There are 100 shares outstanding of a company and Net Income is $10,000 and is paid out to shareholder as dividend without retaining earning so the dividend per share is $100. Assuming a 10 percent required return, the value of a share of stock today.

Why Study Math and Statistics? answer in 100 words or more

A survey of 100 senior citizens was undertaken and it was found that 20 of them had the flu vaccine this year. Do these data suggest that the proportion of senior citizens who get the flu vaccine is significantly less than 23%? Test at α = 0.01 α = 0.01 Round your answers to three decimal places.

(a). Without rounding any interim calculations, compute the test statistic:

(b). Compute the critical value:

(c). Using your answer from part (a), compute the p-value

1. There are identical firms with cost function ?(?) = ? 2 + 100. The market demand is given by the following inverse demand function ? = −0.02? + 220. The industry is a constant cost industry. This is a competitive market where each firm takes the price as given, with $5 per unit tax levied on the producers.

a) Calculate the firm’s MC, AC, AVC and supply ?(?). Graph the cost curves and the supply on a graph.

b) What is the long-run market supply curve? Graph the long-run market supply with the market demand on a graph. Explain how you come to your conclusion.

c) How many firms operate in the long-run? Explain why you will not see a more or smaller number of firms in the long run.

d) What is the short-run market supply if there are 50 firms? What is the profit in the short-run with 50 firms in the market? What is the consumer surplus, producer surplus, and the total welfare in the short run with 50 firms?

g) What is the consumer surplus, producer surplus, and the total welfare in the long-run?

The mean population IQ is 100 with a standard deviation of 15. A principal at a certain school claims that the mean IQ score of their students in his school is greater that 100. A random sample of 30 students IQ scores have a mean score of 112. Significance level α = 0.01

(a) State the null and alternate hypotheses

(b) Calculate the z statistic value 6

(c) Determine the p value. Sketch the graph

(d) Make a decision. Reject or fail to reject H0 ?

(e) Is there sufficient evidence at the 1% significance level to support the principal’s claim? Explain your answer in relation to this context.

A television factory knows that 2% of their televisions are defective. In a batch of 100 new televisions, 4 of them are inspected at random. What is the probability that 1 of them will be defective? What is the probability that they all turn out to be defective?

A cup of coffee is made with boiling water at 100 and stands in a room where the temperature is 25. The change in temperature, H in degrees , with respect to time t, in minutes, is given by the following differential equation. (dH)/(dt)=-k(H-25) Solve this differential equation. If the coffee cools to 90 in 3 minutes, how long will it take to cool to 60 degrees? Round your answer to the nearest integer.

If you collect a sample of size 100 with a sample mean of 50 and a standard error of the mean of 6 and test the hypothesis that the true mean is equal to 38 using a two tailed test with a significance level of 5% would you reject the hypothesis? Click True to reject or False to fail to reject.

True

False