A student at a predominantly African American high school insists on wearing a T-shirt that some say advocates white supremacy ideologies. Using the preferred freedoms approach, convince the school board to allow the student to wear the shirt to class.

Consider the following uneven cash flow stream

What is the present (Year 0) value if the opportunity cost (discount) rate is 10%? Add an outflow (or cost) of $1,000 at Year 0. What is the present value of the cash flow stream?

Your oldest daughter is about to start kindergarten at a private school. Tuition is $10,000 per year payable at the beginning of the school year. You expect to keep your daughter in private school through high school. You expect tuition to increase at a rate of 5% per year over the 13 years of her schooling. What is the present value of the tuition payments if the discount rate is 6% per year?

1. In a survey of 700 community college students, 481 indicated that they have read a book for personal enjoyment during the school year (based on data from the Community College Survey of Student Engagement).
   1. Determine a 90% confidence interval for the proportion of community college students who have read a book for personal enjoyment during the school year. You must show your work. Round the limits to the nearest thousandth.
2. 2. For a 90% confidence interval, would it be unusual if less than 450 students indicated that they have read a book for personal enjoyment during the school year? Justify your answer.
3. 3. For a 99% confidence interval, would it be unusual if less than 450 students indicated that they have read a book for personal enjoyment during the school year? Justify your answer.

Use duality to answer the following application.

The Enormous State University's Business School is buying computers. The school has two models to choose from, the Pomegranate and the iZac. Each Pomegranate comes with 400 GB of memory and 80 TB of disk space, while each iZac has 300 GB of memory and 100 TB of disk space. For reasons related to its accreditation, the school would like to be able to say that it has a total of at least 49,500 GB of memory and at least 12,500 TB of disk space. If both the Pomegranate and the iZac cost $2,000 each, how many of each should the school buy to keep the cost as low as possible?

What are the shadow costs of memory and disk space?

A recent study of high school students shows the percentage of females and males who have at LEAST one notation in their school record for inappropriate behavior. A simple random sample of high school students was interviewed. The students were asked whether they had a notation for inappropriate behavior in their school record. Of the 100 females, 21 answered yes, as did 145 of the 400 males.

Part A: Construct and interpret a 99% confidence interval for the difference in population proportions of females and males who have at LEAST one notation for inappropriate behavior. Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (8 points)

Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain. (2 points) (10 points)

[20pts] In 2005, 45% of parents with children in high school felt it was serious problem that high school students were not being taught enough math and science. A recent survey found that 52 out of 120 parents with children in high school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did in 2005? Conduct a hypothesis test at 5% significance level.

a.What are the null and alternative hypotheses? What is the type of the test (left, right, or two tailed)?

b. Compute the test statistic (Round intermediate steps to 4 decimal places and round to 2 decimal places.)

c. Use the z table to find the P-value

d. What is her conclusion? Show detailed comparison and explanation.

Education: Assume people live 2 years: youth (year 1) and adult (year 2). Youths either go to school or work. If they go to school, they earn zero. If they work they earn $1000. As adults, everyone works. An educated adult earns $3000 while an uneducated adult earns $1800. The interest rate is 12% and the government pays the full cost of schooling at $350 per year.   

Earnings

Earnings: Year 1 Year 2

A. Earnings profile: no school $1000 $1800

B. Earnings profile: with school 0 $3000

C. Earnings gain from schooling -$1000 +$1200

Therefore, calculate the present discounted value of the benefits of schooling and the rate of return for both the individual and society.

Net Private Benefit?

Private Rate of Return?

Net Social Benefit?

Social Rate of Return?

a) A company is considering a new piece of equipment that will save them $1818 per year. The machine costs $9040. After 8 years in service the machine will have to be replaced. It has no salvage value at the end of eight years. Given a MARR of 10.9% per year. What is the present worth of the machine?

b) Sofia an intern from an engineering school finds an alternative manufacturer who offers the same piece of equipment with a guarantee that it will work for 16 years. It cost $10000 and offers the exact same savings for 16 years. It also has no salvage value. What is the present worth of this machine?