(5.1.24) Prove that 1/(2n) ≤ [1 · 3 · 5 · · · · · (2n − 1)]/(2 · 4 · · · · · 2n) whenever n is a positive integer

#1 Let H= Span{v1,v2,v3,v4}. For each of the following sets of vectors determine whether H is a line, plane ,or R3. Justify your answers.

(a)v1= (1,2,−2),v2= (7,−7,−7),v3= (16,−12,−16),v4= (0,−3,−3)

(b)v1= (2,2,2),v2= (6,6,5),v3= (−16,−16,−14),v4= (28,28,24)

(c)v1= (−1,3,−3),v2= (0,0,0),v3= (−2,6,−6),v4= (−3,9,−9)

#2 Plot the linesL1: x= t[4−1] and L2: x= [−4−2] + t[4−1] using their vector forms. If[12k]is onL2. What is the value of k?

A random sample of six employees assigned to each of the three departments showed the number of days absence because of illness during the year: Employee Radiology Laboratory Dietary 1 9 4 10 2 6 2 13 3 7 3 11 4 5 6 9 5 8 5 8 6 7 1 12 if α = 0.05, determine whether the differences among the departments are significant.

1) Identify the null hypothesis.

2) Identify the alternative hypothesis.

3) Determine the value of the F test statistic.

4) Identify the P-value.

5) State a conclusion about the null hypothesis.

6) State a final conclusion that addresses the original claim.

A construction company is purchasing a new Tractor for over the road use. The IRS classifies this as 3-year property. The truck costs $297000.
a) Determine the depreciation allowance for each year using SLN method.
Year 1 $  
Year 2 $  
Year 3 $  
Year 4 $  

b) Determine the depreciation allowance for each year using DDB method.
Year 1 $  
Year 2 $  
Year 3 $  
Year 4 $  

c) Determine the depreciation allowance for each year using MACRS.
Year 1 $  
Year 2 $  
Year 3 $  
Year 4 $  

d) Using a 10% MARR calculate the present worth of the depreciation for each of the 3 methods above.
PW_a = $  
PW_b = $  
PW_c = $

A construction company is purchasing a new Tractor for over the road use. The IRS classifies this as 3-year property. The truck costs $280000.

a) Determine the depreciation allowance for each year using SLN method.

Year 1 $

Year 2 $

Year 3 $

Year 4 $

b) Determine the depreciation allowance for each year using DDB method.

Year 1 $

Year 2 $

Year 3 $

Year 4 $

c) Determine the depreciation allowance for each year using MACRS.

Year 1 $

Year 2 $

Year 3 $

Year 4 $

d) Using a 10% MARR calculate the present worth of the depreciation for each of the 3 methods above.

PWa = $

PWb = $

PWc = $

The residuals for 15 consecutive time periods are as follows:

a) Plot the residuals over time. What conclusion can you reach about the pattern of the residuals over time?

b) Compute the Durbin-Watson statistic. At the 0.05 level of significance, is the evidence of positive autocorrelation among the residuals?

c) Based on (a) and (b), what conclusion can you reach about the autocorrelation of the residuals?

Departments A, B, C, and D need to be assigned to four rooms 1, 2, 3, and 4. These rooms are arranged in a row, in that order, with 20 meters between each. The departmental work flows are contained in the table below.

(a) What is the material handling total of assigning A-1, B-2, C-3, D-4?

(b) What is the material handling total of assigning A-1, B-3, C-4, D-2?

1) find the are of the region that lies inside of the curve r= 1+ cos theta and outside the curve r=3 cos theta.

2) find the sum"

En=1 3^{1-n}:2^{n+2}

3) find
integration ( 2x^2 +1) e^x^2 dx

4) Does:

E n=12 ((2n)!/(n!)^2) converge or diverge ? justify your answer ( what test?)

1) A 1 1/2 -year loan in the amount of $100,000 with 12% interest was taken out on June 1, 2020.

a) Calculate the interest for December 31. (Hint: From June 1 - Dec 31 -- use your fingers)

Note Payable Entries

b) Prepare the journal entry for the issuance of the Note Payable.

c) Prepare the adjusting journal entry for interest expense – December 31, 2020

   (HINT: found amount in a)

d) Prepare the journal entry at maturity – November 30, 2021

1b) Prepare the following Journal entries for Bond Issuance

a) Issued $100,000 in bonds at face value.

b) Issued $100,000 in bonds for 98 (Discount)

c) Issued $100,000 in bonds for 101. (Premium)

1. A pension plan is obligated to make disbursements of $1 million, $2 million, and $1 million at the end of each of the next three years, respectively. Find the duration of the plan obligations if the interest rate is 10% annually. If the level of interest rates goes down by 50 basis points (one basis point is 0.01%), how much do you expect the pension plan obligation to go up (in percentage terms)?