A honey bee of mass 135 mg has accumulated a static charge of +1.6 pC. The bee is returning to her hive by following the path shown in the figure. Because Earth has a naturally occurring electric field near ground level of around 100 V/m

pointing vertically downward, the bee experiences an electric force as she flies.

What is the change in the bee’s electric potential energy, Δ?electric,

as she flies from point A (0 m,0.3 m) to point B (5.5 m,4.0 m)?

Δ?electric=

Compute the ratio of the bee’s change in electric potential energy to her change in gravitational potential energy, Δ?electric/Δ?grav.

Δ?electric/Δ?grav=

We want to study the zinc concentration from a river. We have a sample of measurements taken in 25 different locations in a river with sample mean x = 3 and population standard deviation σ = 0.3. The population is normally distributed.

1. Find the 95% and 99% confidence intervals for the mean zinc concentration in the river.

2. Is the following statement correct? “If we repeat the same experiment multiple times and each time calculate the two confidence intervals in question 1, then they cover x approximately 95% and 99% times respectively.” State your reason.

3. If we simply take x as the estimate for µ, how large a sample is required if we want to be 90% confident that the error will not exceed 0.05?

You are looking at buying a house with a $180,000 loan amount. You have 2 options for this loan: 1) 15 Year Loan, you can get a monthly interest rate of 0.3% monthly. A) What is your monthly payment? B) What is the total amount you would pay out of pocket over the life of the loan? C) How much interest have you paid?

2) 30 year Loan, you can get a monthly interest rate of 0.3125% monthly. A) What is your monthly payment? B) What is the total amount you would pay over the life of the loan? C) How much interest have you paid?

Please do on excel and show formula/calculations

5. Altria is reexamining the costs of capital it uses to decide on investments in its two
primary businessesó food and tobacco. The two divisions have about the same market
value.
Altria has an equity beta of 0.95 and a debt/equity ratio of 25%. The companyís debt is
priced to yield an expected return of 8%. The average equity beta of publicly traded Örms
in the tobacco business is 1.2, the average debt beta is 0.3, and the average debt/equity
ratio of such Örms is 20%. The average equity beta of publicly traded Örms in the food
business is 0.9, the average debt beta is close to zero, and the debt/equity ratio of such
Örms is 80%. The current interest rate is 7.1%.
Estimate the cost of capital for each of the two businesses

A certain firm in the beverage industry is faced with the following Cobb-Douglas production function of Q left parenthesis L comma K right parenthesis equals 4 L to the power of 0.3 end exponent space K to the power of 0.5 end exponent

a) What is A P subscript L and APK? [6 marks]

b) What is the level of M P subscript L space end subscript and M P subscript K when K = 40 and L = 40 [12 marks]

c) According to the Cobb- Douglas function , calculate the MRTS when K =35 and L = 25 [6 marks]

d) Increase capital with 75% and labour with 75% and see what will happened to output level.

(Black-Scholes)

Assume S = $22.00, σ = 0.30, r = 0.05 p.a. continuously compounded, the stock pays a 1.0% p.a. continuous dividend and the option expires in a month.

(a) What is the price of a $20 strike call? (Leave 2 d.p. for the answer)

(b) What is the delta? (Leave 3 sig. fig. for the answer)

(c) If the stock price changes to $22.10 immediately, what is the approximate change of the call price based on delta? (Leave 3 sig. fig. for the answer)

(d) What is the percentage change in the option for a 1% change in the stock? (Leave 3 sig. fig. for the answer)

(e) What is the volatility of the call option? (Leave 2 d.p. for the answer)

(f) If the Sharpe ratio of the stock is 0.3. What is the Sharpe ratio of the call?

You are the new investment manager of Michael and Ariel. You received from the previous investment manager of Michael and Ariel’s partial information regarding their portfolios:
- Both have an optimal portfolio.
- The expected return in Michael’s portfolio is 6%.
- The SD in Ariel’s portfolio is 12%.
You know that the current risk-free interest rate is 5% and the market portfolio has an expected return of 8% and a SD of 10%.
a. What is the proportion of each brother’s investment in a risk-free asset out of their portfolio?

b. Is it possible to rank the brothers’ risk preference? Explain.

c. What is the beta in each brother’s portfolio?

d. Suppose that today Michael and Ariel received an offer to buy a share with an expected return of 6% and beta of 0.3. Will they accept the offer?

They are all in their currency in billions and I need to make them into US dollar. Like Yen is 84.5 billion yen and also 14.2 billion yen, what are they if their converted to US dollars. Do that for all in the table below. Please show formula

Consider an economy with a production function given by Y =K^1/4 (EL)^3/4 . The depreciation rate is = 0.1, the population growth rate is n = 0.02 and the technological growth rate is g = 0.03. The economy's current savings rate is s = 0.3 and the current level of capital per effective worker K₀ = 1. Answer the following questions.

1. What is the consumption per effective worker in the current year (C₀) ?
2. What is the capital per effective worker in the next period (k₁) ?
3. What is the steady state level of output per effective worker (y*) ?
4. Find the golden rule level of output per-effective worker (y_G) ?
5. Compare the economy's savings rate with the golden-rule savings rate. Is the economy saving less ?

A metal cylinder of mass ? = 5 kg with a coaxial hole is sliding horizontally on a metal rod. A spring with spring constant ? = 500 N/m is attached to the cylinder. The other end of the spring is attached on a table at a vertical distance of ℎ = 0.3 m below the cylinder. The spring has an equilibrium length of ?_0 = 0.5 m.

a) What is the horizontal position ?0 of the cylinder when the spring is at its natural equilibrium length of ?0 = 0.5 m? Define the attachment point of the spring on the table as position ? = 0.

b) What is the length ? of the spring when the cylinder is at any given position ??

c) Draw a free-body diagram of the cylinder.

d) Show that the horizontal force from the spring on the cylinder is: ?? = −?? (1 − ?0 √? 2 + ℎ 2 )