At a local dog park, there are 9 dogs in the area of large dogs and 11 in the area for small dogs. A group of six dogs is selected to receive a treat. LEAVING YOUR ANSWERS IN COMBINATORICS FORMAT, what is the probability that:

A) At least one dog is selected?

B) The same number from each area is chosen?

C) Either all selected dogs are small, or all selected dogs are large?

D) At most two large dogs are selected?

A researcher believes that the proportion of a community’s population in favor of a new park is greater than the countywide proportion of 0.65. A survey of 67 people in the community reveals that the estimated proportion of the community in favor of it is equal to 0.76. Use alpha = 0.05. State the null and alternative hypotheses, find the test statistic, compare it with the critical value, make a decision, and find the p-value. (4)

The City of Waterloo is considering the adoption of improvements to Waterloo Park and is presented with three mutually-exclusive options. Option A adds a splash pad which is estimated to offer benefits of $20 million and costs $16 million to build. Option B adds basketball courts has estimated benefits of $26 million and costs of $20 million. Option C is a nature exploration area that is estimated to offer benefits of $10 million and has costs of $2 million. In additional, a fourth option D is an improved path and signage project that has estimated costs of $8 million and standalone benefits of $4 million, but it can be combined with any of the first three, changing their respective benefits as follows: if built with A, it augments its benefits by $16 million, if built with B it increase the benefits of project B by $10 million, but if built with C it reduces the benefits of project C by $2 million.

i. Generate a table with 2 columns: the benefit-cost ratio and net benefits for each possible option.

ii. Which option should be chosen according to the Cost Benefit decision rule?

There is a new amusement park under construction in town and the manager of the project has hired
you to design a "Zero-Gravity" room.
(a) Based on your knowledge of nature of electric charge and electric forces, how will you design
such a facility? Comment on components of the room, and explain how it will work for walk in
customers? What would be the safety concerns and measures?
(b) Assume that your design has been approved and facility has been constructed. Your manager has
asked you to demonstrate the operation of the room. You decided to show him weightlessness
using your own body. In your design of part (a), what parameters will you set for this demon-
stration? (You should choose the parameters to counter the value of your weight, for simplicity
you can approximate your body as a point like particle).

An unconscious woman was found partially clothed in a city park that was not illuminated by lighting. The ambulance brings her to your ED. She has no purse and no identification. She is bleeding profusely from a head laceration and the ED physician calls for two units of blood. While this order is being made, a ward clerk whispers to a nurse that the patient looks familiar and may a member of the city’s Jehovah’s Witness group, but the ward clerk is not sure. The nurse immediately calls for a “Time Out” and relays this information to the team. What are the legal and ethical issues for consideration? What should happen?

A 300kg roller coaster at an amusement park is at rest on top of a 30m hill (Point A). The car starts to roll down the hill and reaches point B, which is 10m above the ground, and then rolls up the track to point C, which is 20m above the ground.

a) Assuming no energy is lost and using energy arguments, how fast is the cart moving at point C?

b) What is the total mechanical energy of the roller coaster at point B (Use the ground as the locaiton where potential energy=0)

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If the final speed at point C is actually measured to be 12 m/s,

a) How much energy is lost?

b) Where did this energy go?

Julius Berger is the junior portfolio manager of the global equities portfolio at BSC Asset Management based in the City. Akinbowale, a recently hired equity analyst, has been assigned to Julius to assist him with the portfolio.

Julius provided the betas estimated by using the Capital Asset Pricing Model (CAPM) for MSFT (MSFT), Lloyds (LLoyd), and CHevron (CVF) are 1.28, 1.63, and 1.03, respectively. The risk-free rate of return is 2.42 percent and the equity risk premium is 7.15 percent. Julius also considers an equal-weighted portfolio from the three stocks.

A private friend of Julius asked him to educate him about alternative asset pricing models to the CAPM. Julius considers the Fama-French 3-factor model. Akinbowale collated the following information to evaluate the price of 106 and park by using the Fama-French model. Treasury bill rate is 2.42 percent.

Exhibit 1: TerraNova Data

Required:

Calculate the individual required rates of return for the three stocks using the CAPM.

Calculate the required rate of return and beta of the portfolio consists of the stocks.

Compare the Fama-French 3-factor model to the CAPM and explain the differences.

Based on the data in Exhibit 1, calculate and compare the required return for 106 and park ltd      using the CAPM and the Fama–French model.

Describe the expected style characteristics of 106 and park based on its factor sensitivities.

Part 1:

Park Co. is considering an investment that requires immediate payment of $29,500 and provides expected cash inflows of $14,400 annually for four years. What is the investment's payback period?

Part 2:

Park Co. is considering an investment that requires immediate payment of $21,530 and provides expected cash inflows of $6,500 annually for four years. If Park Co. requires a 7% return on its investments.

1-a. What is the internal rate of return? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided. Round your present value factor to 4 decimals.)

Part 3:

Peng Company is considering an investment expected to generate an average net income after taxes of $3,400 for three years. The investment costs $50,400 and has an estimated $10,200 salvage value.

Assume Peng requires a 10% return on its investments. Compute the net present value of this investment. Assume the company uses straight-line depreciation. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided. Negative amounts should be indicated by a minus sign.)

Ti Fan and his wife have retired. They are touring the USA in a big recreational vehicle (RV). They are towing a Prius car, which they use for running errands when the RV is parked. However, towing the Prius decreases the gas mileage of the RV by 25%. Ti Fan wonders if they would save gas if his wife drives the Prius instead of towing it. The Prius gets good mileage, 50 miles per gallon. Ti Fan has never wanted to know the mileage of the RV, since it would be discouraging. Nonetheless, he looks at the odometer when he fills the RV's gas tank, then looks again when he fills it again. Towing the Prius, he drove 255 miles and burned 37 gallons of gas. How much would they save, in gallons, if they had travelled the 255 miles with his wife driving the Prius while Ti Fan drove the RV?