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The University of Phoenix Math 212 Finite Mathematics – Online                    Final Exam
Note: For any consideration of partial credit all work must be typed within the space provided – under
each problem (YOU CAN HIT ENTER TO CREATE MORE ROOM) and the answer spaces completely filled

   I.   Linear Equations and System of Linear Equations (Chapter 1 & 2)
            1. Suppose that the national demand and price for a certain type of energy-efficient
                exhaust fan are related by p = D(q) = 495 - q, where p is the price (in dollars) and q is
                the demand (in thousands).

           a.   If the demand is for 80,000 exhaust fans, then the price equals $_______________

           b. At a price of $141, the demand is for ____________thousand exhaust fans.

           2. Find an equation of the line containing the given pair of points (2,5) and (6,6).

                Y = _________________________
                (Use integers or fractions for any number in the expression)

           3. Kara’s Custom Tees experienced fixed costs of $400 and variable cost of $2 a shirt.
              Write an equation that can be used to determine the total expenses encountered by
              Kara’s Custom Tees and graph the equation.

                Y = _________________________

                The GRAPH: Note let y  100’s (1 = 100)
4. The Dispatch Tool Works spend $14,000 to produce 180 parts, achieving a marginal cost
   of $64. Find the linear cost function.

    C(x) = ________________________

                                                                                        D(ft)               T(sec)
5. The Kostas Engine Company manufactures several
                                                                                        2                   3.15
   different sizes of airplane propellers. The relationship
                                                                                        3                   3.86
   between the diameter of a propeller D and the time T for
                                                                                        4                   4.60
   100 complete revolutions is shown in the table.
                                                                                        5                   5.30
   a. What is the equation for the least squares line:                                  6                   6.07
                                                                                        7                   6.79
                                                                                        8                   7.69
         Y = ____________________________________

    b. What is the coefficient of correlation:_________

6. Solve the following system of equations by using the Inverse of the coefficient matrix Q.
   (AX = B).

              - 5x – y + 7z = - 7
                    2y + 6z = - 16
              4x + 4y + 7z = - 26                                    (x, y, z) =____________________

7. Find the production matrix for the following input-output and demand matrices using
   the open model.
       0.1 0.2         4
    A          and D  6 .
       0.55 0.4          
                                               The production matrix is:

    (Round the final answer to the nearest hundredth as needed. Round all intermediate values to four decimal places as

8. Solve the following system by the Method of Elimination:

              2x – 4y = 40
              5x + 3y = -17                               (x, y) = ___________________________
       9. Solve the following system by Graphing:( Attach the graph).

                   X + y = 10
                   X–y=2                          (x, y) = ___________________________

II. Linear Programming (Chapter 4)
        10. Use the simplex method to solve the linear programming problem.
            Maximize: z = 7x + 3y + z
            Subject to: x + 4y + 10z ≤ 110
                        x + 2y + 11z ≤ 247
            with x ≥ 0, y ≥ 0, z ≥ 0.
                                           Maximum z=_______with (x,y,z) = _________________

       11. Find the transpose of the matrix:

               1 2 3
           A  9 5 3
                                                                      AT =
                2 8 5
                     

       12. Use the Graphing method to solve the linear programming problem (Supply Graph here
           Minimize: z = 5x + y
           Subject to: 4x + 4y ≥ 16
                       4x + y ≥ 19
           With x ≥ 0 and y ≥ 0

                                           Minimize z=_______with (x,y) = _________________
13. Convert the following to a maximization problem.
    Minimize: w = 2x + 3y + 5z
    Subject to:     x+y+z≥5
                    2x + y + 3z ≥ 6

    With    x ≥ 0, y ≥ 0, and z ≥0.

    State you Maximization Problem here:

    And the solution for Minimized w =_______with (x,y,z) = _________________

14. Jayanta is raising money for the homeless, and discovers each church group requires 2
    hr of letter writing and 1 hr of follow-up calls, which each labor union needs 2hr of letter
    writing and 3 hr of follow-up. She can raise $150 from each church group and $175
    from each union. She has a maximum of 12 hours of letter writing and 16 hours of
    follow-up available each month. Determine the most profitable mixture of groups she
    should contact and the most money she can raise in a month.
a. Set up the linear programming here:

b. She should contact _________church group(s) and ________labor union(s), to obtain

    $_______________ in donations.
       15. One gram of soybean meal provides at least 2.5 units of vitamins and 5 calories. One
           gram of meat byproducts provides at least 4.5 units of vitamins and 3 calories. One
           gram of grain provides at least 5 units of vitamins and 10 calories. If a gram of soybean
           meal cost 7 cents, a gram of meat byproducts 8 cents, and a gram of grain 9 cents, what
           mixture of these three ingredients will provide at least 54 units of vitamins and 60
           calories preserving at minimum cost? What will be the minimum cost?
               a. Set up the linear programming here:

       b. What is the mixture:_________________________________________

            and what is the minimum cost $_______________ .

