd is of pension age)=0.7 P(3rd is of pension age)=0.7 P(1st is of pension age AND 2nd is of pension age AND 3rd is of pension age)= 0.7x0.7x0.7x=0.3430.

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The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial population P0 has doubled in 5 years. Suppose it is known that the population is 11,000 after 3 years. What was the initial population P0? (Round your answer to one decimal place.) P0 = 1 What will be the population in 10 years? (Round your answer to the nearest person.) 2 persons How fast is the population growing at t = 10? (Round your answer to the nearest person.) 3 persons/year Solution dP/dt = P(t) P = ? P(t) dt P = e^(kt) So P(t) = P0*e^(kt) If P(5) = 2P0: P(5) = P0*e^(k5) 2P0 = P0*e^(5k) 2 = e^(5k) ln(2) = 5k k = ln(2)/5 P(t) = P0*e^(ln(2)t/5) P(t) = P0*2^(t/5) 2) P(t) = 11,000 when t = 3 P(3) = 11,000 P0*2^(3/5) = 11,000 P0 = 11000/(2^(3/5)) P0 = 7257.29, or rounded to 7257 P(10) = 7257*2^(10/5) P(10) = 7257*2.

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The previous help did not produce a correct answer. Archimedes Levers is financed by a mixture of debt and equity. You have the following information about its cost of capital: Calculate the rE, rA, E, D, and A. I received the following response for rE &rA, which are not correct: Re=Riskfree Rate+Beta*(Market Rate-Riskfree Rate)=10+1.6*(15-10)=18% Ra=0.35*11+0.65*18=12.91%rE = ? %rD = 11%rA = ? %E = ?D = .2A = ?rf = 10 %rm = 15%D/V = .35 Solution rE = rf + E * (rm - rf) = 10% + 2.4 * (15% - 10%) = 22% D = (rD - rf) / (rm - rf) = (12% - 10%) / (15% - 10%) = 0.4 A = E/V * (E + D * D/E) = 0.45 * (2.4 + 0.4 * 0.45/0.55) = 1.23 rA = rf + A * (rm - rf) = 10% +1.23 * (15% - 10%) = 16.14% Archimedes repurchases debt and issues equity rE = rf + E * (rm - rf) = 10% + 2.4 * (15% - 10%) = 22% D = (rD - rf) / (rm - rf) = (11% - 10%) / (15% - 10%) = 0.2 A = E/V * (E + D * D/E) = 0.65 * (2.4 + 0.2 * 0.35/0.65) = 1.63 rA = rf + A * (rm - rf) = 10% +1.63 * (15% - 10%) = 18.15%.

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