A subway train starts from rest at a station and accelerates at a rate of 2.00 m/s2 for 14.0 s. It runs at constant speed for 66.0 s and slows down at a rate of 4.00 m/s2 until it stops at the next station. Find the total distance covered.

Prove it's correct or wrong.

A particular version of PARTITION runs in logarithmic time but produces splits where all elements go to the same side of the pivot every time. QUICKSORT based on this PARTITION has the same worse-case running time as the standard version.

How to set up experimental design for 3 factors at 4 different levels. I get in total I should end up with 81 experimental runs. Can you help me to determine how to distribute these 4 levels across 3 factors?

Subject 4

George also believes that the mean of the average room rate in August for 4 stars hotels is smaller than the mean of the average room rate in August for 5 stars hotels.

4.1 State the null and the alternative hypotheses.

4.2 Test the null hypothesis at α = 5%. Use a Student-t statistic and unequal variances in the two populations.

4.3 On the basis of your results, do you agree with George? Explain briefly.

Subject 3

George who is the General Director of the Research Institute for Tourism in Greece, believes that the percentage composition of 5 Stars hotels is not the same in Crete and elsewhere (Southern Aegean Islands and Ionian Islands). In order to test this statement, create two additional binary variables as follows:

5STARS: Yes (Code 1) when STARS = 5; No (Code 0) when STARS ≠ 5.

CRETE: Yes (Code 1) when Region_ID = 1; No (Code 0) when Region_ID ≠ 1.

3.1 State the null and the alternative hypotheses.

3.2 Test the null hypothesis at α = 5%.

3.3 What is your conclusion?

3.4 Let π1 denote the population proportion of 5 stars hotels in Crete and π2 the population proportion of 5 stars hotels elsewhere. Set up a symmetric 95% confidence interval estimate of the difference (π1 - π2). What is your main conclusion?

Beltway Shoe Company sells luxury leather shoes in the United States. The company monitors its shoe sales by collecting randomly chosen data from store locations throughout the country. They record original price, sale price, and number of days it takes to sell each unit. Each pair of shoes is classified as “Eastern Region" if it is sold in the Eastern part of the United States, or as “Western Region" if it is sold in the Western part of the country. Randomly chosen samples provided sales data for 50 Western Region and 50 Eastern Region pairs of shoes. The complete data set is in the file named Shoes, linked at the bottom of the page.

Managerial Report
Prepare a report (see below) that summarizes your assessment of the nature of the shoe market in each region. Be sure to include the following seven (7) items in your report.

Descriptive statistics (mean, median, range, and standard deviation) to summarize each of the three variables for the 50 Western Region shoes. Are there any outliers in the data set for any of the three variables? If there are any outliers in any category, please list them and state for which category they are an outlier. Describe which method you used to make your determination.

Descriptive statistics (mean, median, range, and standard deviation) to summarize each of the three variables for the 50 Eastern Region shoes. Are there any outliers in the data set for any of the three variables? If there are any outliers in any category, please list them and state for which category they are an outlier. Describe which method you used to make your determination.

Compare your summary results from #1 and #2. Discuss any specific statistical results that would help the Beltway Shoes Marketing Department understand the regional shoe market.

Develop a 90% confidence interval estimate of the population mean sales price and population mean number of days to sell for pairs of Beltway Shoes in the Eastern Region. Interpret your results.

Develop a 90% confidence interval estimate of the population mean sales price and population mean number of days to sell for pairs of Beltway Shoes in the Western Region. Interpret your results.

Assume a branch sales manager requested estimates of the mean selling price of Western Region shoes with a margin of error of $5 and the mean selling price of Eastern Region shoes with a margin of error of $4. Using 90% confidence, how large should the sample sizes be for each?

A Western Region store manager just placed on display a pair of Beltway Shoes, with an original price of $120. Also, an Eastern Region store manager just placed on display a pair of Beltway Shoes, with an original price of $125. For each pair of shoes, what is your estimate of the final selling price (based on the percent difference for the sale and list price) and number of days required to sell each of these units?

Tonya Jefferson, a sole proprietor, runs a successful lobbying business in Washington, D.C. She doesn't sell many business assets, but she is planning on retiring and selling her historic townhouse, from which she runs her business in order to buy a place somewhere sunny and warm. Tonya's townhouse is worth $1,000,000 and the land is worth another $1,000,000. The original basis in the townhouse was $600,000, and she has claimed $250,000 of depreciation deductions against the asset over the years. The original basis in the land was $500,000. Tonya has located a buyer that would like to finalize the transaction in December of the current year. Tonya's marginal ordinary income tax rate is 35 percent and her capital gains tax rate is 20 percent.

what effect does the gain or loss on her tax liability or tax savings?

The answer of $ 217500 is not correct.

Tonya Jefferson (single), a sole proprietor, runs a successful lobbying business in Washington, DC. She doesn't sell many business assets, but she is planning on retiring and selling her historic townhouse, from which she runs her business, to buy a place somewhere sunny and warm. Tonya's townhouse is worth $1,000,000 and the land is worth another $1,000,000. The original basis in the townhouse was $600,000, and she has claimed $250,000 of depreciation deductions against the asset over the years. The original basis in the land was $500,000. Tonya has located a buyer that would like to finalize the transaction in December of the current year. Tonya's marginal ordinary income tax rate is 35 percent and her capital gains tax rate is 20 percent.

What amount of gain or loss does Tonya recognize on the sale?

The answer 650,000 is not correct.

Assume that your friend claims that he can run 20 km in less than an hour and a professional sports team will recruit him after graduation based on this outcome so he does not worry about his GPA at the university. You would like to test this claim and take a random sample of 34 runs this year and find that he averaged 58.2 minutes. Assume that the standard deviation of his runs is 8.5 minutes and it is normally distributed. a. State the null and alternative hypotheses. b. Test the hypotheses at the 5% significance level. What is the p-value of the test? c. What is your conclusion in the context of the question? d. Interpret the p-value you found above. e. What type of error you can commit here? Explain in the context of the question. Also, what are the implications of this error?

1. State and explain the definition of big-O.
2. Explain why we use big-O to compare algorithms.
3. Explain why binary search runs in O(log n) time.
4. Under what conditions is it possible to sort a list in less than O(nlog n) time?
5. List and explain the worst-case and average-case running times for each Vector method below:
(a) insert(iterator here, Object item)

(b) insertAtHead

(c) insertAtTail (aka push back)

(d) get(iterator here)

(e) get(index i)

(f) remove(iterator here)

(g) remove(index i)

(h) splice(iterator place here, iterator from here, iterator to here)
(Be sure you understand when (and why) push back runs in constant average time.)