A penguin has decided to jump between two small icebergs floating in the ocean near Antarctica. You may neglect water resistance and treat the motion of the icebergs relative to the water as frictionless. At the beginning of the problem all are at rest with respect to each other. The penguin runs and jumps off the first iceberg and land on the second, where it comes to rest relative to the second iceberg. The mass of the penguin is mp. The two icebergs each have a mass of mice. The penguin jumps with a speed of vp at an angle γp.Find the final relative speed of the two icebergs.

AT&T is the second-largest provider of mobile telephony and the largest provider of fixed telephony in the United States, and also provides broadband subscription television services.

The CEO of AT&T wants to know what will affect the Total Monthly Spending at AT&T (y) for a customer. So far, the company has information on customer’s age (X1). We have total 50 observations.

1). Using the knowledge you learned from Chapter 3 to summarize the Total Monthly Spending at AT&T and customer’s age. What are the characteristics of this sample?

2). Determine the simple linear regression equation and interpret the slope

3) What is the goodness of fit of this model? Interpret the statistic.

4). At the 0.05 level, test the slope of the regression model. Write down 4-step. Do you think customer’s age will significantly affect the Total Monthly Spending at AT&T?

5). what is the 95% confidence interval for the slope? How does it tell you about the significance of the slope? Does this conclusion agree with the conclusion from 4)

6). What is the estimated average Total Monthly Spending at AT&T for 25 years old customers?

7). Calculate the prediction interval of the Total Monthly Spending at AT&T for a 25 years old customer (Show your calculation details in Excel). Interpret the results. (α=0.05)

8). Calculate the confidence interval for the mean of the Total Monthly Spending at AT&T for 25 years old customers (Show your calculation details in Excel). Interpret the results. (α=0.05

9). Comparing results from 7) and 8), which one is wider? Why?

10). Calculate SSR, SSE and SST for this model.

In Python: Program. At the university, passwords for the campus computer system must meet the following requirements:

• The password must be at least seven characters long.
• It must contain at least one uppercase letter.
• It must contain at least one lowercase letter.
• It must contain at least one numeric digit.
• It must include two special symbols
• It must contain no spaces

Start by translating the pseudocode below into a python function. Add the last two requirements to your function.

Please solve the following game: Assume that a total $100 grant will be shared by the three researchers, X, Y, and Z. Each person is rational and selfish. There are six proposals with different shares of (X, Y, Z) for choices as the following.

Proposal I: (X, Y, Z) = (50, 40, 10)

Proposal II: (X, Y, Z) = (60, 10, 30)

Proposal III: (X, Y, Z) = (40, 20, 40)

Proposal IV: (X, Y, Z) = (20, 30, 50)

Proposal V: (X, Y, Z) = (30, 50, 20)

Proposal VI: (X, Y, Z) = (20, 50, 30)

The rule of choosing the final proposal is simple. First, Z is the person to determine who (either X or Y) is the proposal raiser. Then the proposal raiser chooses a particular proposal. Finally, the last person has the right to pass it or reject it. If the last person’s payoff is the smallest among the three, then the proposal will be rejected and no one will get anything. The decision making process can be done by only one time. Which proposal will be the final outcome? Explain the decision briefly.

Please answer all the two questions by one paragraph for each.

Consider two securities that pay risk-free cash flows over the next two years and that have the current market prices shown here:

1. What is the no-arbitrage price of a security that pays cash flows of $100 in one year and $100 in two years?      
2. What is the no-arbitrage price of a security that pays cash flows of $100 in one year and $500 in two years?
3. Suppose a security with cash flows of $50 in one year and $100 in two years is trading for a price of $130. What arbitrage opportunity is available?

Pole Position, a retailer at Destiny Mall, has a variable cost of $5 per lap driven. It has identified two segments of customers: Hard-Core drivers and Just-For-Fun drivers. For simplicity, throughout this problem, assume there is exactly one customer in each of the two segments. Market research has revealed how each segment values the experience, depending on how many laps are raced:

8. Suppose Pole Position offers customers two options: Package A provides a customer a 3-lap race for $42.99; Package B provides a customer a 8-lap race for $86.99.

1. Which package would a Hard-Core driver buy?
2. Which package would a Just-For-Fun driver buy?
3. How much profit would Pole Position earn from this pricing strategy consisting of a menu of two packages?.
4. How does the profit from 8c compare to the profits from the previous pricing strategies?

Consider the following data for 15 subjects with two predictors. The dependent variable, MARK, is the total score for a subject on an examination. The first predictor, COMP, is the score for the subject on a so-called compulsory paper. The other predictor, CERTIF, is the score for the subject on a previous exam.

a.Run a stepwise regression on the dataset

b.Does CERTIF add anything to predicting MARK, above and beyond that of COMP?

c. Write out the prediction equation

d. A statistician wishes to know the sample size needed in a multiple regression study. She has four predictors and can tolerate at most a .10 drop-off in predictive power. But she wants this to be the case with .95 probability. From previous related research, the estimated squared population multiple correlation is .62. How many subjects are needed?

1. Parker Company produces mathematical and financial calculators and operates at capacity. Data related to the two products are presented here:

Total manufacturing overhead costs are as follows:

Total Machining costs            $375,000

Setup costs                              $120,000

Inspection costs                      $105,000

1. Choose a cost driver for each overhead cost pool and calculate the manufacturing overhead cost per unit for each product. (1.5 pt)

2. Compute the manufacturing cost per unit for each product using Activity-based Costing.(2 pts)

solve it in Microsoft word please

A high school runs a survey asking students if they participate in sports. The results are found below. Run an independence test for the data at α=0.01.

Freshmen Sophomores Juniors Seniors

Yes 75 88 55 42

No 30 28 38 40

Enter the test statistic - round to 4 decimal places.

Ramsey Company produces speakers (Model A and Model B). Both products pass through two producing departments. Model A's production is much more labor-intensive than that of Model B. Model B is also the more popular of the two speakers. The following data has been gathered for the two products: Product Data Model A Model B Units produced per year 10,000 100,000 Prime costs $150,000 $1,500,000 Direct labor hours 140,000 300,000 Machine hours 20,000 200,000 Production runs 40 60 Inspection hours 800 1,200 Maintenance hours 10,000 90,000 Overhead costs: Setup costs $270,000 Inspection costs 210,000 Machining

Ramsey Company produces speakers (Model A and Model B). Both products pass through two producing departments. Model A's production is much more labor-intensive than that of Model B. Model B is also the more popular of the two speakers. The following data has been gathered for the two products: