Two air track gliders of mass 400.0 g and 300.0 g are moving towards each other in opposite directions with speeds of 60.0 cm/s and 100.0 cm/s, respectively. Take the direction of the more massive glider as positive. Use units of "g" and "cm/s" in your calculations.

1. Determine the velocity of each glider after the collision if the collision is elastic. (Use units of "g" and "cm/s" for this question.)
2. The most "inelastic" collision would occur if the two gliders stuck together on impact. If this was the case, find the velocity of the pair after the collision, and the kinetic energy lost as a result of the collision. (Determine the energies in standard units of "J.")

Pam is in charge of putting on the NYE fireworks show. The show can either be anywhere from 10 - 20 minutes long. There are 4 neighborhoods in your city that each offer different views of the firework show, and thus each have a different marginal benefit from additional minutes of the show as shown in the table below:

If each additional minute of the show costs $44, what is the optimal length of the show in minutes?

Since each additional minute of the show costs $44, each of the 4 neighborhoods is required to contribute $11 in taxes for each additional minute. Each neighborhood gets a vote on the maximum number of minutes they want the show to run based on this cost. What is the maximum length of the show that 3 of the 4 neighborhoods would accept?

• Compute the quartiles for each sample period and determine if there are any outliers

John Smith is a single taxpayer with an AGI of 162,000. Complete Mr. Smith’s Schedule A given the following deduction on a Schedule A Form 1040 2018.

1. Medical and dental expenses = 2,400

2. Real estate taxes from rental properties = 1,680

3. State income taxes withheld on W-2 = 6,700

4. Real estate taxes from personal residence = 3,550

5. Mortgage interest = 15,800

6. Investment interest = 130

7. Cash charitable contributions = 1,770

8. Noncash charitable contributions = 10,760

9. Unreimbursed employee expenses = 3,759

10. Tax preparation fees = 250

11. Subscriptions for business publications = 410

12. General sales tax = 2,500

A company is considering two mutually exclusive projects, the company’s required return is 8 percent and they do not have any capital constraints. Based on the profitability index, what is your recommendation concerning these projects?

                                    Project            A                                 Project B

                                    Year    Cash Flow                   Year    Cash Flow

                                       0       -$38,500                        0       -$42,000

                                       1         $20,000                        1         $10,000

                                       2         $24,000                        2         $40,000

Two converging lenses, with focal lengths f1 = 8 cm and f2 = 15 cm are separated by 30 cm. The lens on the left has a shorter focal length. An object, 1.5 cm tall, is placed 12 cm to the left of the combination. (i) Determine the position of the final image relative to the lens on the right. (ii) Determine the overall magnification and the height of the final image. (iii) Is the final image real or virtual? Give a reason for your answer. (iv) Is the final image upright or inverted concerning the original object? Give a reason for your answer.

A firm has a WACC of 8% and is deciding between two mutually exclusive projects. Project A has an initial investment of $63. The additional cash flows for project A are: year 1 = $20, year 2 = $39, year 3 = $67. Project B has an initial investment of $73.The cash flows for project B are: year 1 = $60, year 2 = $45, year 3 = $32.

a. What is the payback for project A? (Show your answer to 2 decimals.)

b. What is the payback for project B? (Show your answer to 2 decimals.)

c. Which project is preferred based on the payback method?

Project B

Project A

Accept both A & B

Neither Project should be accepted

d. What is the NPV for project A? (2 decimals)

e. What is the NPV for project B? (2 decimals)

f. Which Project should be accepted?

Project B

Project A

Both A & B

Neither A or B

Consider some 8-sided dice. Roll two of these dice. Let X be the minimum of the two values that appear. Let Y denote the maximum.  

a) Find the joint mass p_X,Y (x,y).

b) Compute p_X│Y (x│y) in all cases. Express your final answer in terms of a table.

Two sections of a pressure vessel are to be held together by 5/8 in-11 UNC grade 5 bolts. You are told that the length of the bolts is 1.5 in, the length of the threaded portion of the bolts is 0.75 in, and that their elastic modulus is E=30 Mpsi. The total load on the joint is 36 kip and the stiffness of the members is given as km=8.95 Mlbf/in. What is the minimum number of bolts that should be used to guard against excess proof strength with a factor of safety of np=1.2? Be sure to make an estimate for the preload.