You are given a transition matrix P. Find the steady-state distribution vector. HINT [See Example 4.]

P = [0.6 0 0.4

1 0 0

0 0.2 0.8]

Question 1: Given the following probability distributions for stock A and stock B

Calculate (a) expected return, (b) standard deviation (c) coefficient of variation for each stock (analyze single stock separately: do expected return for A, standard deviation for A, CV for A. Then repeat the steps for stock B)

A massive oil spill in the gulf unleashes approximately 20,311 barrels of oil into the Gulf each hour. This creates an expanding circular layer of oil on the water’s surface about 1/16 inches thick with the center being the source of the spill. Letting R(t) represent the radius (in miles) t hours after 6:00pm, the growing radius of this oil spill can be modeled by the formula: R(t)=1/2 √(t+1) A.) What time did this spill start? (When was the radius zero?) B.) Fill in the table below: (round your answer to 2 decimal places) Table 1 t hours 0 .5 1 1.5 2 2.5 3 3.5 4 4.5 R(t) miles C.) If left unchecked, how long will it take this oil spill to reach a 2 mile radius? The nearest containment crew is on the Louisiana coast 50 miles away. At 6:00 pm, containment vessels instantly head towards the center of this spill, but the fastest these containment ships can travel is only 15 mph. D.) Write an equation that represents the distance D(t) in miles that the containment vessel is from the center of the spill t hours after 6:00 pm. E.) Fill in the table below: Table 2 t hours 0 .5 1 1.5 2 2.5 3 3.5 4 4.5 D(t) miles F.) When will the containment vessels reach the center of spill? G.) By observing the two tables above, in which 30 minute interval will the containment vessels reach the outer edge of the spill? H.) Algebraically find exactly (to the nearest minute) when the containment vessels will reach the outer edge of the oil spill. You should get two answers…explain them. I.) What is the radius of the oil spill at this time? J.) To manage the spill, one containment vessel is needed every 800 feet around the outer circumference of the spill. How many vessels do they need? (5280 ft. = 1 mile)

Cincinnati Paint Company sells quality brands of paints through hardware stores throughout the United States. The company maintains a large sales force who call on existing customers and look for new business. The national sales manager is investigating the relationship between the number of sales calls made and the miles driven by the sales representative. Also, do the sales representatives who drive the most miles and make the most calls necessarily earn the most in sales commissions? To investigate, the vice president of sales selected a sample of 25 sales representatives and determined:

• The amount earned in commissions last month (y)
• The number of miles driven last month (x₁)
• The number of sales calls made last month (x₂)

The information is reported below.

Develop a regression equation including an interaction term. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.)

Comissions= ______+_______ calls +__________ Miles +__________

Complete the following table. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Compute the value of the test statistic corresponding to the interaction term. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Cincinnati Paint Company sells quality brands of paints through hardware stores throughout the United States. The company maintains a large sales force whose job it is to call on existing customers as well as look for new business. The national sales manager is investigating the relationship between the number of sales calls made and the miles driven by the sales representative. Also, do the sales representatives who drive the most miles and make the most calls necessarily earn the most in sales commissions? To investigate, the vice president of sales selected a sample of 25 sales representatives and determined:

The amount earned in commissions last month (Y).

The number of miles driven last month (X1)

The number of sales calls made last month (X2)

Click here for the Excel Data File

Develop a regression equation including an interaction term. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

A.) Commissions =_______ +________ Calls +________ Miles +______ X1X2

B.) Complete the following table. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

Predictor Coefficient    SE Coefficient    T P-value

Constant _______         __________    ___   _________

Calls

Miles

X1X2

C.) Compute the value of the test statistic corresponding to the interaction term. (Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)

IN JAVA PLEASE

Program 4: Is there a Prius version? Did you know that the average Boeing 747 airplane uses approximately 1 gallon of fuel per second? Given the speed of the airplane, that means it gets 5 gallons to the mile. No, not 5 miles to the gallon, 5 gallons to the mile. You may be questioning why such a horribly inefficient machine is allowed to exist, but you’ll be happy to find out that, because this airplane hold 568 people, it averages about 0.01 gallons per person – (100 miles per gallon per person). Your job is to design (pseudocode) and implement (source code) a program that asks the user for a distance the plane has to fly (i.e. the length of the trip) and also asks the cost of jet fuel (which is currently $1.80 per gallon). The program should then calculate the total fuel charges to make the trip. Next, ask the user how many people will fly, as well as the average cost of a ticket. Finally, print the total profit made (or lost) and the average gas mileage per person. Document your code and properly label the input prompts and the outputs as shown below.

