Suppose a firm's marginal product of capital and marginal product of labor schedules are as shown in the table below. The firm hires both capital and labor competitively for $4 and $8, respectively. Its output is sold in a competitive market for $.50 per unit.

1. Suppose the firm is currently using 4 units of capital and 4 units of labor. Is the corresponding output being produced at least cost? How do you know?
   
   
   
   
2. What combination of labor and capital should the firm use to maximize its profit? Show.
   
   
   
   
3. If the marginal product of each resource does not depend on the quantity of the other resource, what output level corresponds to the input combination you just found? Show how.
   
   
   
4. Does this combination produce this output level at least cost?

Suppose scores on a college entrance exam are normally distributed with a mean of 550 and a standard deviation of 100.

Find the score that marks the cut-off for the top 16% of the scores. Round to two decimal places.

Question 5 options:

Question 6 (1 point)

Suppose scores on a college entrance exam are normally distributed with a mean of 550 and a standard deviation of 100.

Find the cut-off scores that define the middle 60%. Round to two decimal places.

Question 6 options:

Question 7:

Suppose scores on a college entrance exam are normally distributed with a mean of 550 and a standard deviation of 100.

What is the probability that the sample mean score will be greater than 565, in a random sample of 100 entrance exams? Round to 4 decimal places

Question 7 options:

Question 8 (1 point)

The running time for videos submitted to YouTube in a given week is normally distributed with a mean of 390 seconds and a standard deviation of 148 seconds.

Suppose that a sample of 40 voters is selected. What is the probability that the mean running time for the sample exceeds six minutes? (Don't overlook: How many seconds are in 1 minute?)

Question 8 options:

Question 9 (1 point)

On a certain television channel, 18% of commercials are local advertisers. A sample of 120 commercials is selected.

What is the probability that more than 20% of the commercials in the sample are local advertisers?

Question 9 options:

Question 10 (1 point)

On a certain television channel, 18% of commercials are local advertisers. A sample of 120 commercials is selected.

Would it be unusual for more than 25% of the commercials in the sample are local advertisers?

Question 10 options:

This is a Microbiology essay question. Please provide detailed answers.

There is no single gene that determines whether a bacterial cell is gram positive or negative.
a. Give examples of two genes that code for parts of the cell wall (gram positive, negative, or both).
b. Some phenotypes, like resistance to a particular antibiotic, are gained and lost by a bacterial lineage frequently. Why don’t we see bacterial lineages changing back and forth between gram positive and negative?

Harry lost his watch and offers a reward of $100 to the person who returns it to him. Jim finds the watch, sees Harry's name and address on the watch and returns it (Jim never knew of the reward.) Two days later Joe told Jim that Harry had offered a reward and since he (Jim) had found the watch, he should collect it. Can Jim require Harry to pay him the reward?

Result:

Reason:

Exception:

1) On January 1 of this year, Shannon Company completed the following transactions (assume a 8% annual interest rate): (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use the appropriate factor(s) from the tables provided.)

1. Bought a delivery truck and agreed to pay $60,200 at the end of three years.
2. Rented an office building and was given the option of paying $10,200 at the end of each of the next three years or paying $28,200 immediately.
3. Established a savings account by depositing a single amount that will increase to $90,400 at the end of seven years.
4. Decided to deposit a single sum in the bank that will provide 8 equal annual year-end payments of $40,200 to a retired employee (payments starting December 31 of this year).

d. What single sum must be deposited in the bank on January 1 of this year? (Round your answer to nearest whole dollar.)

2) An investment will pay $15,600 at the end of each year for eight years and a one-time payment of $156,000 at the end of the eighth year. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use the appropriate factor(s) from the tables provided.)

Determine the present value of this investment using a 7% annual interest rate. (Round your answer to the nearest whole dollar.)

A copper ball of temperature 100 °C is immersed to a water bath of 50 °C. After 10 minutes the temperature of the ball is 80 °C and the temperature of the water is 60 °C. You may assume that Newton’s Law of Cooling is obeyed and all the heat lost by the ball is absorbed by the water. Find the equilibrium temperature of the ball as a function of time.

An alternating annuity pays $1 in one year, −$2 in two years, $4 in three years, −$8 in four years, which each subsequent payment doubling and changing sign for 20 years. If the risk-free discount rate is 5%, what is the value of this alternating annuity?

Assume that the market rate of interest rises from 6% to 12%. Which one of the following two bonds would have higher price risk? Show your work.

1. An 8-year 9% annual coupon rate bond
2. A 10-year zero coupon bond