The equation of an ellipse is x2/a2+y2/b2=1, where a and b are positive constants, a ³ b. The foci of this ellipse are located at (c, 0), and (-c, 0), where c = (a² – b²)^1/2. The eccentricity, e, of this ellipse is given by e=c/a, while the length of the ellipse’s perimeter is

  \int_0^((\pi )/(2)) 4a(1-e^(2)sin^(2)\theta )^((1)/(2))d\theta .

If 0 < e < 1, this integral cannot be integrated in terms of “well-known” functions. However, fnInt, may be used to approximate the integral.

The path of the earth lies in a plane, and follows an ellipse, with the sun at one of its foci. It takes one year for the earth to orbit the sun. The closest the earth comes to the sun is 91.5 million miles, and the furthest is 94.5 million miles.

1.      For the earth and sun configuration, what are the values of a, b, c, and e?

2.      How far does the earth travel in one orbit of the sun?

3.      What is the average speed of the earth, around the sun, in miles per second? Why is this the average speed?

1. Suppose it is claimed that the typical adult travels an average distance of 16 miles to get to work each day. You believe this average is too low for Columbus residents. You survey a random sample of 98 adults from Columbus and find that your sample travels an average distance of 17.6 miles to work each day, with a sample standard deviation of 7.8 miles.   Use this information to conduct the appropriate hypothesis test by going through the steps you learned about from our Chapter 22 and Chapter 23 lecture videos (and from your reading of Chapters 22 and 23). Assume the alpha level is .05 (or 5%).

1. What will the hypotheses be?

H_o:

H_a:

2. Use the following formula to compute the test statistic.

3. Based on what you see in Table B, what should the p-value be?

4. Will you reject or fail to reject the null hypothesis? Please state your decision and the reason why you are making that decision.

5. In general, if we end up rejecting the null hypothesis when conducting a hypothesis test, we say our results are __________________ significant.

Accounting Ethics In your role as an internal auditor for a car manufacturer, you discovered that your employer can produce a car engine that will get 8 more miles per gallon than the existing engine. However, the cost of producing this car engine would be an additional $3,000 per car. Assume that a typical driver drives a car for 5 years and 200,000 miles. Also, assume that the cost of a gallon of gas is $5 per gallon and a typical car gets 24 miles per gallon. The company is wondering if it is ethical to not produce this more efficient engine. a. Is this an ethical question or just a simple cost accounting problem? b. How would you analyze this from the perspective of shareholder theory? c. How would you analyze this from the perspective of stakeholder theory? d. If this car manufacturer does decide to produce the more fuel-efficient car, would you consider it to be an act of corporate social responsibility? e. Would your answer to the preceding question be different if the car manufacturer's motivation was simply to increase its profits by selling more cars?

Sam Suffolk is a student in MAT103 at SCCC. Sam has data from a random sample of 20 students that represents how many miles​ (rounded to the nearest whole​ mile) each student lives from the SCCC Ammerman campus. Sam organizes this data in the following frequency distribution table. Look at the table carefully and answer the questions that follow.

Sam made two mistakes when creating the classes for this table. Assuming​ Sam's frequencies are​ correct, despite the errors in the class​ limits, answer each of the following.

​Note: The first two lower class limits are correct.

​(a) Identify​ Sam's mistakes.

​(b) Can we determine how many students live 10 miles from the​ campus? If​ so, how​ many? If​ not, why​ not?

​(c) Give an estimate of the number of students in the sample that live more than 25 miles from the campus. If more than one frequency is​ possible, state all possible values.

9. Alpha Company has the following items in its equipment account: Asset &Date Purchased Method of Depreciation Cost Salvage Value 1 Delivery Truck (4/30/15) Units of Activity $60,000 $11,000 2 Office Furniture (6/1/15/) Straight line $15,000 $500 3 Computer Double Declining $5,000 $700 The delivery truck is estimated to have a life cycle of 200,000 miles. It was driven for 1. 16,500 miles in 201 24,600 miles in 2016 2. The Computer Furniture has a life expectancy of 7 years 3. The Computer has a life expectancy of 4 years Round any per unit calculations to the nearest half penny. Round all annual depreciation expenses to the nearest dollar. Use this information to compute for Fiscal Year 2016 the following values: 1. Book Value of the Delivery Truck 2. Depreciation Expense- Truck 3. Book value of the office furniture 4. Depreciation Expense- Office Furniture 5. Book value of the Computer 6. Depreciation Expense- Computer

ACCOUNTING ETHICS:

