1.On June 30, 2021, the Johnstone Company purchased equipment from Genovese Corp. Johnstone agreed to pay Genovese $20,000 on the purchase date and the balance in five annual installments of $8,000 on each June 30 beginning June 30, 2022. Assuming that an interest rate of 10% properly reflects the time value of money in this situation, at what amount should Johnstone value the equipment?

2. Johnstone needs to accumulate sufficient funds to pay a $500,000 debt that comes due on December 31, 2026. The company will accumulate the funds by making five equal annual deposits to an account paying 9% interest compounded annually. Determine the required annual deposit if the first deposit is made on December 31, 2021.

3. On January 1, 2021, Johnstone leased an office building. Terms of the lease require Johnstone to make 20 annual lease payments of $130,000 beginning on January 1, 2021. A 10% interest rate is implicit in the lease agreement. At what amount should Johnstone record the lease liability on January 1, 2021, before any lease payments are made?

1. Assume that you held a Treasury note that makes coupon payments on May 15 and November 15.   The number of days between each coupon payment is 184.  Suppose you sold the bond on June 27, 2016.  If the number of days between May 15 and June 27 is 43, the bond carried a coupon rate of 3.875% and matures as of May 15, 2026 ($1,000 par value),

a) What would have been the settlement (dirty) price on June 27, 2016 if the bond was priced to yield 4.0369%?  

b) What was the accrued interest?  

c) What was the market price (quoted on the Wall Street Journal)?

Determine whether the lines ?1:?=6+3?,?=6+2?,?=13+4? and ?2:?=−11+4??=−8+4??=−13+7? intersect, are skew, or are parallel. If they intersect, determine the point of intersection; if not leave the remaining answer blanks empty.

Consider the quarterly electricity production for years 1-4:

Year 1      2         3            4
Q1   99   120     139        160
Q2   88   108     127        148
Q3   93   111     131        150
Q4 111   130     152        170

(a) Using a classical additive decomposition, calculate the seasonal component.
(b) Explain how you handled the end points.
(c)  Estimate the trend using a centered moving average.

There are 3 coins which when flipped come up heads, respectively, with probabilities 1/4, 1/2, 3/4. One of these coins is randomly chosen and continually flipped.

1. (a) Find the expected number of flips until the first head.

2. (b) Find the mean number of heads in the first 8 flips.

Let X = {1, 2, 3, 4, 5, 6} and let ∼ be given by {(1, 1),(2, 2),(3, 3),(4, 4),(5, 5),(6, 6),(1, 3),(1, 5),(2, 4),(3, 1),(3, 5), (4, 2),(5, 1),(5, 3)}.

Is ∼ an equivalence relation? If yes, write down X/ ∼ .

Question 1

The probability that a teacher will see 0, 1, 2, 3, or 4 students

(a)        What is the probability that the teacher see 3 students?                                              

(b)       What is the probability that the number of students the teacher will see is between 1 and 3 inclusive?         

(c)        What is the expected number of students that the teacher will see?

(d)       What is the standard deviation?

Question 2

The probability that a house in an urban area will be burglarized is 5%. A sample of 50 houses is randomly selected to determine the number of houses that were burglarized.

(a)        Define the variable of interest, X.                                                      

(b)       What are the possible values of X?                                                    

(c)        What is the expected number of burglarized houses?                                    

(d)       What is the standard deviation of the number of burglarized houses?                      

(e)        What is the probability that none of the houses in the sample was burglarized?

Question 3

A sales firm receives an average of three calls per hour on its toll-free number. Suppose you were asked to find the probability that it will receive at least three calls, in a given hour:

(a) (i)   which distribution does this scenario fit and why?                           

    (ii) define the variable of interest, X.                                                       

    (iii) what are the possible values of X?                                                     

(b)       What is the probability that in a given hour it will receive at least three calls?

1. What will print?
int[][] numbers = { { 1, 2, 3, 4 },{ 5, 6, 7, 8 },{ 9, 10, 11, 12 } };
System.out.println(numbers[1][3]);

a) 13

b) 4

c) 8

d) 12

2. With what value does currYear = yearsArr[2] assign currYear?
int[ ] yearsArr = new int[4];
yearsArr[0] = 1999;
yearsArr[1] = 2012;
yearsArr[2] = 2025;         

a) 4

b) 1999

c) 2012

d) 2025

3. What will print?
String [][] names = { { "Elliot", "Darlene", "Angela", "Tyrell" },
{ "Joanna", "Phillip", "Tomero", "Trenton" },
{ "Mobley", "Whiterose", "Cisco", "Leon", "Mr. Robot" } };
System.out.println(names[2][4]);

a) Elliot

b) Angela

c) Joanna

d) Mr. Robot

4. What will print?
int[][] myNumbers = { {1, 2, 3, 4}, {5, 6, 7, 8}, {1, 2, 3, 4} };
int x = myNumbers[2][2];
System.out.println(x);

a) 5

b) 3

c) 7

d) 8

5. What will print?
int[][] myNumbers = { {1, 2, 3, 4}, {5, 6, 7, 8} };
int x = myNumbers[1][2];
System.out.println(x);

a) 5

b) 3

c) 7

d) 8

1.What will the result of this form be? (cadr ‘(1 2 3 4 5 6))

a. '(1 2 3 4 5 6)

b. 2

c. '(2 3 4 5 6)

d. 1

.

2.How does Prolog try to resolve our Queries?

a.The programmer specifies the algorithmic approach, performance is all in the hands of how clever the programmer writes their algorithms.

b.The language applies some AI to our query and precludes obviously false information.

c.Row by agonizing row. There is nothing particularly clever about the solve, it just brute forces its way through the data looking for resolutions.

Create a square, almost symmetric 4 X 4 matrix B with values 1, 2, 3 and 4 on the diagonal. Let values off diagonal be between 0.01 and 0.2. Almost symmetric matrix is not a scientific term. It just means that most of the off diagonal terms on transpose positions are close in value:

1. Determine matrix BINV which is an inverse of matrix B;

2. Demonstrate that the matrix multiplied by its inverse produces a unit matrix. Unit

matrix has all elements on the diagonal equal to 1 and all other equal to 0;

3. Find eigen values of Matrix B and matrix BINV;

4. Find eigen values of matrix t(B) where t(0 is transpose function.

Please R studio.