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# Finite Math

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Math 212 Finite Mathematics

Show all work and any explanations:

1) An unprepared student takes a three-question, true/false quiz in which he guesses the
answers to all three questions, so each answer is equally likely to be correct or wrong.

a) (4) The student gets three answers wrong.

b) (4) The student gets exactly two answers correct.

c) (4) The student gets only the first answer correct

2) (4) An automobile manufacturer produces 7 models, each available in 6 different exterior
colors, with 4 different upholstery fabrics and 5 interior colors. How many varieties of
automobile are available?

3. (8) Construct a frequency distribution and construct a histogram for the following data
Use seven intervals, starting with 30-39.

79 71 78 87 69 50 63 51
60 46 65 65 56 88 94 56
74 63 87 62 84 76 82 67
59 66 57 81 93 93 54 88
55 69 78 63 63 48 89 81
98 42 91 66 60 70 64 70
61 75 82 65 68 39 77 81
67 62 73 49 51 76 94 54
83 71 94 45 73 95 72 66
71 77 48 51 54 57 69 87

4. The number of unemployed workers (in millions) from 1992 to 2001 are recorded below.
9.61 8.94 8.00 7.40 7.24 6.74 6.21 5.88 5.66 6.74

a) (8) Compute the median and mode number of unemployed workers

b) (2) Is there a mode?

c) (6) Compute the standard deviation of the number of unemployed works.

5. (4) Below is the simplex tableau for a linear programming problem.
x y s1 s2 z C
5 3 1 0 0 34
3 5 0 1 0 30
-2 -14 0 0 1 0
The pivot column is the y column and the pivot element is five in the middle row. Use this information to make the entry 0 in the first row, second column.

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In the textile industry, filament and yarn sizes are reported in denier which is defined as the mass in grams of a length of 9000 meters. If a synthetic fiber has an average specific gravity of 1.32 and a filament of this material has a denier of 5.0, what is the mass per unit length in pounds-mass per yard? What is the cross sectional area of this fiber in square inches? The specific gravity is defined as specific gravity = density/density of water.

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