Sample run 1: Enter the flight distance: 1000 Enter the current cost of jet fuel: $2 The flight will cost $10000.0 in fuel. Enter the number of passengers: 5 Enter the average cost of a ticket: 1000 You will make a profit of $-5000.0 You averaged 1.0 miles per person per gallon!

Sample run 2: Enter the flight distance: 500 Enter the current cost of jet fuel: $3 The flight will cost $7500.0 in fuel. Enter the number of passengers: 500 Enter the average cost of a ticket: 300 You will make a profit of $142500.0 You averaged 100.0 miles per person per gallon!

Sample run 3: Enter the flight distance: 4200 Enter the current cost of jet fuel: $1.80 The flight will cost $37800.0 in fuel. Enter the number of passengers: 550 Enter the average cost of a ticket: 600 You will make a profit of $292200.0 You averaged 110.0 miles per person per gallon!

Cade Industries operates a fleet of delivery vehicles that make scheduled pickups and deliveries for its customers in the Boulder area. The company is implementing an activity based costing system that has four activity cost pools: Travel, Pickup and Delivery, Customer Service and Other. The activity measures are as follows for each of the cost pools: Travel – Miles; Pickups and Deliveries - # of Pickups and Deliveries; Customer Service - # of Customers. The Other cost pool has no activity measure because it is an organization-sustaining activity. The following costs will be assigned using the activity based costing system:

The distribution of resource consumption across the activity cost pools is as follows:

1. If the company had the following activity, complete the Second Stage Allocations. Calculate to the nearest tenth of a penny.
   1. Miles Driven – 1,000,000
   2. Pickups and Deliveries – 5,000
   3. Number of Customers – 1,500
2. During 2018, Cade completed a number of deliveries for one of it’s customer’s Tank 7 Industries. Cade calculates revenues based on the miles driven. During the year, Cade drove 25,000 miles on 30 deliveries for Tank 7 Industries. Cade charges a premium on any deliver that is 250 miles or less of $100/delivery. Six of Tank 7’s deliveries were subject to this $100 surcharge. Cade charges Tank 7 $1.75/mile driven (plus any surcharges). Determine the profitability of Tank 7 Industries in 2018 for Cade.
3. Just do question 2. Please show all work

Given two independent uniform random variables U1 and U2 both with parameters [0,1],

1) Calculate the probability that 0.3 <= X + Y <= 0.8

2) Calculate the PDF of X+Y

3) Calculate the PDF of X-Y

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $14 million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federal-plus-state tax rate is 40%. The CFO has estimated next year's EBIT for three possible states of the world: $4.9 million with a 0.2 probability, $2.5 million with a 0.5 probability, and $0.7 million with a 0.3 probability. Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations.

1) Debt/Capital ratio is 0.

2)Debt/Capital ratio is 10%, interest rate is 9%.

3) Debt/Capital ratio is 50%, interest rate is 11%.

4) Debt/Capital ratio is 60%, interest rate is 14%.

A 4.5m4.5m foundation carries a load of 3000 kN. The foundation rests at a depth of 1.5m
below the ground surface. The bearing soil is an extended sand with a saturated unit weight
(γsat) of 19 kN/m3
, modulus of elasticity (E) of 35 MPa, and Poisson’s ratio (µ) of 0.3. The
water level coincides with the ground surface.
a) Determine the effective vertical stresses (σ̍v) for points underneath the corner and
center of the foundation and located at a depth of 6.0 m from the ground surface.
Note: for estimating Δσ̍v (i.e., the additional vertical stresses), use both of the
influence coefficient and approximate methods. Comment on your results.
b) If we consider this foundation as a rigid element, what would be its uniform
settlement under the given load? Is it safe (and why)?
c) Calculate the time-dependent maximum, minimum, and differential settlements of the
foundation if sand is interrupted by a 2m-thick clay layer that starts at a depth of 5m
below the ground surface. Is it safe (and why)?
Note: For the clay, take Cc = 0.2 and e = 0.7.