In a class of 87 people, 27 wear glasses, 32 are blonde, and 38 are neither blonde nor wear glasses. Find the probability that a student chosen at random will have blonde hair and wear glasses?

27) A firm has a production function Q = KL, where Q is the quantity of output, K is the amount of capital and L is the amount of labor. MPL=K and MPK=L.

a) Suppose that capital is fixed at K=10 in short run. In this case, the marginal product of labor is MPL=10. Does this production function exhibit diminishing marginal returns to labor?

b) Suppose that in the short run, K is fixed at 10. The interest rate is r=4 and the wage is w=1. What is the short run total cost curve?

c) In (b), what are the functions for fixed cost, variable cost, average fixed cost, average variable cost and average cost?

d) In the long-run, capital is also variable. Does this production function exhibit increasing, decreasing or constant returns to scale?

e) What is the long run cost function? What is average cost in the long run? Hint: Use MRTS=-MPL/MPK = -w/r as we discussed in class. Note that MPL=K and MPK=L.

f) Does this cost function exhibit increasing or decreasing economies of scale?

Reid Company is considering the production of a new product. The expected variable cost is $27 per unit. Annual fixed costs are expected to be $810,000. The anticipated sales price is $72 each.

Determine the break-even point in units and dollars using each of the following:

a. Use the equation method.

b. Use the contribution margin per unit approach.

c. Use the contribution margin ratio approach. (Do not round intermediate calculations. Round "Contribution margin ratio" to 1 decimal place. (i.e., .234 should be entered as 23.4))

Use the equation method.

A long, straight wire carries a current of 20.0 A, as shown in Figure 27-63. A rectangular coil that has two sides parallel to the straight wire has sides that are 5.00 cm long and 10.0 cm long. The side nearest to the wire is 2.00 cm from the wire. The coil carries a current of 5.00 A. (a) Find the force on each segment of the rectangular coil due to the current in the long, straight wire. What is the net force on the coil?

You are scheduled to receive annual payments of $8,600 for each of the next 27 years. The discount rate is 7.0 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?

A random sample of 27 observations is used to estimate the population variance. The sample mean and sample standard deviation are calculated as 44 and 4.5, respectively. Assume that the population is normally distributed. (You may find it useful to reference the appropriate table: chi-square table or F table)

a. Construct the 95% interval estimate for the population variance. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

b. Construct the 99% interval estimate for the population variance. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

A uniform cylinder of radius 14 cm and mass 27 kg is mounted so as to rotate freely about a horizontal axis that is parallel to and 9.3 cm from the central longitudinal axis of the cylinder. (a) What is the rotational inertia of the cylinder about the axis of rotation? (b) If the cylinder is released from rest with its central longitudinal axis at the same height as the axis about which the cylinder rotates, what is the angular speed of the cylinder as it passes through its lowest position?

A Pharma company has recently recruited 4 scientists at an average age of 27 and is looking to develop quite a few pharmacological formulations. With a view to retain them the company proposes to offer a housing scheme to them on the following terms and conditions:

1. The number of beneficiaries will be four in number
2. The total cost of purchasing apartments will be Rs.1 crore
3. PNBHFL offers an 18 year term @ 9.00% interest and HDFC offers 15 years term @ 8% interest.
4. The company will pay the housing finance company on an installment basis.
5. A Down payment of 5% of the cost of the apartment has to be made and recoverable from the employee in 24 installments. The upfront payment will be made by the company.
6. In case of availing the loan from HDFC, 50% of the installment will be recovered from the employee on a monthly basis and in case of availing the loan from PNBHFL 45% will be recovered from the employee. The option of choosing the service rests with the company only.
7. Assume that employee deductions happen on the first day of the month and housing loan payments made by the company happens on the last day of the year.
8. The housing loan is offered on a fixed interest basis and EMI will not change.
9. Assume the individual apartments are of equal value.

You are called upon to do the following:

1. Calculate the two EMI options and choose the best one.

The following are option price quotations for The North West Company on July 27, 2019:

The North West Company stock market price $29.89

a. What is the intrinsic value and time value for each option?

b. Calculate the breakeven share price for each option.

c. Suppose on July 27, 2019 you take the long position (buy) in one August 16, 2019 call option on The North West Company and hold your position to the expiry date. Calculate your net profit given the following stock prices (Po) $ 20, 25, 30, 35, and 40.

d. Suppose on July 27, 2019 you take the short position (sell) in one August 16, 2019 put option on The North West Company and hold your position to the expiry date. Calculate your net profit given the following stock prices (Po) $ 20, 25, 30, 35, and 40.

Enter the last usable host on the network of which the host 74.200.198.88/27 is a part.