Ironman steps from the top of a tall building. He falls freely from rest to the ground a distance of h. He falls a distance of h/ 4 in the last interval of time of 1.0 s of his fall.

Hint: First, compute the velocity when Ironman reaches the height equal to the distance fallen. This requires that you do the following: define origin as the bottom of the building. Then use x-x0 = -v0*(t-t0)-(1/2)g(t-t0)^2 where x=0 and x0= (distance fallen) and t-t0 is the time interval given. In this formulation, you are going to get magnitude of v0 since you already inserted the sign. You then insert v0 that you just calculated into the kinematic equation that involves v, g, and displacement (v^2-v0^2 = 2g(height-(distance fallen)), but now v (which is the final velocity is v0 from above) and v0 in this case is the velocity that the Ironman has when he begins to fall, which is 0. This gives a quadratic equation for height h, and you will need to use the binomial equation to solve for h. Choose the larger of the two solutions.

Part A

What is the height h of the building?

Express your answer using two significant figures.

Be sure to answer all parts. In 2006, an ex-KGB agent was murdered in London. Subsequent investigation showed that the cause of death was poisoning with the radioactive isotope 210Po, which was added to his drinks/food. (a) 210Po is prepared by bombarding 209Bi with neutrons. Write an equation for the reaction. Show the mass number and atomic number of all species. Tip: use the sup-subscript button to insert all symbols. (b) Who discovered the element polonium? Marie and Pierre Curie Enrico Fermi (c) The half-life of 210Po is 138 d. It decays with the emission of an α−particle. Write an equation for the decay process. Show the mass number and atomic number of all species. Tip: use the sup-subscript button to insert all symbols. (d) Calculate the energy of an emitted α−particle. Assume both the parent and daughter nuclei to have zero kinetic energy. The atomic masses are: 210Po (209.98285 amu), 206Pb (205.97444 amu), α−particle (4.00150 amu). (Enter your answer in scientific notation). × 10 J (e) Ingestion of 1.0 mg of 210Po could prove fatal. What is the total energy released by this quantity of 210Po, assuming every atom decays? (Enter your answer in scientific notation). × 10 J

The following data represent petal lengths (in cm) for independent random samples of two species of Iris.

Petal length (in cm) of Iris virginica: x₁; n₁ = 35

Petal length (in cm) of Iris setosa: x₂; n₂ = 38

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to two decimal places.)

(b) Let μ₁ be the population mean for x₁ and let μ₂ be the population mean for x₂. Find a 99% confidence interval for μ₁ − μ₂. (Round your answers to two decimal places.)

Directions: Place all answers on this sheet and show your work.

1. Calculate a client’s intake and output (I&O) in milliliters (mL) from 0700 to 1500.

Breakfast:        3/4 cup of coffee

                        3 oz glass orange juice

Lunch:             4 oz diet soda

                        6 oz chicken broth

Voided:           200mL at 1000

200mL at 1400

            Emesis:            125mL at 1300

IV fluids:         Lactated Ringers @ 100 mL/hr

Total 8 hour intake =   mL

Total 8 hours output = ml

2. The nurse receives an order to give atropine 300mcg SQ now. The medication is available in 1mg/mL vial. How many mL should the nurse administer? (Do not round)

300/100 = 0.3 ml/hr

3. Calculate the IV infusion rate using a pump (mL/hr) for 1L LR over 8 hours.

1000/

4. Calculate the blood transfusion rate using a pump (mL/hr). 1 unit PRBC (225mL) over 2 hours. (round to the nearest whole number)

5. Calculate the following IVPB infusion using a pump (mL/hr). Zofran 20mg IVPB every 6 hours infused over 30 minutes. The IV bag contains 20mg in 100mLs NS.