In your role as an internal auditor for a car manufacturer, you discovered that your employer can produce a car engine that will get 8 more miles per gallon than the existing engine. However, the cost of producing this car engine would be an additional $3,000 per car. Assume that a typical driver drives a car for 5 years and 200,000 miles. Also, assume that the cost of a gallon of gas is $5 per gallon and a typical car gets 24 miles per gallon. The company is wondering if it is ethical to not produce this more efficient engine. Is this an ethical question or just a simple cost accounting problem? How would you analyze this from the perspective of shareholder theory? How would you analyze this from the perspective of stakeholder theory? If this car manufacturer does decide to produce the more fuel-efficient car, would you consider it to be an act of corporate social responsibility?Would your answer to the preceding question be different if the car manufacturer's motivation was simply to increase its profits by selling more cars?

1. The mean life span of a brand name tire is 50,000 miles. Assume that the life spans of the tires are normally distributed, and the population standard deviation is 800 miles.
   • a. If you select one tire, what is the probability that its life span is less than 48,500 miles?
   • b. If you select 100 tires, what is the probability that their mean life span is more than 50,200miles?
   • c. What is the distribution of the sample mean in part b?
2. The proportion of students at a college who have a GPA higher than 3.5 is 19%.
   • a. You take repeated random samples of size 25 from that college and find the proportion of student who have a GPA higher than 3.5 for each sample. What is the mean and the standard error of the sampling distribution of the sample proportions?
   • b. You take repeated random samples of size 50 from that college and find the proportion of student who have a GPA higher than 3.5 for each sample. What is the mean and the standard error of the sampling distribution of the sample proportions?
   • c. Compare the results of parts a and b, and sketch the sampling distributions.

1. The manufacturer of a gasoline additive claims that the use of this additive increases gasoline mileage. A random sample of six cars was selected, and these cars were driven for 1 week without the gasoline additive and then for 1 week with the gasoline additive. The following table gives the miles per gallon for these cars without and with the gasoline additive.

a. Assume that the population of paired differences is approximately normally distributed. You would like to test whether the use of gasoline additive increases the gasoline mileage. Let μ_d denote the mean difference in miles per gallon for cars with and without the gasoline additive. Calculate the test statistic. Round your intermediate calculations and final answer to the nearest hundredth.

b. Let μ_d denote the mean difference in miles per gallon for cars with and without the gasoline additive. The test statistic for this case is 2.97. Calculate the p-value. Round your final answer to the nearest ten thousandth (e.g, 0.1234).

I am a travel agent, I book in-city ride tickets and also ship your luggage to the next destination. 1-NYC All Around Town it is $29.00 2-Big Bus NYC Tour it is $49.00 3-NYC one day guided Sightseeing Tour it is $89.00 4-Circle Line Complete Manhattan Island Cruise is $44.00 5-Viator VIP: Empire State Building, Statue of Liberty and 9/11 Memorial is $129.00 I also provide a quote for your shipment to be mailed to your next destination. In order to calculate our quote, we need to know the total weight of the shipment in pounds, the distance in miles and whether or not there are hazardous materials in the shipment (e.g. batteries). The calculation for the quote is as follows: Quote = .65 * # of miles + .83 * # of pounds If there is hazardous materials in the shipment, there is an extra cost of .20 * # of pounds If the distance for the delivery is less than 150 miles and the total weight for the shipment is greater than 500 pounds, then there should be a 10% discount off of the total quote. Create a c# console app using conditional statement

Kansas Enterprises purchased equipment for $60,000 on January 1, 2015. The equipment is expected to have a five-year life, with a residual value of $5,000 at the end of five years.

(1) Using the straight-line method, depreciation expense for 2015 would be: $   




(2) Using the double-declining balance method, depreciation expense for 2016 would be: $   



7 / 10

4. Crestview Estates purchased a tractor on January 1, 2015, for $65,000. The tractor’s useful life is estimated to be 30,000 miles and has a residual value of $5,000. If Crestview used the tractor 5,000 miles in 2015 and 3,000 miles in 2016, what is the balance for accumulated depreciation at the end of 2016 using the activity-based method?

$   



5. The Surf’s Up issues 2,000 shares of 5%, $100 par value preferred stock at the beginning of 2014. All remaining shares are common stock. The company was not able to pay dividends in 2014, but plans to pay dividends of $28,000 in 2015. Assuming the preferred stock is cumulative.  

(1) The annual cash dividend normally paid to preferred stock is:

$   



(2) The cash dividend paid to common stockholders in 2015 is:

$