Let us divide the odd positive integers into two arithmetic progressions; the red numbers are 1, 5, 9, 13, 17, 21, ... The blue numbers are 3, 7, 11, 15, 19, 23,....

(a) Prove that the product of two red numbers is red, and that the product of two blue numbers is red.

(b) Prove that every blue number has a blue prime factor.

(c) Prove that there are infinitely many blue prime numbers. Hint: Follow Euclid’s proof, but multiply a list together, multiply the result by four, then subtract one.

1. (13pt) The U.S. Census Bureau computes quarterly vacancy and homeownership rates by state and metropolitan statistical areas. The following data are the rental vacancy rates in percentage (%) grouped by region for the last quarter of 2018 using a sample of 4 statistical metropolitan areas.

                                     Vacancy rates (%)

1. (10pt) You are hired as statistician to test whether there are any differences among the regions regarding vacancy rates and you should allow for 10% error.

2. (3pt) Do you think that the mean vacancy rate is the same for these regions? Why?

HW 1-6 (please explain) greatly confused

1. At a price of $50 a ticket, the local hockey team discovers that there are many empty seats. This is evidence that: A the current price should be raised. B a shortage exists at the current price. C the equilibrium price is higher than $50. D the current price is higher than the equilibrium price.

2. Larry, Curly, and Moe each like funny movies. The current movie costs $7. Larry values it at $12, Curly at $10, and Moe at $8. Suppose that if the government taxes books at $2 each, the selling price will rise to $9. A consequence of the tax is that A consumer surplus shrinks by $9 and tax revenues increase by $6, so there is a deadweight loss of $3. B consumer surplus shrinks by $6 and tax revenues increase by $6, so there is no deadweight loss. C consumer surplus shrinks by $5 and tax revenues increase by $6, so there is no deadweight loss. D consumer surplus shrinks by $5 and tax revenues increase by $4, so there is a deadweight loss of $1. E consumer surplus shrinks by $6 and tax revenues increase by $4, so there is a deadweight loss of $2.

3. Suppose that deforestation in Alaska has led to dangerously low numbers of Sitka spruce trees. Taylor guitars are made with solid Sitka spruce tops. Deforestation in Alaska will cause prices to and consumer surplus to in the market for Taylor guitars. A increase; increase B decrease; increase C increase; decrease D decrease; decrease

4. Consider a market characterized by the following supply and demand equations: P = 130 − 6QD P = 9 + 5QS The government imposes a price floor of $60 in this market. What are the equilibrium price and quantity? (Round to the nearest tenth if necessary.) A P=$60, Q=10.2 B P=$60, Q=11 C P=$60, Q=11.7 D P=$64, Q=10.2 E P=$64, Q=11

5. Harvey, Cleo, and Jack each like pet treats. The current treat costs $2. Harvey values it at $5, Cleo at $4, and Jack at $3. Suppose that if the government taxes treats at $1.50 each, the selling price will rise to $3.50. A consequence of the tax is that A consumer surplus shrinks by $4 and tax revenues increase by $3, so there is a deadweight loss of $1. B consumer surplus shrinks by $4 and tax revenues increase by $4, so there is no deadweight loss. C consumer surplus shrinks by $1.50 and tax revenues increase by $1.50, so there is no deadweight loss. D consumer surplus shrinks by $1.50 and tax revenues increase by $4.50, so there is a deadweight loss of $3. E consumer surplus shrinks by $4 and tax revenues increase by $6, so there is a deadweight loss of $2.

6. Supply and demand for Carolina basketball tickets can be characterized by the equations P = 21 + 11QS and P = 51 − 4QD. In equilibrium, consumer surplus is and producer surplus is . A) $18 ... $8 B) $15 ... $15 C) $43 ... $30 D) $8 ... $22 E) $16 ... $44

A car insurance company has determined that 7% of all drivers were involved in a car accident last year. Among the 11 drivers living on one particular street, 3 were involved in a car accident last year. If 11 drivers are randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year? Group of answer choices 0.0317 0.0370 0.9683 0.481

You have a market portfolio and the risk premium for holding it is 5% per year. rf = 5%. There are two new stock issues: A or B. A stock has a standard deviation of 40%, a beta of 0.5, and an expected return of 8.0%. B stock has a standard deviation of 30%, a beta of 1.0, and an expected return of 9.0%. If you can add at most one stock to your portfolio, which one do you choose?

NEED EXACT NUMBERS PLEASE and how to place into excel The National Sleep Foundation used a survey to determine whether hours of sleeping per night are independent of age (Newsweek, January 19, 2004). The following show the hours of sleep on weeknights for a sample of individuals age 49 and younger and for a sample of individuals age 50 and older. Hours of Sleep Age Fewer than 6 6 to 6.9 7 to 7.9 8 or more Total 49 or younger 39 58 76 67 240 50 or older 32 64 71 93 260 Conduct a test of independence to determine whether the hours of sleep on weeknights are independent of age. Use = .05. Use Table 12.4. Compute the value of the 2 test statistic (to 2 decimals). The p value is What is your conclusion? Using the total sample of 500, estimate the percentage of people who sleep less than 6, 6 to 6.9, 7 to 7.9, and 8 or more hours on weeknights (to 1 decimal). Less than 6 hours % 6 to 6.9 hours % 7 to 7.9 hours % 8 or more hours %

Answer questions 5-9 below using the information in this experimental description. Dr. Meyer wants to study the effect of Kava root on insomnia. She recruits 150 people who experience long term insomnia (more than 4 months experiencing insomnia) and divides them into two groups. One group of 75 individuals takes 125 mg of kavalactones one hour before bedtime. The other group of 75 individuals takes a placebo every day. For the duration of the study, the two groups follow two common guidelines: no added sugars or caffeine intake after 12pm and no screen time an hour before bedtime. Dr. Meyer follows the individuals during four weeks. She collects data on sleep patterns which include the number of hours slept each night and a scale of difficulty to fall asleep scored 1 to 5 (1 = feel asleep right away; 5 = more than one hour awake in bed).

5. 1pt. What is the independent variable?

6. 1pt. What is the dependent variable?

7. 1pt. What is the experimental group?

8. 1pt. Which is/are Dr. Meyer’s controlled variable(s)?

9. 1pt. Write a possible hypothesis for this experiment.

10. 1.5pts. Is the following statement a prediction or a theory? How do you know?

“If Vitamin C supplementation shortens the length of the common cold, then adults taking 1g of Vitamin C a day will recover from the common cold faster than adults who aren’t taking Vitamin C supplementation.”

Problem 4.3 part 2

On October 5, 2015, you purchase a $10,000 T-note that matures on August 15, 2027. (Settlement occurs two dayws after purchase, so you receive actual ownership of the bond on October 7, 2015). The coupon rate on the T-note is 4.375% and the current price quoted on the bond is 105.250%. The last coupon payment occurred on May 15, 2015 (145 days before settlement) and the next coupon payment will be paid on November 15, 2015 (39 days from settlement).

A) Calculate the annual yield to maturity (based on the clean price) for the bond purchased on October 7, 2013, and maturing on August 15, 2024 (or in 10.8603 years).

B) Explain in an essay of at least one full paragraph exactly why the bond in this problem is selling at a premium (ignore the accrued interest). That is, explain exactly why investors would be willing to pay more than face value for this bond, and in your answer address the issue of how newly issued bonds compete with this bond, which is being sold in the secondary market as a previously issued bond.