Q1) Two identical pucks collide on an air hockey table. One puck was originally at rest. If the incoming puck has a speed of 6.50 m/s and scatters to an angle of 30.0º,what is the speed of the second puck after the collision?

(You may use the result that θ₁−θ₂=90º for elastic collisions of objects that have identical masses.)

Q2)A block of mass m = 3.0 kg, moving on a frictionless surface with a speed 2.9 m/s makes a perfectly elastic collision with a block of mass M at rest. After the collision, the 3.0 kg block recoils with a speed of 0.8 m/s. In Fig. 1, the mass M (in kg) is closest to:

For a three-period binomial model for modeling the price of a stock, you are given:

1. The current price of the stock is 125.
2. The length of each period is one year.
3. u = 1.2, where u is one plus the rate of capital gain on the stock if the price goes up.
4. d = 0.8, where d is one plus the rate of capital loss on the stock if the price goes down.
5. The continuously compounded risk-free interest rate is 6%.
6. The price of a three-year $90-strike European put option is $0.89.

Calculate the price of a three-year $100-strike European put option.

1. 1.23

2. 1.49

3. 1.78

4. 2.01

5. 2.48

Please provide full explanation

The mean height of an adult giraffe is 18 feet. Suppose that the distribution is normally distributed with standard deviation 0.8 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. What is the median giraffe height? ft.

c. What is the Z-score for a giraffe that is 21 foot tall?

d. What is the probability that a randomly selected giraffe will be shorter than 18.6 feet tall?

e. What is the probability that a randomly selected giraffe will be between 17.3 and 18.3 feet tall? f. The 75th percentile for the height of giraffes is ft.

Consider the two (excess return) index-model regression results for stocks A and B. The risk-free rate over the period was 6%, and the market’s average return was 15%. Performance is measured using an index model regression on excess returns.

a. Calculate the following statistics for each stock: (Round your answers to 4 decimal places.)

b. Which stock is the best choice under the following circumstances?

The preparations of two aqueous solutions are described in the table below. For each solution, write the chemical formulas of the major species present at equilibrium. You can leave out water itself.

Write the chemical formulas of the species that will act as acids in the 'acids' row, the formulas of the species that will act as bases in the 'bases' row, and the formulas of the species that will act as neither acids nor bases in the 'other' row.

You will find it useful to keep in mind that

NH3

is a weak base.

A gas turbine unit has a pressure ratio of 5/1 and a maximum cycle temperature of 550⁰C. The turbine drives the compressor and an electric generator., the mechanical efficiency of the drive being 97%. The ambient temperature is 20⁰C and the isentropic efficiencies of the compressor and turbine are 0.8 and 0.83 respectively.

Calculate the power output in kilowatts for an airflow of 15kg/s. Calculate also the thermal efficiency and the work ratio. Neglect changes in kinetic energy, and the loss of pressure in the combustion chamber.

Take c_p = 1.005 kJ/kg K and ɣ=1.4 for the compression process, and take c_p = 1.15 kJ/kg K and ɣ=1.333 for all combustion and expansion processes.

Maverick company is a publicly-traded company, with 20 million shares trading at $ 70 a share and $ 600 million in debt (market value as well as book value) outstanding. The firm derives 70% of its value from cloud storage and hosting, and the remaining 30% from technical service. The un-levered beta is 0.8 for firms in the cloud business and 1.2 for firms in the technical service business. Maverick company is rated A and can borrow money at 5%. The risk-free rate is 2% and the market risk premium is 8%; the corporate tax rate is 30%, and the firm has a capital gains tax rate of 20%

1. Estimate the cost of capital for Maverick Company.

1. A 3-phase, 20 kVA, 208 V, 4-pole Y-connected synchronous generator has a synchronous reactance of X_s = 1.5 W per phase. The resistance of the stator winding is negligible. The machine is connected to a 3-phase 208 V infinite bus. Neglect losses.

1. The field current and the mechanical input power are adjusted so that the synchronous machine delivers 10 kW at 0.8 lagging power factor. Determine the excitation voltage E_f and the power angle d.
2. The mechanical input power is kept constant but the field current is adjusted to make the power factor unity. Determine the percent change in the field current with respect to its value in part (a).

Consider the two (excess return) index-model regression results for stocks A and B. The risk-free rate over the period was 5%, and the market’s average return was 13%. Performance is measured using an index model regression on excess returns. Stock A Stock B Index model regression estimates 1% + 1.2(rM − rf) 2% + 0.8(rM − rf) R-square 0.605 0.451 Residual standard deviation, σ(e) 10.8% 19.6% Standard deviation of excess returns 22.1% 25.9% a. Calculate the following statistics for each stock: (Round your answers to 4 decimal places.) b. Which stock is the best choice under the following circumstances?

Kris Kringle Company has one employee who is paid a salary of $8,000 per month. Federal income tax withheld was $220. State income tax withheld was $60.The FICA social security tax rate is 6.2% and the FICA Medicare tax rate is 1.45%. The federal unemployment (FUTA) tax rate is 0.8% on the first $7,000 of wages. The state unemployment (SUTA) tax rate is 5.4% on the first $7,000 of wages. In addition, $590 of medical insurance was withheld from the employees pay.

Prepare Kringle’s journal entry to record the first month’s salary expense. Round to the nearest cent.

Prepare Kringle’s journal entry to record the employer’s payroll taxes for the first week’s payroll.

Bona Foodie Company has one employee who is paid a salary of $10,000 per month. Payroll information for the first month of the year is:

Part I: Prepare Bona Foodie Company’s journal entry to record the first month’s salary expense and employee withholdings. Payroll tax expense will be recorded in part 2.

Part 2: Prepare Bona Foodie Company’s journal entry to record employer payroll taxes for the first month’s payroll.