The table below contains distance and recessional velocity data for ten galaxies.

1. a) Plot the ‘Hubble Diagram’ for these galaxies. This is simply a plot of the observed velocity on the y-axis and the distance on the x-axis.

2. b) Fit a line to the data that goes through the origin of the plot (that is, where the dis- tanceandvelocityarebothzero). TheslopeofthislineistheHubbleconstant.What is the Hubble constant for these data? NOTE: The value is not the same as the Hubble constant we are adopting in the text.

3. c) Calculate the redshift, ? = ∆?/?& for each galaxy. HINT: Go back to the definition of the Doppler effect in Destination 6 to recall what = ∆?/?& is equal to (or just look at question 1c above). You will see that have the information you need in the table above to calculate the redshift (though, strictly speaking, only for redshifts that are significantly smaller than 1.0).

4. d) Notice that galaxies 2-5 in the table are all at about the same distance, but their ve- locities differ rather significantly. Explain what is likely happening to account for this behavior.

Your friend has decided to make some money during the next State Fair by inventing a game of skill. In the game, as she has developed it so far, the customer shoots a rifle at a 5.0 cm diameter target falling straight down. Anyone who hits the target in the center wins a stuffed animal. Each shot would cost 50 cents. The rifle would be mounted on a pivot 1.0 meter above the ground so that it can point in any direction at any angle. When shooting, the customer stands 100 meters from where the target would hit the ground if the bullet misses. At the instant that the bullet is fired (with a velocity of 1200 ft/sec according to the manual), the target is released from its holder 7.0 meters above the ground. (You see, the trigger is electronically connected to the release mechanism.) Your friend asks you to try out the game which she has set up on a farm outside of town. Before you fire the gun you calculate where you should aim. You may, as usual, neglect any effects of air resistance. Your conclusion? At what angle from the vertical should you aim?

Superior Technologies Inc. sells a product at the unit price of $2,000. Its credit sales in the 2019 financial year were reported at 500 units. The variable cost per unit is $1,350. The firm is now considering a tightening of credit standards that is expected to result in the following: (1) a 10% decrease in unit sales; (2) a decrease in bad-debts expense from 2.0% to 1.0% of sales; (3) a decrease of $2,000 in collection expenses and (4) a decrease in the accounts receivable period from 60 days to 30 days. TTL’s required rate of return is 15% p.a.

Fill in the blanks A-F below to weigh up the financial costs and benefits of such decision and to determine whether the company should tighten its credit standards or not.

Do not use comma (,) or a dollar sign ($) in your answers. If the change is a positive value (benefit) enter it with a plus sign (+) and if it is a negative value (loss) enter it with a minus sign (-) WITHOUT any space between the number and the minus/plus sign. Example: if the answer is a loss of $10000, enter your answer as -10000.

Additional Profit/loss from ΔSales: $

Benefit/loss from ΔBad_Debts: $

Benefit/loss from ΔCollection_Expenses: +2000

Benefit/loss from ΔA/R: $

Δ Net Profit: $

1. What are the main data types in Python? Which data types are sequences?

2. What are some general guidelines for naming a ‘variable’ in Python? Give at least three examples of variable names that follow these guidelines

3. Provide an example of the Python syntax to create a variable to hold the age of a building (for example,40 years old).

a. Provide the Python syntax to test whether the variable created above is more than 35, and print the test result

4. What are some of the key similarities and differences between lists and tuples in Python? Give an example, using geospatial information, of when a list would be more appropriate to use and when a tuple would be a more appropriate data type?

6. Name three methods of string objects in Python, and provide an example of each one's use.

7. Given the code below: leftovers = [‘cake’,’ice cream’] t_list = [[2.5, 1.0], ‘32’, ‘alabi’, ‘Alaska’, ‘Ohio’, ‘Armenia’, 29.05, leftovers]

a. What is the ‘data type’ of the first element in t_list?

b. What is the ‘data type’ of the second t_list element?

c. What is returned by the following code snippet? print(t_list[1])

d. What is returned by the following code snippet? print(t_list[-2])

Design and construct a computer program in one of the approved languages (C, C++, C#, Java, Pascal, Python, etc.) that will illustrate the use of a fourth-order
explicit Runge-Kutta method of your own design. In other words, you will first have to solve the Runge-Kutta equations of condition for the coefficients
of a fourth-order Runge-Kutta method.

Then, you will use these coefficients in a computer program to solve the ordinary differential equation below.
Be sure to follow the documentation and programming style policies of the Computer Science Department.

The initial value problem to be solved is the following:

                          x'(t) = 3 x² cos(5 t)

subject to the initial condition:  x(0) = 1.0   

Obtain a numerical solution to this problem over the range from t=0.0 to t=2.0

for seven different values of the stepsize,

h=0.1, 0.05 , 0.025 , 0.0125 , 0.00625 , 0.003125 , and 0.0015625 .

In other words, make seven runs with 20, 40, 80, 160, 320, 640, and 1280 steps, respectively.
For each run, print out the value of h, then a table of t and x, and then the error at t=2. You may use the following
very precise value for your "true answer" in order to compute the error at t=2:   0.753913186469598763502963347.

