A study found that highway drivers in one state traveled at an average speed of 59.7 miles per hour​ (MPH). Assume the population standard deviation is 6. MPH. Complete parts a through d below.

a. What is the probability that a sample of 30 of the drivers will have a sample mean less than 58 ​MPH? (Round to four decimal places as​ needed.)

b. What is the probability that a sample of 45 of the drivers will have a sample mean less than 58 ​MPH? (Round to four decimal places as​ needed.)

c. What is the probability that a sample of 60 of the drivers will have a sample mean less than 58​ MPH? (Round to four decimal places as​ needed.)

d. Explain the difference in these probabilities. (Select one each) As the sample size​ increases, the standard error of the mean (Same, Increase, Decrease) As the sample size​ increases, the standard error of the mean (Same, Move farther, Move closer) the population mean of 59.7 MPH.​ Therefore, the probability of observing a sample mean less than 58 MPH (Same, Increase, Decrease).

Consider a projectile launched at a height h feet above the ground and at an angle θ with the horizontal. If the initial velocity is v₀ feet per second, the path of the projectile is modeled by the parametric equations

x = t(v₀ cos(θ))

and

y = h + (v₀ sin(θ))t − 16t².

The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit h = 3 feet above the ground. It leaves the bat at an angle of θ degrees with the horizontal at a speed of 107 miles per hour (see figure).

(a) Write a set of parametric equations for the path of the ball. (Write your equations in terms of t and θ.)

(b) Use a graphing utility to graph the path of the ball when θ = 15°. Is the hit a home run?

YesNo    

(c) Use a graphing utility to graph the path of the ball when θ = 23°. Is the hit a home run?

YesNo    

(d) Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run. (Round your answer to one decimal place.)
  °

Adrian is a salesperson who represents several wholesale companies. On January 2, 2018, she receives by mail a commission check from Ace Distributors in the amount of $10,000 and dated December 30, 2017. Adrian is concerned about the year in which the $10,000 is taxable. Although the check is dated 2017, she contends that it would have been unreasonable for her to drive the 50 miles to the Ace offices on a holiday to collect the check. Further, Adrian maintains that even if she had made the trip to collect the check, by the time she returned home, her bank would have closed and she could not have received credit for the check until after the first of the year. Adrian would like you to determine whether she should include the $10,000 on her 2017 or 2018 tax return. §61; Reg. §1.451-1; Murphy v. U.S., 71 AFTR 2d 93-1862 (CA9, 1993); Kahler, 18 T.C. 31 (1942); Zahirdueen Premji, et ux. v. Commissioner, TC Memo 1996-304.

Marsha Jones has bought a used Mercedes horse transporter for her Connecticut estate. It cost $36,000. The object is to save on horse transporter rentals.

Marsha had been renting a transporter every other week for $201 per week plus $1.05 per mile. Most of the trips are 90 miles in total. Marsha usually gives the driver a $45 tip. With the new transporter she will only have to pay for diesel fuel and maintenance, at about $.46 per mile. Insurance costs for Marsha’s transporter are $1,250 per year.

The transporter will probably be worth $16,000 (in real terms) after eight years, when Marsha’s horse Nike will be ready to retire. Assume a nominal discount rate of 10% and a forecasted inflation rate of 4%. Marsha’s transporter is a personal outlay, not a business or financial investment, so taxes can be ignored. Hint: All numbers given in the questions are in real terms. Assume CF at end of year, for simplicity.

Calculate the NPV of the investment. (Do not round intermediate calculations. Round your answer to the nearest whole dollar amount.)

Marsha Jones has bought a used Mercedes horse transporter for her Connecticut estate. It cost $50,000. The object is to save on horse transporter rentals.

Marsha had been renting a transporter every other week for $215 per week plus $1.75 per mile. Most of the trips are 90 miles in total. Marsha usually gives the driver a $40 tip. With the new transporter she will only have to pay for diesel fuel and maintenance, at about $.60 per mile. Insurance costs for Marsha’s transporter are $1,950 per year.

The transporter will probably be worth $30,000 (in real terms) after eight years, when Marsha’s horse Nike will be ready to retire. Assume a nominal discount rate of 7% and a forecasted inflation rate of 3%. Marsha’s transporter is a personal outlay, not a business or financial investment, so taxes can be ignored. Hint: All numbers given in the questions are in real terms. Assume CF at end of year, for simplicity.

Calculate the NPV of the investment. (Do not round intermediate calculations. Round your answer to the nearest whole dollar amount.)

