Survey analysis In a survey of the dining preferences of 110 dormitory students at the end of the spring semester, the following facts were discovered about Adam’s Lunch (AL), Pizza Tower (PT), and the Dining Hall (DH).

4 liked AL but not PT
19 liked AL only
42 liked AL
55 liked PT
29 liked DH
14 liked PT and AL but not DH
24 liked PT and DH

How many liked PT or DH?
a.  37
b.  19
c.  20
d.  18


e. 60

Mathematics

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Draw a Venn diagram to determine whether the argument is valid.Premise: All clowns wear makeup.Premise: Bozo is a clown.Conclusion: Bozo wears makeup.

What will be an ideal response?

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Provide an appropriate response. Identify the correct order of operations.

A. Exponents, multiplications and divisions, parentheses, additions and subtractions B. Additions and subtractions, multiplications and divisions, exponents, parentheses C. Parentheses, multiplications and divisions, exponents, additions and subtractions D. Parentheses, exponents, multiplications and divisions, additions and subtractions

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Use the two-stage method to solve.Find x1 ? 0, x2 ? 0, x3 ? 0 such that  x1 + 2x2 + x3 ? 40 2x1 + x2 + x3 ? 26and z = 4x1 + x2 + 2x3 is maximized.

A. x2 = 20, x1 = 0, x3 = 0, z = 20 B. x3 = 40, x1 = 0, x2 = 0, z = 80 C. x1 = 30, x3 = 15, x2 = 0, z = 135 D. x1 = 40, x2 = 0, x3 = 0, z = 160

Mathematics

Refer to the double-bar graph below which shows the number of male and female athletes at a university over a four-year period. Solve the problem.Find the increase in the number of male athletes from 2002 to 2004.

A. 275 B. 175 C. 150 D. 125

Mathematics