About 30,000 Joules of energy is stored in a typical 1.5 volt D-cell battery. If two such batteries are joined to produce a total of 3 volts in a circuit and cause 1.2 amps of current, how long will the batteries be able to deliver power to the circuit at this level? The resistance of an electric heater is 8 ohms when connected to 120 volts, how much energy does it use during 40 minutes of operation?

1. Consider a forward contract for one share of a stock, with T = 0.5 (6 months).
The current stock price is S0 = 50. We assume that the risk-free interest rate is r = 0.05,
and that the stock pays discrete dividends, there being exactly one dividend payment, of
size 0.75, between times 0 and T, and the payment happens at time t = 1/3 (4 months).
Calculate the price of the forward contract. Show your work. Use two decimal places in your
answer. Use sufficiently many decimals in intermediate calculations to make sure that your
two decimals in the final answer are correct.

Consider a forward contract for one share of a stock, with T = 0.5 (6 months).
The current stock price is S0 = 50. We assume that the risk-free interest rate is r = 0.05,
and that the stock pays discrete dividends, there being exactly one dividend payment, of
size 0.75, between times 0 and T, and the payment happens at time t = 1/3 (4 months).
Calculate the price of the forward contract. Show your work. Use two decimal places in your
answer. Use sufficiently many decimals in intermediate calculations to make sure that your
two decimals in the final answer are correct.

Melbourne Pty Ltd has an average weekly payroll of $600,000. The employees receive entitlements to two weeks sick leave per year. The sick leave entitlements are classified as non-vesting. Past experience suggests that 50% of employees will use their full two weeks entitlements each year, 25% of employees will take one weeks sick leave each year and 15% of employees will take one day’s sick leave each year.

1. Calculate the expected sick leave expense for Melbourne Pty Ltd (on the basis of average salaries).
2. Provide the monthly journal entries necessary to recognise the sick leave entitlement expense as it accrues.

Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean μ = 75 and estimated standard deviation σ = 50. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.

(a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)


(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1.

The probability distribution of x is approximately normal with μ_x = 75 and σ_x = 25.00.The probability distribution of x is approximately normal with μ_x = 75 and σ_x = 35.36.     The probability distribution of x is not normal.The probability distribution of x is approximately normal with μ_x = 75 and σ_x = 50.

What is the probability that x < 40? (Round your answer to four decimal places.)


(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)


(d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)

1. A company has recorded data on the weekly sales for its product (y) and the unit price of the competitor’s product (x). The data resulting from a random sample of 7 weeks follows. Use Excel’s Regression Tool to answer the following questions.

1. 
   What is the estimated regression equation?
2. Perform a t test and determine whether or not x and y are related. Use a = 0.05.
3. Perform an F test and determine whether or not x and y are related. Use a = 0.05.
4. Find and interpret the coefficient of determination.

How much should you invest in Y so that your portfolio will have a risk of 13%, given the following:

The correlation between the returns of the two assets is 0.

Answer in decimal form and, if you have two answers report the one that will produce the higher expected returns.

A stock price is currently $100. Over each of the next two six-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a one-year European call option with a strike price of $100 using a two-step Binomial tree? (Draw the tree)

If the class contains 35 people, 12 have brown hair, 11 are blondes, 8 have black hair, and the rest are redheads, what is the probability of randomly selecting a redhead and a blonde on two random selections (of one each).

Given the above distribution:

A. how many permutations of redheads are there ?

B. How many combinations of redheads taken two at a time ?

3. An urn contains 12 red balls and 8 green balls. Six balls are drawn randomly with replacement

a. Find the probability of drawing exactly two red balls?

b. Find the probability of drawing at least one green ball?

c. Find the probability of drawing exactly two green balls when the drawings are done without replacement?