III. Finance (Chapter 5)
         16. Fritz Benjamin buys a car costing $10,900. He agrees to make payments at the end of
             each monthly period for 7 years. He pays 9.6% interest, compounded monthly. What is
             the amount of each payment? Find the total amount of interest Fritz will pay.

       a.   Fritz’s monthly Payment is $___________________(round to the nearest cent.)

       b. Fritz will pay a total of $______________in interest (round to the nearest cent).

       17. A family’s plan to retire in 15 years and expect to need $200,000. Determine how much
           they must invest today at 6.1% compounded semiannually to accomplish their goal.

            The Family should invest $____________________(round to the nearest $100)
        18. John plans to invest $3000 at 5% interest over 6 years compounded quarterly.

            a. The total amount after 6 years will be $________________

            b. The total amount of interest earned is $_______________

        19. Find the payment necessary to amortize a 8% loan of $2400 compounded quarterly,
            with 12 quarterly payments.

            The payment size is $_______________

        20. Find the present value of an ordinary annuity which has payments of $1800 per year for
            14 years at 8% compounded annually.

            The present value is $__________________

IV. Probability & Statistics (Chapter 8 & 9)
       21. Mixed in a drawer are 6 blue socks, 4 white socks, and 2 gray socks. You pull out one at
           a time without looking.

                a. The probability of getting 2 white socks is _______________ (type your answer
                   as a fraction in lowest terms.)

                b. The probability of getting 2 socks of the same color is _____________(type your
                   answer as a fraction in lowest terms.)

        22. A health inspector must visit 3 of 15 restaurants on Monday. In how many ways can she
            pick a first, second, and third restaurant to visit?

            There are ___________ways.
23. Assume the probability that a telephone in any given telephone booth is defective is 0.2.
    Determine the probability that if 8 phone booths are examined, the number of defective
    phones is exactly 3.

    The probability is _____________(round answer to 4 decimal places.)

24. Pizza House offers 4 different salads, 5 different kinds of pizza, and 4 different desserts.
    How many different three course meals can be ordered?

    _____________different three course meals can be ordered.

25. Assume the probability is ½ that a child born is a girl. If a family has three children, what
    is the probability that they have:

        a.   Exactly one girl:_________________

        b. At most two boys:_______________
26. Find the range, median, mean and the standard deviation of the following set of data.

                                 163, 167, 158, 169, 157, 176, 172

    Range:_________ Median:_________ Mean:_________ Standard Deviation:________

27. The figure below contains the salaries of employees at the Raggs, Ltd. Clothing Store.

              Number              Type                Salary
                  1               Owner              $26,900
                  5            Salesperson           $18,100
                  3             Secretary            $14,100
                  1             Custodian            $13,000
    What is the mean salary, median salary, mode salary and what can be said about its

    Mean Salary:____________ Median Salary:____________Mode Salary:_____________

    The Distribution is:
28. What is the percentage of area under the normal curve between the mean and – 0.40
    standard deviations from the mean?

     The percentage is _________% (round to the nearest percent)

29. In a certain distribution, the mean is 50 with a standard deviation of 4. Use the
    Empirical Rule to tell the probability that a number lies between 42 and 58.

     The probability a number lies in between 42 and 58 is _____________ (round to the
     nearest thousand.)

30. An assembly-line machine turns out washers with the following thickness (in mm).

     1.26   2.05    1.79    1.86    1.38    1.55     1.33    1.85
     1.54   1.55    1.36    1.27    1.33    1.36     1.88    1.46

a.   The mean of the thickness is ___________mm. (round to 4 decimal places)

b. The standard deviation is _____________mm (round to 4 decimal places)

c. What is the probability that if I randomly chose a washer that it would be at least


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