Jim is a lawyer who works for GT Law Firm in Dallas, Texas. Jim lives in Frisco, Texas which is 25 miles from his office in Dallas. Jim does not like Frisco and ankdecides it would be best to move to Fort Worth, Texas and commute the 109 miles to the firm in Dallas. Jim incurs $2,500 of moving expenses. After moving to Fort Worth, the partners in the law firm take notice of Jim’s dedication and give him 100 stock options as part of his compensation. The value of the firm’s stock is $100 per share and the option exercise price is $105. Two years after receiving the options,Jim exercises the options when the stock price is $125 per share. Three years after that, Jim sells the stock for $120 per share and then leaves the firm to start his own firm. How much (if any) of a deduction for moving expenses is Jim entitled to? What are the tax consequences of the transactions related to the stock options?

Karen Battle​, owner of Flower Hour​, operates a local chain of floral shops. Each shop has its own delivery van. Instead of charging a flat delivery​ fee, Battle wants to set the delivery fee based on the distance driven to deliver the flowers. Battle wants to separate the fixed and variable portions of her van operating costs so that she has a better idea how delivery distance affects these costs. She has the following data from the past seven​ months:

Data Set:

1. Use the​ high-low method to determine Flower Hour​'s operating cost equation.

2. Use the operating cost equation you determined above to predict van operating costs at a volume of

14,500 miles.​

Show Calculations.

(a)Evaluate the following set of data for possible and probable outliers.
5 8 2 9 5 3 7 4 2 7 4 10 4 3 17

(b) A firm pays 5/12 of its labor force an hourly wage of $5, 1/3 of the labor force a wage
of $6 and ¼ a wage of $7. Determine the average wage paid by the firm.

(c)For the same amount of capital invested in each of 3 years, an investor earned a rate of
return of 1%during the first year, 4% during the second year and 16% during the third.
Find the simple arithmetic mean and the geometric mean. Which do you think is a more
appropriate in this case? Explain.

(d) A plane travelled 200 miles at 600 mph and 100 miles at 500mph. What was the
average speed for the entire journey?

(e) A driver purchased $10 worth of gasoline at $0.90 per gallon and another $10 at
$1.10 per gallon. What is the average price per gallon?

Rauschenberg Manufacturing is investigating which locations would best position its new plant relative to three important customers​ (located in cities​ A, B, and​ C). As shown in the table​ below, all three customers require multiple daily deliveries. Management limited the search for this plant to those three locations and compiled the following​ information:

a. Which of these three locations yields the smallest​ load-distance score, based on Euclidean​ distances?

Location ____yields the smallest​ load-distance score of _____ ​(Enter your response rounded to one decimal​ place.)

b. Which of these locations is​ best, based on rectilinear​ distances?

Location ____is the​ best, yielding a​ load-distance score of ______​(Enter your response as a whole​ number.)

c. What are the coordinates of the center of​ gravity?

The center of gravity is x*=_____​miles, y*=____miles. ​(Enter your responses rounded to one decimal​ place.)

1. Suppose you are in the market for a new car. You identify two models that you like and are considering a final purchase decision. The vehicle details are as follows:

• One is a high fuel efficient vehicle with a fuel cost per mile of $0.10 and the other is a low fuel efficient vehicle with a fuel cost per mile of $0.15.
• The high efficiency vehicle costs $47,500 in time period 0 (no discounting); the low efficiency vehicle costs $32,500
• You plan to drive the car for five years (time periods 1 to 5)
• In addition to the fuel costs in period 5, you also face depreciation costs of $17,500 for the low efficient vehicle and depreciation costs of $40,000 for the high efficient vehicle

1. 1. Suppose you drive 10,000 miles per month and have an internal discount rate of 5%. Which car has the lower total cost of ownership? Show your work on a separate page or attach a printout of your excel model, clearly labeled.
2. 2. Suppose you drive 17,000 miles per month and have an internal discount rate of 5%. Which car has the lower total cost of ownership? Show your work on a separate page or attach a printout of your excel model, clearly labeled.
3. 3. Suppose you drive 7,500 miles per month and have an internal discount rate of 20%. Which car has the lower total cost of ownership? Show your work on a separate page or attach a printout of your excel model, clearly labeled.
4. 4. In general, what characteristics (in terms of driving habits and discount rates) describe an individual that finds a lower total cost of ownership in high fuel efficient vehicles?

part 1)

A road perpendicular to a highway leads to a farmhouse located 1 mile away. An automobile traveling on the highway passes through this intersection at a speed of 65mph. How fast is the distance between the automobile and the farmhouse increasing when the automobile is 6 miles past the intersection of the highway and the road? The distance between the automobile and the farmhouse is increasing at a rate of miles per hour.

part 2)

A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is attached to the front of the boat, which is 10 feet below the level of the pulley. If the rope is pulled through the pulley at a rate of 20 ft/min, at what rate will the boat be approaching the dock when 110 ft of rope is out?

The boat will be approaching the dock at  ft/min.

Hint: Sketch a diagram of this situation.

part 3)

Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 6 mi2/hrmi2/hr. How rapidly is radius of the spill increasing when the area is 10 mi2mi2?

The radius is increasing at  mi/hr.

part 4)

At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 18 knots and ship B is sailing north at 15 knots. How fast (in knots) is the distance between the ships changing at 6 PM?

