Ted Williams hits a baseball with an initial velocity of 120 miles per hour (176 ft/s) at an angle θ = 35o to the horizontal. The ball is struck 3 feet above home plate. You watch as the ball goes over the outfield wall and lands in the bleachers. After you congratulate Ted on his hit, he tells you: “You think that was something! If there was no air resistance I could have hit that ball clear out of the stadium!” Since you are now taking PH131, you can easily verify Ted’s claim. Assume that the outer wall of the stadium is 100 feet high and 565 feet away from the home plate. Note: 1 mile = 1609 m, 1 foot = 0.3 m Figure 7:

(a) What are the horizontal and vertical components of the ball’s initial velocity? (b) How long does it take for the ball to fly the horizontal distance to the wall? (c) How high above the ground is the ball at that time? Is Ted Williams right? (d) What is the maximum hight above the ground which the ball reaches during its flight? (e) What is the horizontal distance the ball travels before hitting the ground? Bonus: What are the ball’s velocity components at the moment it hits the ground?

Assume you have created a 2-stock portfolio by investing $30,000 in stock X with a beta of 0.8, and $70,000 in stock Y with a beta of 1.2. Market risk premium is 8% and risk-free rate is 6%.

The followings are the probability distributions of Stocks X and Y’s future returns:

1. Calculate the portfolio’s expected rate of return and the standard deviation of its future returns
2. Calculate the required rate of return of your portfolio.
3. Which stock in your portfolio is currently under-valued? Explain.

1. A rancher owns 500 acres of land which is suitable for growing sorghum, corn, and wheat. She expects net profits per acre from each crop to be: $55 for sorghum, $60 for corn, and $50 for wheat. She is able to supply 3,000 hours per year of on-farm labor. Additionally, she has 4,500 hours of tractor time available for the production of these three crops. The requirements of each crop are summarized below.

1. Write out the linear programming problem, including the objective function and all constraints. Please represent the problem and constraints in general equation form.

1. In 2021 there will be 3 candidates for the post of Director- Mr. Arun, Mr. Varun, and Mr.
Tharun- whose chances of getting the appointment are in the proportion 3: 2: 4 respectively.
The probability that Mr. Arun if selected would introduce online-teaching in the college is
0.3. The probabilities of Mr. Varun and Mr. Tharun doing the same are respectively 0.5 and
0.8. (a) What is the probability that there will be online-teaching in the college in 2022? (b) If
there is online-teaching in the college in 2022, what is the probability that Mr. Tharun is the

. In preparation for your Biology midterm, you decide to look up past exams to see what kinds of questions were on it. Let B be the event “a question about bacteria shows up on the exam”, and let M be the event “a question about mitosis shows up on the exam”. From past exams, you know that P(B) = 0.3, P(M) = 0.8, and P(M and B) = 0.4. What is the probability of either/or of these types of questions showing up on your Biology midterm?

Consider the following multiple regression equation relating a machinist's performance rating on a new machine (RATING) to the following three independent variables.

WKEX - number of years work experience as a machinist

TSCORE - mechanical aptitude score

Years - age

^Rating = 12.5 + 0.8 WKEX + 0.32 TSCORE + 0.3 YEARS

a) Explain all of the steps for finding the value of R^2 (coefficient of determination) which are associated with finding the variance inflation factor (VIF) associated with the independent variable YEARS.

Home Warehouse is considering marketing one of two new electric saws for the coming holiday season: XL2000 or the Saw Warrior 3000. XL2000 is a unique saw and appears to have no competition. Estimated profits (in thousands of dollars) under high, medium, and low demand are as follows:

Home Warehouse is optimistic about its Saw Warrior 3000 saw. However, the concern is that profitability will be affected by a competitor’s introduction of a electric saw viewed as similar to Saw Warrior. Estimated profits (in thousands of dollars) with and without competition are as follows:

1. Develop a decision tree for the Home Warehouse problem.

2. For planning purposes, Home Warehouse believes there is a 0.7 probability that its competitor will produce a new game similar to Saw Warrior. Given this probability of competition, the director of planning recommends marketing the Saw Warrior saw . Using expected value, what is your recommended decision?

3. List 3 other factors you should advise Home Warehouse to thing about when trying to solve this problem? Think outside the box. Be Creative.

In 2019, Bill Jones drove 3,800 miles for medical reasons. He spent $500 for gas, $30 for oil, and $100 for tolls and parking. Using either actual expenses or standard mileage rate, what is the largest amount he can include for car expenses in his medical expenses on his tax return?

(If possible please explain. I thought the answer was 890, but apparently i'm wrong)

A manufacturer claims that the average mileage of his automobiles is at least 25mpg. In a previous study it was found that the standard deviation of the mileage of his automobiles is 3mpg. For a .05 level of significance, what sample size would be recommended if the researcher wants an 80% chance of detecting that is less than 25 miles per gallon when it is actually 24 (to the next whole number)?

A. 71

B. 95

C. 56

D. 28