6. How long will it take to finish infusing 1L of D5NS 100mL/hr?

7. The nurse receives an order to give heparin 1,500 units/hr. The IV bag contains 20,000 units heparin in 500mL D5W. Calculate the IV rate in mL/hr. (do not round)

4. Consider the random variable Z from problem 1, and the random variable X from problem 2.

Also let f(X,Z)represent the joint probability distribution of X and Z.  f is defined as follows:

f(1,-2) = 1/6
f(2,-2) = 2/15
f(3,-2) = 0
f(4,-2) = 0
f(5,-2) = 0
f(6,-2) = 0
f(1,3) = 0
f(2,3) = 1/30
f(3,3) = 1/6
f(4,3) = 0
f(5,3) = 0
f(6,3) = 0
f(1,5) = 0
f(2,5) = 0
f(3,5) = 0
f(4,5) = 1/6
f(5,5) = 1/6
f(6,5) = 1/6

Compute the covariance of X and Z.

Then, compute the correlation coefficient of X and Z. (Note: You will need values that you computed in problems 1 and 2.)

These are questions 1 and 2.

1. Let Z be a random variable with the following probability distribution f:

f(-2) = 0.3
f(3) = 0.2
f(5) = 0.5

Compute the E(Z), Var(Z) and the standard deviation of Z.

2. Tossing a fair die is an experiment that can result in any integer number from 1 to 6 with equal probabilities. Let X be the number of dots on the top face of a die. Compute E(X) and Var(X).

Ginny is endowed with $10 million and is deciding whether to invest in a restaurant. Assume perfect capital markets with an interest rate of 6%.

2. Which investment option should Ginny choose?

Ginny is actively pursuing another business venture as a ticket scalper. She estimates that for a $2 million investment in inventory she can resell her tickets for $6 million over the next year (cash flows realized in exactly one year).  Assume the same 6% interest rate.

3. What is the NPV of the Ticket Brokering venture?
4. What is the new value of Ginny’s Corporation?
5. Suppose Ginny does not want to use her own $2 million to start the new venture. Instead, she wants to raise equity capital by issuing 100,000 new shares. What price will new investors be willing to pay?
6. How many shares will need to be sold to outside investors?
7. How will your answer differ if Ginny is not guaranteed to resell the tickets for $6 million?
8. According to Ginny’s prospectus, cash flows from ticket sales (net of expenses) are expected to follow the following distribution:

What is the new value of Ginny’s Corporation?

9. What price will new investors be willing to pay for Ginny’s shares?

Please only answer Q6, Q7, Q8, Q9 four questions. Thanks.

A kitchen appliance manufacturer is deciding whether or not to introduce a new product. Management has identified three possible demand regimes, with associated projected income for the first year of operation. In addition, if the company decides to produce the new product, it can do so by using its existing facilities, which will cost it $3,500,000 in renovations; or build a new facility, which will cost $6,500,000. Expanding will allow it to make more product and so its potential sales can be higher. The following table contains a summary of management expectations:

The company believes that if the new product is not introduced, in the first year of operation the company will lose $10,500,000 in sales to competitors in a high demand regime, $1,500,000 in a medium demand regime, and $0 in a low demand regime.

(a) Construct a payoff table and decision tree for this problem.

(b) Using the expected value approach, what should the company do?

(c) The company finds itself in a difficult financial situation. How does this information affect your recommendation in part (b)?

(d) A consulting company claims it can perform a more thorough market research study. In your opinion, should this study be performed?

(e) The company has the option of constructing a new facility after 1 year of operation. In your opinion, which conditions would warrant an expansion after year 1?

The following data are for the two products produced by Shakti Company.

The company's direct labor rate is $20 per direct labor hour (DLH). Additional information follows.

I am getting stuck on the following:

4.1 How Much gross profit is generated by each customer of Product A and Product B.

Gross profit (loss) per unit Product A $5.71 Product B $24.98

Units purchased per customer 20 5

Gross Profit (loss) per customer ? ?

4.2 Is the gross profit adequate for each customer of Product A and Product B?

Gross profit (loss) per customer Product A ? Product B ?

Service Cost Per Customer 90 90

Profit (loss) per customer ? ?