NPV = $ ________

Transportation management systems (TMS) provide greater _______ and optimize the _________.

Group of answer choices

a. costing; value chain

b. regulations; demand chain

c. visibility; supply chain

d. profits; internet of things

___________________________________

Supply chains rely on three flows: _______, ___________, and _________.

Group of answer choices

a. regulation; land bridges; demand

b. product; money; information

c. sight; costs; electronic

d. agency; principal; contingent  

_________________________________________________  

Which mode of transportation is most important in terms of freight ton-miles?​

Group of answer choices

a. Air Carriers

b. Rail Carriers

c. Motor Carriers

d. Pipelines

__________________________________________-

Transportation systems are critical to industrialized societies because?

Group of answer choices

a. They allow employees to work longer hours

b. They allow producers to expand their market areas

c. They provide access to recreation areas

d. None of these are correct  

________________________________________________________

The volume of global trade over the course of the last 50 years has:

Group of answer choices

a. Remained almost constant

b. Doubled

c. Tripled

d. Decreased

COURSE: PURCHASING  

Marsha Jones has bought a used Mercedes horse transporter for her Connecticut estate. It cost $41,000. The object is to save on horse transporter rentals.

Marsha had been renting a transporter every other week for $206 per week plus $1.30 per mile. Most of the trips are 90 miles in total. Marsha usually gives the driver a $45 tip. With the new transporter she will only have to pay for diesel fuel and maintenance, at about $.51 per mile. Insurance costs for Marsha’s transporter are $1,500 per year.

The transporter will probably be worth $21,000 (in real terms) after eight years, when Marsha’s horse Nike will be ready to retire. Assume a nominal discount rate of 8% and a forecasted inflation rate of 3%. Marsha’s transporter is a personal outlay, not a business or financial investment, so taxes can be ignored. Hint: All numbers given in the questions are in real terms. Assume CF at end of year, for simplicity.

Calculate the NPV of the investment. (Do not round intermediate calculations. Round your answer to the nearest whole dollar amount.)

Do the Math 6-3
A Recent Graduate’s Debt Status

Chelsea Menken, of Providence, Rhode Island, recently graduated with a degree in food science and now works for a major consumer foods company earning $70,000 per year with about $57,600 in take-home pay. She rents an apartment for $1,100 per month. While in school, she accumulated about $38,000 in student loan debt on which she pays $385 per month. During her last fall semester in school, she had an internship in a city about 100 miles from her campus. She used her credit card for her extra expenses and has a current debt on the account of $7,000. She has been making the minimum payments on the account of about $240 a month. She has assets of $14,000.

1. Calculate Chelsea’s debt payments-to-disposable income ratio. Round your answer to two decimal places.

     %

2. Calculate Chelsea’s debt-to-income ratio. Round your answer to two decimal places.

     %

Marsha Jones has bought a used Mercedes horse transporter for her Connecticut estate. It cost $47,000. The object is to save on horse transporter rentals.

Marsha had been renting a transporter every other week for $212 per week plus $1.60 per mile. Most of the trips are 90 miles in total. Marsha usually gives the driver a $50 tip. With the new transporter she will only have to pay for diesel fuel and maintenance, at about $.57 per mile. Insurance costs for Marsha’s transporter are $1,800 per year.

The transporter will probably be worth $27,000 (in real terms) after eight years, when Marsha’s horse Nike will be ready to retire. Assume a nominal discount rate of 9% and a forecasted inflation rate of 3%. Marsha’s transporter is a personal outlay, not a business or financial investment, so taxes can be ignored. Hint: All numbers given in the questions are in real terms. Assume CF at end of year, for simplicity.

Calculate the NPV of the investment. (Do not round intermediate calculations. Round your answer to the nearest whole dollar amount.)

NPV            $   

Your company has a travel policy that reimburses employees for the “ordinary and necessary” costs of business travel. Employees often mix a business trip with pleasure by either extending the time at the destination or traveling from the business destination to a nearby resort or other personal destination. When this happens, an allocation must be made between the business and personal portions of the trip. However, the travel policy is unclear on the allocation method to follow.

Consider this example. An employee obtained a business-class ticket for $9,558 and traveled the following itinerary:

On the date of the flights between Chicago and Paris (and return), a restricted round-trip fare of $4,980 was available.

Required:

a. Compute the business portion of the airfare and state the basis for the indicated allocation that is appropriate according to each of the following independent scenarios:

1. Based on the maximum reimbursement for the employee.

2. Based on the minimum cost to the company.