A man is hiking at a park. At the beginning, he followed a straight trail. From the starting point, he traveled two miles down the first trail. Then he turned to his left by 30 degree angle to follow a second trail for one point five miles. Next, he turned to his right by 160 degree angle and follow a third trail for one point seven miles. At this point he was getting very tired and would like to get back as quickly as possible, but all of the available trails seem to lead him deeper into the woods. He would like to take a shortcut directly through the woods. How far to his right should you suggest him to turn, and how far do he have to walk, to go directly back to his starting point?

Q1: The man has to turn ____ degree to the right and walk ___ miles to the starting point.

Define the regression if the raw material used in production of a certain synthetic fiber measurement of the relative humidity the storage location and the moisture content.

Relative Humidity x 0.1×H+1 0.2×H+2 0.3×H+3 0.4×H+4 0.6×H+1 0.7×H+3 Moisture Content y 0.2×H×2 0.3×H×3 0.1×H+1 0.6×H+1 0.7×H+2 0.4×H+3 (a) Plot a graph Y vs. X showing these points or the graph is also called scatter diagram. (b) Calculate ∑ X, ∑ Y, ∑X2 , ∑Y2 , ∑XY, mean of X and mean of Y. (c) Calculate regression equation Y on X. (d) If ? = 82 find the estimated value of Y.

The following three games are scheduled to be played at the World Curling Championship one morning. The values in parentheses are the probabilities of each team winning their respective game.
Game 1: Finland (0.2) vs. Canada (0.8)

Game 2: USA (0.3) vs. Switzerland (0.7)

Game 3: Germany (0.4) vs. Japan (0.6)
(a) The outcome of interest is the set of winners for each of the three games. List the complete sample space of outcomes and calculate the probability of each outcome.

(b) Let X be the number of European teams that win their respective games. Find the probability distribution of X.

(c) Find the expected value and variance of X.

(d) If two European teams win their games, what is the probability that Finland is one of them?

4. You are visiting the rainforest, but unfortunately your insect repellent has run out. As a result, at each second, a mosquito lands on your neck with probability 0.5. If one lands, with probability 0.2 it bites you, and with probability 0.8 it never bothers you, independently of other mosquitoes.
a. What is the expected time between successive mosquito bites? What is the variance of the time between successive mosquito bites?
b. In addition, a tick lands on your neck with probability 0.1. If one lands, with probability 0.7 it bites you, and with probability 0.3, it never bothers you, independently of other ticks and mosquitoes. Now, what is expected time between successive bug bites? What is the variance of the time between successive bug bites?

Please add formula answer included

1. Bill sold 3 times as many cars as Doug last month. Laurel sold 45 cars, which was 1 1/2 times as many cars as Bill. How many cars did Doug sell? answer is 10 cars
2. 2. The local grocery store sells two cans of soup for $1.28. It has a special sale of six cans for $3.12. A customer buys 12 cans at the special sale price. How much did the customer save over the regular price? answer is 1.44

3. A hotel has 15 floors. Each floor has 26 single-person rooms and 38 two-person rooms. What is the total guest capacity at the hotel? answer is 1530

4. Linda leaves Boise to travel the 2,160 miles to Austin, driving at a speed of 55 mph. Mark leaves Austin driving the same 2,160 mile route to Boise at 65 mph. How many miles will Mark have traveled when they meet? (Hint – distance = speed x time) answer is 1170 miles

5. Autzen Stadium in Eugene holds 59,000 screaming Duck fans. The games have been sold out for years. 18,500 fans walk to the game, 12,000 take the local bus and the remainder drive and park at the stadium. The average car brought 4 people. On average, how many cars parked at the stadium? answer is 7125

6. You are in charge of organizing the annual stockholders’ meeting and luncheon for your company, Making Big Bucks Now. The meal will cost $13 per person, entertainment will cost $2,100, facility rental is $880, invitations and annual reports printing costs are $2,636, and other expenses come to $1,629. If 316 stockholders plan to attend, what is the total cost of the luncheon? What is the cost per stockholder? answer is $11,353 and also $35.93

Tornado Length (in miles)

d) Use statistical software to construct a 95​% confidence interval for the mean tornado length. Select the correct choice below and fill in the answer boxes to complete your choice.

​(Use ascending order. Round to two decimal places as​ needed.)

A.There is 95​% probability that the true mean length of a tornado is between _____ miles and _____ miles.

B.We are 95​% confident that the population mean length of a tornado is between _____ miles and _____ miles.

C.If repeated samples are​ taken, 95​% of them will have a sample mean between ____ miles and ______ miles.

Suppose the speeds of people driving from Dallas to Houston normally distributed, with a mean average speed of 92 miles per hour. (a) If the probability that the speed is more than 108 mph is 0.8%, what is the standard deviation? (6 points) (b) Given the standard deviation in (a), what is the probability that a person drove less than 85 miles per hour? (5 points) (c) If Ben drove at a speed that exceeds 85% of all other people. What was her speed? (6 points)

Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the miles per gallon were recorded each time the gas tank was filled, and the computer was then reset. In addition to the computer's calculations of miles per gallon, the driver also recorded the miles per gallon by dividing the miles driven by the number of gallons at each fill-up. The following data are the differences between the computer's and the driver's calculations for that random sample of 20 records. The driver wants to determine if these calculations are different. Assume that the standard deviation of a difference is σ = 3.0.

6.0 7.5 −0.6 1.5 3.7 4.5 6.0 2.2 4.8 3.0

4.4 0.3 3.0 1.1 1.1 5.0 2.1 3.7 −0.6 −4.2

(a) State the appropriate

H₀  and H_a  to test this suspicion.