The distance is changing at  knots.

(Note: 1 knot is a speed of 1 nautical mile per hour.)

part 5)

A spherical balloon is inflated so that its volume is increasing at the rate of 3.8 ft3/minft3/min. How rapidly is the diameter of the balloon increasing when the diameter is 1.8 feet?

The diameter is increasing at  ft/min.

The US consumer fleet (cars, SUV’s, vans, cross-overs and light trucks) has an average drag coefficient of 0.4, an average miles driven per year of 12,500 at 50 MPH and an average frontal area of 5.5 m2. Being that there are 265 million of these ‘average’ vehicles on the road driven by consumers, calculate:

a. Gasoline consumed per vehicle annually assuming 25% overall efficiency

b. Gasoline consumed per vehicle annually assuming if the speed limit on federal highways was cut down from 70 to 55 MPH resulting in a decrease in the average speed to 43 MPH.

c. How many barrels of oil would be saved annually by lowering the speed limit?

d. If instead of 55 MPH there were an absolute federal speed limit on all roads of 45 MPH, lowering the average speed to 35 MPH, repeat b) and c) above.

e. If instead of lowering the speed limit the aerodynamics of all vehicles were improved such that the average vehicle now has a drag coefficient of 0.35, how many barrels of oil would that save annually?

f. If the size of engines were cut down on every vehicle in the fleet equivalent to the efficiency of the average vehicle above increasing to 40%, how many barrels of oil would that save annually?

g. What if by force of tax we were all limited in driving a certain number of miles and this resulted in the original average vehicle driving 10,000 miles per year, how many barrels of oil would that save annually? How many gallons of gas is that per capita and how much would each person save dollar-wise per year?

9. Let f (x) = x^3 − 10. Find all numbers c in the interval (-11, 11) for which the line tangent to the graph of f is parallel to the line joining (−11, f (−11)) and (11, f(11)). How many such numbers exist in the given interval?

. 0

. 1

. 2 (correct)

. 3

Enter points in increasing order (smallest first). Enter DNE in any empty answer blank.

c =

c =

c = DNE (correct)

10. Let g(x) = x² − (5/x)

First find the slope m of the line joining (1, g(1)) and (2, g(2)). Then use the Newton-Raphson method to estimate the values of c for which g'(c) = m. Check that your calculator is set for at least 10 digit display. Continue the process until successive iterations obtained by the calculator are identical.

m = 0.5 (incorrect)

0

1 (correct)

2

3
Enter values of c below in order from least to greatest. Enter DNE in any empty answer blanks.
c =  
c = DNE (correct)
c = DNE (correct)

11. A landowner wishes to use 15 miles of fencing to enclose an isosceles triangular region of as large an area as possible. What should be the lengths of the sides of the triangle?
Let x be the length of the base of the triangle. Write the area as a function of x. [First write the length of the equal-length sides in terms of the base, x, then write the height of the triangle in terms of the base.]

A(x) =_______________

Length of base = ____________ miles

Length of the other two (equal-length) sides = ______________ miles each

On

January

1​,

2018​,

On Time

Delivery Service purchased a truck at a cost of

$75,000.

Before placing the truck in​ service,

On Time

spent

$2,200

painting​ it,

$1,700

replacing​ tires, and

$9,100

overhauling the engine. The truck should remain in service for five years and have a residual value of

$10,000.

The​ truck's annual mileage is expected to be

27,000

miles in each of the first four years and

12,000

miles in the fifth

year—120,000

miles in total. In deciding which depreciation method to​ use,

Jacob Nealy​,

the general​ manager, requests a depreciation schedule for each of the depreciation methods​ (straight-line, units-of-production, and​ double-declining-balance).Read the requirements

LOADING...

.

Requirement 1. Prepare a depreciation schedule for each depreciation​ method, showing asset​ cost, depreciation​ expense, accumulated​ depreciation, and asset book value.

Begin by preparing a depreciation schedule using the​ straight-line method.

Part I

Find the standard-normal curve area that lies a)To the right of 0.65 b) To the left of z = -2.13 c) between z = -0.34 and z = 0.62.

d) A tire store finds that the thread life of its tires is normally distributed, with a mean of 26,640 miles and a standard deviation of 4000 miles. The store sold 9000 tires this month. How many of them can be expected to last between 25,000 and 30,000 miles?

Part II 15

a)From a random sample of 36 business days , the average closing price of Apple Stock was $116.16 with a standard deviation of $10.27. Construct a 90% and 95% confidence interval. Which interval is wider?

b) Determine the minimum sample size required   when you want to be 95% confident that the sample mean is within one unit of the population mean and σ=4.8.(population standard deviation)

Part III (Hypothesis testing )

A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 40 milligrams. You want to test this claim. During your tests, you find that a random sample of twenty 12 ounce-bottles of cola has a mean caffeine content of 39.2 milligrams. Assume the population is normally distributed and the population standard deviation is 7.5 milligram. At α = .01, can you reject the company’s claim?

1. Identify the claim. State the null and alternative hypotheses
2. Identify the level of significance , the critical value and the direction of the test
3. Find the standardized test statistic z.
4. Construct the rejected region and decide whether to reject the Null Hypothesis.
5. Find the p-value
6. Interpret the result in the context of the original claim