Practice Integrals to describe Motion A cart’s acceleration is described by the function a = (10 - t) (m/s/)/s. The initial conditions are xi = -2 m and vi = -2 m/s at t = 0 s.

Plot the acceleration function in the interval 0s-12s

Find and graph the velocity function. Find any turning times?

Find and graph the position function.

Place 4 charges at the corners of a square which is 2 meters by 2 meters (4 large squares along each length). Place two +1 nC charges at adjacent corners and two -1 nC charges at the other two corners.

Determine the direction of the electric field at the following three points:
Point E halfway between two like charges. (-120 degrees, 50 V/m)
Point F halfway between two opposite charges. (-90.5 degrees, 309 V/m)
Point G at the center of the square. (90 degrees, 210 V/m)

1. For the points E, F and G, draw a diagram showing both charges and the two individual field vectors (one for each charge) and explain why their vector sum points in the direction that you.

2. Determine the electric potential at the points E, F and G. List them numerically and give an explanation for their value  

Maintaining a clean shopping environment is a key success factor for Turner?, a large grocery chain based in Minnesota. Three of the most costly resources needed to clean a supermarket are? labor, equipment, and cleaning supplies.

The cost driver for all these resources is? "number of times? cleaned." Wages for cleaning laborers? (called porters) and rent for cleaning equipment are the same regardless of the number of times the supermarket is cleaned. Supplies used for each regular daily cleaning and for each special cleaning are about the same. A typical store has 52,000 square feet. Regular cleaning is performed each day from midnight until? 7:00 AM. Special cleaning of floors and fixtures is performed in the various departments as needed. Special cleaning varies from 10 to 30 times a month depending on the amount of traffic through the store. ? Thus, the number of times a store is cleaned varies from 40 to 60 times a month.

Suppose that in one of Turner?'s stores in? Minneapolis, cleaning was performed 60 times during March. For the? month, the cost of labor and rent on equipment was $ 21,000 and cleaning supplies used cost $ 9,600. The sales budget for the next quarter? (April through? June) and better weather conditions indicate that the store will need to be cleaned 50?, 48?, and 35 times in? April, May, and June respectively.

Requirement 1. Prepare a table that shows how labor? cost, rent, cleaning supplies? cost, total? cost, and total cost per cleaning changes in response to the number of times the store is cleaned. Show costs for 35?, 40?, 45?, 50?, 55?, and 60 cleanings. What is the predicted total cost of cleaning the Minneapolis store for the next? quarter? ?(Round the cost per cleaning amounts to two decimal? places.

Prepare a table that shows how labor cost, rent, cleaning supplies cost, total cost, and total cost per cleaning changes in response to the number of times the store is cleaned. Show costs for 35, 40, 45, 50, 55, and 60 cleanings. What is the predicted total cost of cleaning the Minneapolis store for the next quarter?

2. Prepare a single graph that can be used to predict the fixed, variable, and total cleaning cost of the Turner store.

3. Suppose the manager of the Turner store can hire an outside cleaning company to clean the store as needed. The charge rate is $ 680 per cleaning. If the outside cleaning company is hired, Turner can lay off the workers who are now cleaning the store, eliminate the need for equipment rent, and stop purchasing cleaning supplies. Will Turner save money with the outside cleaning company over the next quarter? Prepare a schedule that supports your answer.

a.) Suppose that government data show that 8% of adults are full‑time college students and that 30% of adults are age 55 or older. Complete the passage describing the relationship between the two aforementioned events. Although (0.08)⋅(0.30)=0.024, we cannot conclude that 2.4% of adults are college students 55 or older because the two events __________(are/are not) ________(independent/disjoint)

b.) In New York State's Quick Draw lottery, players choose between one and ten numbers that range from 11 to 80.80. A total of 2020winning numbers are randomly selected and displayed on a screen. If you choose a single number, your probability of selecting a winning number is 2080,2080, or 0.25.0.25. Suppose Lester plays the Quick Draw lottery 66 times. Each time, Lester only chooses a single number.

What is the probability that he loses all 66 of his lottery games? Please give your answer to three decimal places.

c.) Consider the sample space of all people living in the United States, and within that sample space, the following two events.

??=people who play tennis=people who are left‑handedA=people who play tennisB=people who are left‑handed

Suppose the following statements describe probabilities regarding these two events. Which of the statements describe conditional probabilities? Select all that apply:

-Two‑tenths of a percent of people living in the United States are left‑handed tennis players.

-Two percent of left‑handed people play tennis.

-Of people living in the United States, 3.7% play tennis.

-There is a 10.2% chance that a randomly chosen person is left‑handed.

-The probability is 5.4% that a tennis player is left‑handed.