2. Geniue Antique Egyptian Artifacts, Inc. produces three varieties of antique artifacts for sale to tourists: statuettes, lamps, and urns. All of the artifacts include special clay. A statuette requires 13 ounces of clay, a lamp uses 18 ounces, and each urn takes 17 ounces. Existing capacity of clay is 28,000 ounces per month. A special material is also used to produce the three artifacts, with each statuette needing 0.8 ounces, each lamp 0.7 ounces, and a typical urn requiring 1.0 ounces. The company has inventory of 1,200 ounces of special material per month. The owner of the company wishes to maintain a balanced marketing program, and has ordered that production of statuettes to be limited to 275. The overall per unit profit for artifacts is the following: $199 per statuette, $99 per lamp, and $145 per urn. The owner wants to know how much of each type of antique to fabricate monthly in order to optimize profit.

a. What are the objective function, decision variables, and constraints for this optimization problem?

b. Develop an Excel spreadsheet and use Excel-Solver to find an optimal solution for this problem.

c. Describe the optimal solution in words.

Jackie, a 44-year-old female, has had HIV for 12 years. Her physician has recently diagnosed her with AIDS due to a decline in her CD4+ T cells over the past five years, an elevated viral load, and recurrent bacterial pneumonia. She has ongoing lipodystrophy; she lost approximately 30 pounds in the past year and has had diarrhea for the past six weeks. Her roommate reports that Jackie’s appetite has been minimal lately and he attributes this to a thrush infection that has been resistant to medical treatment. Her current weight is 112 pounds.

1. Calculate Jackie’s estimated kcalorie and protein needs using the following factors: 30 to 35 kcalories/kilogram, 1.0 to 1.6 grams protein/kilogram (show your work).

2. What suggestions do you have for the chewing and swallowing problems Jackie is having related to thrush?

3. What advice do you have for Jackie and her roommate regarding food safety?

4. What can Jackie do to manage the metabolic complications associated with lipodystrophy?

5. What dietary modifications might help Jackie manage her ongoing diarrhea?

NDR, Inc., an unlevered firm, has expected earnings before interest and taxes of $2 million per year. NDR's tax rate is 40%, and the market value is V=E=$12 million. The stock has a beta of 1.0, and the risk free rate is 9%. [Assume that E(Rm)- Rf = 6%]. Management is considering the use of debt; debt would be issued and used to buy back stock, and the size of the firm would remain constant. The default free interest rate on debt is 12%. Since interest expense is tax deductible, the value of the firm would tend to increase as debt is added to the capital structure, but there would be an offset in the form of the rising cost of bankruptcy. The firm's analysts have estimated, approximately, that the present value of any bankruptcy cost is $8 million and the probability of bankruptcy will increase with leverage according to the following schedule: Value of Probability Debt of Failure $2,500,000 0.00% $5,000,000 8.00% $7,500,000 20.50% $8,000,000 30.00% $9,000,000 45.00% $10,000,000 52.50% $12,500,000 70.00% a. What is the cost of equity and WACC at this time? b. What is the optimal capital structure when bankruptcy costs are considered? c. What will the value of the firm be at this optimal capital structure?

Halogen Inc. is an unlevered firm, has expected earnings before interest and taxes of $2 million per yearHalogen Inc tax rate is 40%, and the market value is V=E $12 million. The stock has a beta of 1.0, and the risk free rate is 9%. Assume that E(Rm)-Rf-6%). Management is considering the use of debt; debt would be issued and used to buy back stock, and the size of the firm would remain constant. The default free interest rate on debt is 12%. Since interest expense is tax deductible, the value of the firm would tend to increase as debt is added to the capital structure, but there would be an offset in the form of the rising cost of bankruptcy. The firm's analysts have estimated, approximately, that the present value of any bankruptcy cost is $8 million and the probability of bankruptcy will increase with leverage according to the following schedule: Value of Probability Debt of Failure $2,500,000 0.00% $5,000,000 8.00% $7,500,000 20.50% $8,000,000 30.00% $9,000,000 45.00% $10,000,000 52.50% $12,500,000 70.00% a. What is the cost of equity and WACC at this time? b. What is the optimal capital structure when bankruptcy costs are considered? c. What will the value of the firm be at this optimal capital structure?

Based on the inputs below prepare a capital budget analysis for this Base Case using the Net Present Value, Internal Rate of Return, Profitability Index and Payback in years methods, determining whether the project is feasible. Please show your spreadsheet calculations and your final determinations of “go” or “no go” on the project. Use your Investment Return Analysis as an example for this capital budget analysis. PLEASE show formulas

Project Inputs:

WACC – Debt is 70% and Equity is 30% of this firm’s capital structure. Interest rate on the debt is 7.5%, firm’s tax rate is 22%. Firm’s beta is 1.50, Risk Free Rate is 1.0%, Market Return Rate is 7.0%.

Project Investment Outlay, Year 0 - $1,000,000
Project Investment Life – 10 years
Project Depreciation - $100,000 / year
Project Salvage Value - $30,000

Working Capital Base of Annual Sales – 10%
Expected inflation rate per year – 3.0%
Project Tax Rate – 30%

Units sold per year – 40,000
Selling Price per Unit, Year 1 - $40.00
Fixed operating costs per year excluding depreciation - $175,000
Manufacturing (Variable) costs per unit, Year 1 - $30.00