The data in the table below presents the hourly quantity of production for three lines of production processes over the first 4 days in XYZ Company. Answer the questions based on the Excel Output given below. Day Process 1 Process 2 Process 3 1 33 33 28 2 30 35 36 3 28 30 30 4 29 38 34 ANOVA: Single Factor SUMMARY Groups Count Sum Average Variance Process 1 4 120 30 4.66667 Process 2 4 136 34 11.3333 Process 3 4 128 32 13.3333 ANOVA Source of Variation SS df MS F P value Between Groups 32 ? ? ? Within Groups 88 ? ? Total 120 11

a. State the null and alternative hypothesis for single factor ANOVA. (1 mark)

b. State the decision rule (α = 0.05).

c. Calculate the test statistic.

d. Make a decision. (2 marks

Compute the bits number 15, 26, 49, and 61 of the output L1 and R1 of the first round of DES encryption, assuming that the input plaintext block consists of the sequence F0F0F0F0F0F0F0F0, and the key consists of all zeros. Use the S-Box Below

For the given quarterly sales data, a) calculate seasonal indices for each quarter, b) the year 4 annual forecast based on a linear regression trend forecasting method, c) the seasonally adjusted trend based quarterly forecasts for that 4th year, d) the year 4 annual forecast based on the Naive forecasting method, and e) the seasonally adjusted Naive based quarterly forecast for that 4th year.

a) Seasonal indices: Q1   ; Q2   ; Q3  ; Q4  

b) Year 4 forecast, trend based: Year 4  

c) Seasonally adjusted trend forecast, year 4: Year 4 Q1   ; Year 4 Q2   ; Year 4 Q3   ; Year 4 Q5  

d) Year 4 forecast, Naive based: Year 4  

e) Seasonally adjusted Naive forecast, year 4: Year 4 Q1   ; Year 4 Q2   ; Year 4 Q3   ; Year 4 Q5  

1. What is the formula for the indifference curve associated with U = xy3 = 8?

2.Given the utility function U = x 1 3 y, what is the slope of the indifference curve at the point (x, y) = (2, 3)?

3.Question 1 Suppose U = x 3 4 y 1 4 . What is the marginal utility of x? What is the marginal utility of y?

Gatson manufacturing company produces 2 types of tires: Economy tire; Premium tire. The manufacturing time and the profit contribution per tire are given in the following table.

​

Answer the following assuming that the company is interested in maximizing the total profit contribution.

Let E = number of economy tires manufactured

      P = number of premium tires manufactured

1. What is the maximum allowable decrease in the profit for economy tires, before the optimal decision changes, rounded to the closest whole number?

2. What is the shadow price for final inspection, rounded to the closest whole number?

1. For each of the following, write C++ statements that perform the specified task. Assume that unsigned integers are stored in four bytes and that the starting address of the built-in array is at location 1002500 in memory.

1. Declare an unsigned int built-in array values with five elements initialized to the even integers from 2 to 10. Assume that the constant size has been defined as 5.
2. Declare a pointer vPtr that points to an object of type unsigned int.
3. Use a for statement to display the elements of built-in array values using array subscript notation.
4. Write two separate statements that assign the starting address of built-in array values to pointer variable vPtr.
5. Use a for statement to display the elements of built-in array values using pointer/offset notation.
6. Use a for statement to display the elements of built-in array values using pointer/offset notation with the built-in array’s name as the pointer.
7. Use a for statement to display the elements of built-in array values by subscripting the pointer to the built-in array.
8. Refer to the fifth element of values using array subscript notation, pointer/offset notation with the built-in array name’s as the pointer, pointer subscript notation and pointer/offset notation.
9. What address is referenced by vPtr + 3? What value is stored at that location?
10. Assuming that vPtr points to values[4], what address is referenced by vPtr -= 4? What value is stored at that location?

2. Combine the statements in part 1 into one C++ program. Here is a sample output of your program.

On December 31, 2016 Berry Corporation sold some of its product to Flynn Company, accepting a 3%, four-year promissory note having a maturity value of $900,000 (interest payable annually on December 31). Berry Corporation pays 6% for its borrowed funds. Flynn Company, however, pays 8% for its borrowed funds. The product sold is carried on the books of Berry at a manufactured cost of $560,000. Assume Berry uses a perpetual inventory system.

Prepare the journal entries to record the transaction on the books of Berry Corporation at December 31, 2016. (Assume that the effective interest method is used. Use the interest tables below and round to the nearest dollar.)

Make all appropriate entries for 2017 on the books of Berry Corporation.

Make all appropriate entries for 2018 on the books of Berry Corporation.

Table 1

Future Value of 1

Table 2

Present Value of 1

Table 3

Future Value of Ordinary Annuity of 1

Table 4

Present Value of Ordinary Annuity of 1

For each of the following strong base solutions, determine [OH−],[H3O+], pH, and pOH.

1. 6.77×10⁻³ M LiOH,

2. 0.0412 M Ba(OH)2

3. 5.9×10⁻⁴ M KOH

4. 3.0×10⁻⁴ M Ca(OH)2

1) a) From the set {-8, -2/3, 5i, √(-9), √2, 0, 3+3i, -2.35, 7}

i) List the set of          Natural Numbers

ii) List the set of          Integers

iii) List of the set of    Rational Numbers

vi) List the set of         Real Numbers                                               

b) i) -30 ÷ -6 - (-12 + 8) – 4 x 3 =                           ii) 10(-2) - (-6)4

                          (-10) – 6(-3) =       (4, 4 marks)

2) a) 1²/₅ x 2 ¹/₇ ÷ 1⁴/₅ =                                                                          

2. After winning from a lottery were divided in the ratio 2 : 3 : 5,

If the largest amount received was $150,000.xx

How much was:-         i) The smallest amount =

                                   ii) The Total amount of prize money =         (3, 2 marks)

3) a) i) Calculate the simple interest earned if a deposit of $ 900,000 is

                        left for 12 years at an interest rate of 3% .                           

          ii) Calculate the interest rate for a 12 years investment of $600,000 to gained

                         $180,000 interest.                                                                 

2.    Solve

                             2(3x – 2 )= 6x - 2    + 1

                                      3             4                           (6 marks )                                                                         

c) Solve the following pairs of simultaneous equations

                      3x + y = 7   and     2x - 2y = 2        

Q3) Ahmed plays a game where he tosses two balanced 4 sided-dice, each with faces labeled by 1, 2, 3 and 4. He wins 2 points if the sum is 4. He wins 1 point if the sum is greater than 4. He loses k points if the sum is less than 4.

i. Find the probability distribution sum.

ii. Find the value of k which achieves the fairness of game. (i.e. The fairness is achieved if the game is not biased neither to loss or win)