-There is a 13.7% probability that a person is a tennis player or left‑handed.

d.)

Of all college degrees awarded in the United States, 50%50% are bachelor's degrees, 59%59% are earned by women, and 29%29% are bachelor's degrees earned by women. Let ?(?)P(B) represent the probability that a randomly selected college degree is a bachelor's degree, and let ?(?)P(W) represent the probability that a randomly selected college degree was earned by a woman.

What is the conditional probability that a degree is earned by a woman, given that the degree is a bachelor's degree? Please round your answer to the two decimal places.

You are provided the following information:

Capital Structure:

Debt                                         $    60000

Equity                                       $   180000

The firm sold 50 year; $ 1000 face value, 5% bonds 10 years ago. These bonds trade at $ 930. You expect the yield on these bonds to be a good proxy for the cost of issuing new bonds.

The shares trade at $ 20; the growth rate is 6%. Dividends paid last year - $ 1.00.

The firm has a 30% tax rate.

Kemper, Goebel & Benkato, Investment Bankers have informed you that new shares can be sold with a 10% transaction cost.

New 50 year bonds can be sold. The firm can collect:

$ 0          --             $      120000            6%

The firm added $ 180000 to retained earnings last year.

As the intern, compute the cost of capital {WACC} for the CFO.

a) Compute the yield till maturity on the old bonds. So, what is the proxy for the sale of new bonds?

b) What return do the shareholders expect?

c)What are the weights of debt and equity in the capital structure of the firm?

d) Compute the WACC.

e) WHY do you compute the WACC?

f) How much can you borrow with the amount you have added to retained earnings last year? Note: NO change in capital structure.

g) Compute the WACC IF your CFO wants a ‘NEW’ capital structure with 60% debt. [use old costs]

h) What is the cost of equity when new shares are sold?

i. Compute the WACC if you borrow over $ 60001 with the ‘OLD’ capital structure.

The firm has the following projects:

I                              IRR

1.      30,000                     8%

2.     70,000                     11%

3.     50,000                     10%

4.     25,000                     7%

Help the CFO make a decision.

Firm A’s new project needs $325,000 for new fixed assets (long term assets), $160,000 for additional inventory and $35,000 for additional accounts receivable. This is a five year project. Use straight line depreciation approach to calculate the depreciation expenses. By the end of the fifth year, the value of the fixed assets = 0. However, the market value of the assets = 25% of their original cost. At the end of the project, the net working capitals tend to return to its original level. Annual sales is expected to be $554,000 and costs = $430,000. The tax rate = 35%. Required rate of return = 15%.

1.What is the initial cost of this project?

2. What is the operating cash flows from year 1 to year 4

3. What is the operating cash flows in year 5 (last year)

4. Calculate npv

Cullumber Corporation had two issues of securities outstanding: common shares and a 7% convertible bond issue in the face amount of $8 million. Interest payment dates of the bond issue are June 30 and December 31. The conversion clause in the bond indenture entitles the bondholders to receive 40 no par value common shares in exchange for each $1,000 bond. The value of the equity portion of the bond issue is $48,000. On June 30, 2020, the holders of $2.40 million of the face value bonds exercised the conversion privilege. The market price of the bonds on that date was $1,240 per bond and the market price of the common shares was $38. The total unamortized bond discount at the date of conversion was $515,000.

Prepare the entry to record the exercise of the conversion option, using the book value method. Assume the company follows IFRS. (Credit account titles are automatically indented when the amount is entered. Do not indent manually.)

You are considering the following two mutually exclusive projects. Both projects will be depreciated using straight-line depreciation to a zero book value over the life of the project. Neither project has any salvage value.

The required rate of return is 10%.

(7). (4 points) Define and find the crossover rate.

(8). (7 points) Sketch the NPV profile. Plot all the relevant coordinates (i.e., the points on the x and y axis; and the cross-over rate) on the graph.

On July 1, 2018, Gupta Corporation bought 20% of the outstanding common stock of VB Company for $110 million cash. At the date of acquisition of the stock, VB’s net assets had a total fair value of $500 million and a book value of $290 million. Of the $210 million difference, $46 million was attributable to the appreciated value of inventory that was sold during the last half of 2018, $130 million was attributable to buildings that had a remaining depreciable life of 10 years, and $34 million related to equipment that had a remaining depreciable life of 5 years. Between July 1, 2018, and December 31, 2018, VB earned net income of $60 million and declared and paid cash dividends of $40 million. Required: 1. Prepare all appropriate journal entries related to the investment during 2018, assuming Gupta accounts for this investment by the equity method. 2. Determine the amounts to be reported by Gupta.