The office of admissions and records of a large western university released the accompanying information concerning the contemplated majors of its freshman class. (round your answers to three decimal places.) major % of freshmen choosing this major % of major that is female % of major that is male business 23 39 61 humanities 10 58 42 education 8 63 37 social science 5 60 40 natural sciences 10 56 44 other 44 48 52 (a) what is the probability that a student selected at random from the freshman class is a female? (b) what is the probability that a business student selected at random from the freshman class is a male? (c) what is the probability that a female student selected at random from the freshman class is majoring in business?

a) 0.4953; b) 0.61; c) 0.181

Step-by-step explanation:

For part a,

We multiply the percentage of students in each major by the percentage of them that are female.  We then add these together:

0.23(0.39)+0.10(0.58)+0.08(0.63)+0.05(0.60)+0.10(0.56)+0.44(0.48) = 0.4953.

For part b,

We are looking strictly at the percentage of business students that are males.  Out of the business majors, 61% are male; this makes the answer for part b 0.61.

For part c,

The percentage of female students is 0.4953.  Out of these, 0.23(0.39) = 0.0897 are female.  This gives us

0.0897/0.4953 = 0.181.

c

step-by-step explanation:

there is vertical asymptote at x = 2 and x = 0

vertical asymptote occurs at the points where the denominator is 0. so we can say that

x = 2 occurs when there is a factor (x-2) in the denominator, and

x = 0 occurs when there is a factor "x" in the denominator

thus, the denominator of the equation would have "x * (x-2)", this is option c only. that's the correct answer.