CORRECT: H₀: μ = 0 mpg;    H_a: μ ≠ 0 mpg

(b) Carry out the test. Give the P-value. (Round your answer to four decimal places.)

Nilam Patel is the primary stockholder in two hotel corporations. One corporation owns a 90‐room economy property located in the suburbs of a large western town. The other corporation is a 350‐room full‐service convention hotel in the downtown city center for which Nilam has employed a management company to operate the property. Nilam is preparing balance sheets for both properties using a common size format. Complete the two balance sheets. Then answer the questions that follow.

1. What was the amount of cash in the 90‐room property's Cash in House Banks account at year end?
2. What is the amount of Allowance for Doubtful Accounts in the 350‐room property? Do you think it is excessive? Explain your answer?
3. What would explain the lack of a beverage inventory value in the 90‐room hotel?
4. What was the dollar amount of Total Assets in the 90‐room hotel?
5. What was the dollar amount of Total Assets in the 350‐room hotel?
6. What was the dollar amount of Current Maturities of Long‐Term Debt in the 350‐room property? Why is that amount likely so much higher than for the 90‐room property?
7. What was the dollar amount of Paid in Capital for the 90‐room property?
8. What is the Owners' Equity percentage of Total Assets in the 90‐room property? What is it in the 350‐room property?

1. 8. BONUS: Nilam Patel is the primary stockholder in two hotel corporations. One corporation owns a 90‐room economy property located in the suburbs of a large western town. The other corporation is a 350‐room full‐service convention hotel in the downtown city center for which Nilam has employed a management company to operate the property. Nilam is preparing balance sheets for both properties using a common size format. Complete the two balance sheets. Then answer the questions that follow.

   Nilam Patel's Two Hotel's Balance Sheets

   	December 31		Common Size
   	90‐Room Property	350‐Room Property	90‐Room Property (%)	350‐Room Property (%)
   ASSETS
   Current Assets
   Cash
   Cash in House Banks		$86,000
   Cash in Demand Deposits	85,000	330,250
   Total Cash	103,500	416,250
   Short‐Term Investments	56,000	165,000
   Receivables
   Accounts Receivable	150,000	327,150
   Notes Receivable	35,000	136,250
   Other	750	30,800
   Total Receivables	185,750	494,200
   Less Allowance for Doubtful Accounts	19,250
   Net Receivables	166,500	431,900	1.4	1.1
   Due from Management Company	—	50,000	0.0	0.1
   Food Inventories	15,125	69,750	0.1	0.2
   Beverage Inventories	—	42,550	0.0	0.1
   Gift Shop Inventories	300	6,950	0.0	0.0
   Supplies Inventories	6,550	13,550	0.1	0.0
   Prepaid Expenses	56,000	120,100	0.5	0.3
   Deferred Income Taxes—Current	48,000	135,000	0.4	0.3
   Total Current Assets
   Investments	72,500	274,150	0.6	0.7
   Property and Equipment
   Land	2,000,000	8,450,000
   Building	6,500,000	18,500,000
   Leaseholds and Leasehold improvements	2,037,250	5,850,000
   Furnishings and Equipment	1,288,000	3,105,000
   Total Property and Equipment	11,825,250	35,905,000
   Less Accumulated Depreciation and Amortization	575,000	2,575,000
   Net Property and Equipment	11,250,250	38,480,000
   Other Assets
   Intangible Assets	—	75,000	0.0	0.2
   Deferred Income Taxes—Non‐current	66,000	158,000	0.6	0.4
   Operating Equipment	35,100	111,000	0.3	0.3
   Restricted Cash	25,000	95,000	0.2	0.2
   Total Other Assets	126,100	439,000	1.1	1.1
   TOTAL ASSETS			100.0	100.0
   LIABILITIES AND OWNERS' EQUITY
   Current Liabilities
   Notes Payable
   Banks	17,500	116,250	0.1	0.3
   Others	8,000	17,500	0.1	0.0
   Total Notes Payable	25,500	133,750	0.2	0.3
   Accounts Payable	2,500	125,100
   Accrued Expenses	45,000	42,500
   Advance Deposits	500	42,250
   Income Taxes Payable	15,000	78,000
   Deferred Income Taxes—Current	40,000	235,000
   Current Maturities of Long‐Term Debt	420,000
   Other	50,000	58,000
   Total Current Liabilities	598,500	2,399,600	5.0	5.9
   Long‐term Debt, Net of Current Maturities
   Mortgage Note		24,383,030
   Obligations Under Capital Leases	18,000	385,000	0.2	0.9
   Total Long‐Term Liabilities	6,868,000
   Owners' Equity
   Common Stock	500,000	2,000,000
   Paid in Capital		8,711,500
   Retained Earnings	879,325	2,765,070
   Total Owners' Equity	4,434,325	13,476,570
   TOTAL LIABILITIES AND OWNERS' EQUITY			100	100

   1. What was the amount of cash in the 90‐room property's Cash in House Banks account at year end?
   2. What is the amount of Allowance for Doubtful Accounts in the 350‐room property? Do you think it is excessive? Explain your answer?
   3. What would explain the lack of a beverage inventory value in the 90‐room hotel?
   4. What was the dollar amount of Total Assets in the 90‐room hotel?
   5. What was the dollar amount of Total Assets in the 350‐room hotel?
   6. What was the dollar amount of Current Maturities of Long‐Term Debt in the 350‐room property? Why is that amount likely so much higher than for the 90‐room property?
   7. What was the dollar amount of Paid in Capital for the 90‐room property?
   8. What is the Owners' Equity percentage of Total Assets in the 90‐room property? What is it in the 350‐room property?