Determine if the following set W spans R^3 .

W = {(1, 3, 1),(2, 1, 1),(−1, 0, 1)}

1.Prove the following statements:

.

(a) If bn is recursively defined by bn =bn−1+3 for all integers n≥1 and b0 =2,

then bn =3n+2 for all n≥0.

.(b) If cn is recursively defined by cn =3cn−1+1 for all integers n≥1 and c0 =0,

then cn =(3n −1)/2 for all n≥0.

.(c) If dn is recursively defined by d0 = 1, d1 = 4 and dn = 4dn−1 −4dn−2 for all integers n ≥ 2,

then dn =(n+1)2n for all n≥0.

The production function of a firm is given by F(K, L)=KL. Assume that capital (K) is fixed at K=1 in the short run. Then the amount of labor (L) needed to produce 4 unit of output is equal to ___. Group of answer choices 16 1 4 8 2

On February 1, 2018, Cromley Motor Products issued 6% bonds, dated February 1, with a face amount of $95 million. The bonds mature on January 31, 2022 (4 years). The market yield for bonds of similar risk and maturity was 8%. Interest is paid semiannually on July 31 and January 31. Barnwell Industries acquired $95,000 of the bonds as a long-term investment. The fiscal years of both firms end December 31. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)

Required:
1. Determine the price of the bonds issued on February 1, 2018.
2-a. Prepare amortization schedules that indicate Cromley’s effective interest expense for each interest period during the term to maturity.
2-b. Prepare amortization schedules that indicate Barnwell’s effective interest revenue for each interest period during the term to maturity.
3. Prepare the journal entries to record the issuance of the bonds by Cromley and Barnwell’s investment on February 1, 2018.
4. Prepare the journal entries by both firms to record all subsequent events related to the bonds through January 31, 2020.

(Req-3 JE's: FEB 1, 2018: Record the issuance of the bonds by Cromley. FEB 1 2018: Record the Bond investment by Barnwell.)

(Req-4(Cromley): 1 Record the payment of interest for Cromley Company. 2 Record the accrued interest for Cromley Company. 3 Record the payment of interest for Cromley Company. 4 Record the payment of interest for Cromley Company. 5 Record the accrued interest for Cromley Company. 6 Record the payment of interest for Cromley Company.)

(Req-4(Barnwell): 1 Record the receipt of interest for Barnwell Company. 2 Record the accrued interest for Barnwell Company. 3 Record the receipt of interest for Barnwell Company. 4 Record the receipt of interest for Barnwell Company. 5 Record the accrued interest for Barnwell Company. 6 Record the receipt of interest for Barnwell Company.)

Let W be a discrete random variable and Pr(W = k) = 1/6, k = 1, 2 ,....., 6. Define
X =
{
W,  if W <= 3;
1,  if W >= 4;

}
and Y =
{
3,  if W <= 3;
7 -W,  if W >= 4;

}
(a) Find the joint probability mass function of (X, Y ) and compute Pr(X +Y = 4).
(b) Find the correlation Cor(X, Y ). Are X and Y independent? Explain.

Match the following aqueous solutions with the appropriate letter from the column on the right.
1)

2)

3)

Consider a 2-period binomial non-recombining model. Let r = 0.05 be the discrete interest rate for each of the periods, S(0) = 100 and suppose that the stock price follow four possible scenarios:

It is known that the risk-neutral probability for each scenario ?i , i = 1, 2, 3, 4 satisty P ? (?1) = 0.2, P? (?2) = 0.4, P? (?3) = 0.3, P? (?4) = 0.1.

(a) Draw the tree of the stock prices using S^u , S^uu, and S^du, and find the risk-neutral probability for each route on the tree.

(b) Find the prices S^u , S^uu, and S^du

(c) Find today’s price of a European call option with strike price K = $100 maturing after two steps.

(d) Find today’s price of an American put option with strike price $110 and expiration date in two steps. Should the American option be exercised early? If so, when?

A company that manufactures snow shovels has one plant and two distribution centers (DCs). Given the following information for the two DCs, calculate the gross requirements, projected available, and planned order releases for the two DCs and the gross requirements, projected available, and planned order releases for the central warehouse.

Distribution Center A Transit Time:   2 weeks Order Quantity:   500 units

Distribution Center B

Transit time: 2 weeks

Order Quantity: 200 weeks

Central Supply

Lead time : 1 week

Order Quantity= 600 units

Please show all work.

8. The following data are taken from the financial market pages of an Australian newspaper.

Forward Margins

A) What do the forward rates indicate in terms of whether the A$ is expected to strengthen or weaken with respect to the US dollar?

Many regions in North and South Carolina and Georgia have experienced rapid population growth over the last 10 years. It is expected that the growth will continue over the next 10 years. This has motivated many of the large grocery store chains to build new stores in the region. The Kelley’s Super Grocery Stores Inc. chain is no exception. The director of planning for Kelley’s Super Grocery Stores wants to study adding more stores in this region. He believes there are two main factors that indicate the amount families spend on groceries. The first is their income and the other is the number of people in the family. The director gathered the following sample information.

Food and income are reported in thousands of dollars per year, and the variable size refers to the number of people in the household. Click here for the Excel Data File a-1. Develop a correlation matrix. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.) a-2. Do you see any problem with multicollinearity? b-1. Determine the regression equation. (Round your answer to 3 decimal places.) b-2. How much does an additional family member add to the amount spent on food? (Round your answer to the nearest dollar amount.) c-1. What is the value of R2? (Round your answer to 3 decimal places.) c-2. Complete the ANOVA (Leave no cells blank - be certain to enter "0" wherever required. Round SS, MS to 4 decimal places and F to 2 decimal places.) c-3. State the decision rule for 0.05 significance level. H0: = β1 = β2 = 0; H1: Not all βi's = 0. (Round your answer to 2 decimal places.) c-4. Can we reject H0: = β1 = β2 = 0? d-1. Complete the table given below. (Leave no cells blank - be certain to enter "0" wherever required. Round Coefficient, SE Coefficient, P to 4 decimal places and T to 2 decimal places.) d-2. Would you consider deleting either of the independent variables? State true or false. picture From the graph the residuals appear normally distributed. True False Choose the right option from the following graph. picture There is a homoscedasticity problem. There is no homoscedasticity problem.