1. The space force developed a new weapon system that makes an object experience no air drag. The objects have a mass of 100 kg. If one of the objects is dropped from a space weapons platform from a height of 136.3 miles, how much Kinetic Energy would it be able to release upon impact? ( Only work in the y dimension) A stick of dynamite has 1.7 MJ of energy. How many sticks of dynamite equivalent would this be?

2. It takes a delta launch vehicle 8 min to get to low earth orbit about 100 miles up. If it went in a straight line (it doesn’t) and its speed on orbit was 17,500 mph, how many g’s would the space force service members go through? Ignore the rotation of the Earth and just solve as the rocket is in one dimension. Convert all values to metric and show the conversions.

A consumer advocacy group is doing a large study on car rental practices. Among other things, the consumer group would like to estimate the mean monthly mileage, μ , of cars rented in the U.S. over the past year. The consumer group plans to choose a random sample of monthly U.S. rental car mileages and then estimate μ using the mean of the sample. Using the value 750 miles per month as the standard deviation of monthly U.S. rental car mileages from the past year, what is the minimum sample size needed in order for the consumer group to be 95 % confident that its estimate is within 135 miles per month of μ ?

Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.)

A random sample of 5 states gave the following areas (in 1000 square miles; same data as Problem 2-38, incidentally): 147, 84, 24, 85, 159 a) Find the 95% confidence interval for the mean area for all 50 states in the United States. 13. A real estate agent wants to estimate the average selling price of houses in a suburb of Atlanta. It randomly samples 25 recent sales and calculates the average price = $148,000 and the standard deviation s = $62,000. a) Calculate a 95% confidence interval for the mean of all recent selling prices. 12. A random sample of 5 states gave the following areas (in 1000 square miles; same data as Problem 2-38, incidentally): 147, 84, 24, 85, 159 a) Find the 95% confidence interval for the mean area for all 50 states in the United States.

1. ) 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 car was set to 60 miles per hour by cruise control, and the mpg were recorded at random times.  Here are the mpg values from the experiment:

37.2     21.0     17.4     24.9     27.0     36.9     38.8     35.3     32.3     23.9

19.0     26.1     25.8     41.1     34.4     32.5     25.3     26.5     28.2     22.1

The vehicle sticker information for the vehicle states a highway average of 27 mpg.  Perform a hypothesis test at 5% significance level to determine if the results of this experiment are consistent with the vehicle sticker.

1. (30 points) Give the hypotheses, test statistic, rejection region, p-value, decision, and interpretation.
2. (5 points) What would a Type II error be in this situation?

Car A has a mass of 2000 kg and speed of 10 miles per hour. Car B has mass of 1000 kg and speed of 30 miles per hour. The two cars collide to each other and stick together after collision in three different situations. Calculate the velocity of the two cars after the collision.

1. Car A moves East and car B moves West and had a head to head collision. Calculate the velocity of the two cars after the collision (speed and direction).

2. Car B follows car A and both head toward the East. Car B had a head to tail collision with car A. Calculate the velocity for the two cars after the collision(speed and direction).

3.Car A moves to the East and car B moves to the North and collide in a cross road. Calculate the velocity for the two cars after the collision (speed and the angle of the velocity).

A certain statistics instructor participates in triathlons. The accompanying table lists times​ (in seconds) he recorded while riding a bicycle. He recorded every time he rode and randomly picked five laps through each mile of a​ 3-mile loop. Use a .05 significance level to test the claim that it takes the same time to ride each of the miles. Mile 1 194 205 203 202 201

Mile 2 198 201 200 196 200

Mile 3 215 211 209 212 209

a) State the null and alternative hypothesis (2 points).

b) Check the requirements (3 points)

c) Carry out the hypothesis test (make sure you write everything down) (3 points)

. d) What is your conclusion? (2 points)

e) Does one of the miles appear to have a​ hill? (2 points)

1. A study of a disease reveals that there is an average of 1 case every 22 square miles. Residents of a town that has an area of 10 square miles are concerned because there are two cases in their area. The state’s Department of Health has decided to investigate further if the probability of getting two or more cases in this town is less than 0.05. Does the Department of Health investigate further?   (3)

2. A lottery is carried out by choosing five balls, without replacement, from a box of 35 balls. The lottery ticket has five numbers on it. Find the probability that exactly four of the balls that come out of the box match the numbers on the lottery ticket. (3)

3. A neighborhood has 32 households – 27 white, and 5 nonwhite. A subset of 9 of these households move to an adjacent neighborhood. What is the probability that less than two of the households in the new neighborhood are nonwhite? (3)

AA purchased a van (cost: $50,000, salvage value: $5,000, useful life: 5 years).

1. Under straight-line method, how much is the book value at the end of 3^rd year of its useful life?

$18,000

$20,000

$23,000

$27,000

2. Under double-declining balance method, how much is the book value at the end of 5^thyear?

$2,333

$5,432

$6,221

None of the above

3. Under sum-of-years’ digits method, how much is the accumulated depreciation at the end of 3^rd year?

4. Under sum-of-years’ digits method, how much is the annual depreciation expense for 2^ndyear?

5. AA estimated the total usage of this van would be 100,000 miles. During the first year, this van was used for 30,000 miles. What is the amount of book value at the end of 1^st year?

The daily rainfall in Cork (measured in millimeters) is modelled using a gamma distribution with parameters α = 0.8 and β = 0.3.

1) Use Markov’s inequality to upper bound the probability that the observed rainfall in a given day is larger than 3 mm, and compare the value to the result of cdf calculation.

2) Consider the overall rainfall in 365 days, and use moment generating functions and their properties to prove that this is Ga (292, 0.3).

3) Use the central limit theorem to approximate the probability that the annual rainfall exceeds 800mm (write down the analytical formula and the code used to calculate the cdf value).