PLEASE ANSWER THE LAST QUESTIONS (as many as you can starting with the last question)

On January 1, 2016, the following information was drawn from the accounting records of Carter Company: cash of $400; land of $2,400; notes payable of $700; and common stock of $1,540. Required a. Determine the amount of retained earnings as of January 1, 2016.

g. During 2016, Carter Company earned cash revenue of $660, paid cash expenses of $380, and paid a cash dividend of $58. (Hint: It is helpful to record these events under an accounting equation before preparing the statements.) (Enter any decreases to account balances with a minus sign. Select "NA" if there is no effect on the "Account Titles for Retained Earnings".)

g-2. Prepare a statement of changes in stockholders’ equity dated December 31, 2016.

g-3. Prepare a balance sheet dated December 31, 2016. g-4.

Prepare a statement of cash flows dated December 31, 2016. (Amounts to be deducted should be indicated with a minus sign.)

j. What is the balance in the Revenue account on January 1, 2016?

Assume that customer arrivals at a barber shop are random and independent of one another, and the number of customer arrivals at a barber shop and the time until the next customer arrives is independent.

(a) In city A, on average, 3 customers arrive at a barber shop every hour. Using an appropriate probability distribution,

(i) find the probability that at least 5 customers arrive at a barber shop every hour.

(ii) A sample of 25 barber shops in city A was obtained. Find the probability that at least 3 barber shops were visited by at least 5 customers.

(iii) A customer has just arrived in a barber shop. Find the probability that the time, until the next customer arrives will be at most 2 hours (from now).

Customers arrive in a certain shop according to an approximate Poissonprocess on the average of two every 6 minutes.

(a) Using the Poisson distribution calculate the probability of two or more customersarrive in a 2-minute period.

(b) Consider X denote number of customers and X follows binomial distribution withparametersn= 100. Using the binomial distribution calculate the probability oftwo or more customers arrive in a 2-minute period.

(c) Let Y denote the waiting time in minutes until the first customer arrives. (i) Whatis the pdf ofY? (ii) Findq1=π0.75

(d) Let Y denote the waiting time in minutes until the first customer arrives. What isthe probability that the shopkeeper will have to wait more than 3 minutes for thearrival of the first customer ?

(e) What is the probability that shopkeeper will wait more than 3 minutes before bothof the first two customers arrive?

Suppose you know that a company’s stock currently sells for $74 per share and the required return on the stock is 9.9 percent. You also know that the total return on the stock is evenly divided between a capital gains yield and a dividend yield. It's the company’s policy to maintain a constant growth rate in its dividends. What is the current dividend per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Hint: First, compute the current dividend yield. Then, use that to compute the next dividend paid (in dollars per share). Then, using the constant dividend growth rate, compute the last dividend paid. The dividend is equal to the dividend yield multiplied by the stock price. Remember that the current stock price reflects future dividends, starting with D1, where D1 = D0(1 + g).

A person of mass 74 kg stands at the center of a rotating merry-go-round platform of radius 3.5 m and moment of inertia 880 kg⋅m2 . The platform rotates without friction with angular velocity 0.90 rad/s . The person walks radially to the edge of the platform.

Calculate the angular velocity when the person reaches the edge.

Calculate the rotational kinetic energy of the system of platform plus person before and after the person's walk.

Each "2p" electron deep inside a Tungsten atom is influenced mostly by 74 protons in the nucleus (treat as a point), and the 4 electrons (treat as shells around the nucleus) which are interior to it (2 in 1s and 2 in 2s). How fast does one of these "2p" electrons need to be moving, to travel around a circular orbit with radius 3.158[pico-meter]? {m_e=0.911E−30[kg]}

1. A random sampling of 60 pitchers from the National League and 74 pitchers from the American League showed that 38 National and 36 American League pitchers had E.R.A's below 3.5.

Find the test statistic that would be used to test the claim that the proportion of the NL pitchers with E.R.A. below 3.5 is higher than the proportion of the AL pitchers with similar stats.

Round your answer to three decimal places.

2. Two independent samples are randomly selected and come from populations that are normal. The sample statistics are given below:

n1 = 47 n2 = 52

1 = 24.2 2 = 18.7

s1 = 5.0 s2 = 5.6

Find the standardized test statistic t to test the hypothesis that μ1 = μ2. Round your answer to three decimal places.

A certain tennis player makes a successful first serve 74​% of the time. Suppose the tennis player serves 110 times in a match.​ What's the probability that she makes at least 86 first​ serves?

Suppose you run a regression containing observations for each of the 74 kinds of cars released in 1978 in the United States, and you regress price (in dollars) on weight (in pounds). You get the following results:
ˆ β0 is -6.71, with SE 1174.4. ˆ β1 (slope coefficient on weight) is 2.04 with SE .377.
• (a) Say, in words, what the slope coefficient means in this case, without taking a stand on causality.

• (b) Suppose I give you the following information: the sum of squares total is roughly equal to 635 million, and the sum of squares explained is equal to 185 million. Please report the R2 and the correlation coefficient between price and weight.

• (c) Use your regression model to predict what the price would be for a car that weighs 3000 pounds.

• (d) Use the SER to add uncertainty and make this prediction an interval. • (5 points) Build a 95% confidence interval for the slope coefficient and report the p-value for comparing it to 0. Interpret your results.