A survey of 93 college students was taken to determine the musical styles they liked. Of those, 36 students listened to rock, 34 to classical, and 43 to jazz. Also, 23 students listened to rock and jazz, 15 to rock and classical, and 22 to classical and jazz. Finally, 13 students listened to all three musical styles. Construct a Venn diagram and determine the cardinality for each region. How many students listened to classical and jazz, but not rock?

area = length x width

length = 2 x width

32 = 2 x width x width

32 = 2 x width^2

36 = width ^2  

width = 6

length = 12

area is 32

perimeter = 2 x 12 + 2 x 6 = 24 + 12 = 36

step-by-step explanation:

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step-by-step explanation:

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.

it is contrapositive

i could not see the question too well so check yourself again too . this is because i want you to get it correct.