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In a recent survey of 100 women, the following information was gathered.

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42 use shampoo A.54 use shampoo B.30 use shampoo C.12 use shampoos A and B.20 use shampoos A and C.5 use shampoos B and C.4 use all three.

Use the figure to answer the question in the problem.

How many are using shampoo A only (Region I)?1[removed]
[removed][removed] women

     4.             Question PartPoints1–/0.36Total–/0.36A poll was taken of 100 students at a commuter campus to find out how they got to campus. The results are below. How many are not using any of the three?33 said they drove alone.31 rode in a carpool.31 rode public transportation.5 used both carpools and public transportation.8 used both a carpool and sometimes their own cars.6 used buses as well as their own cars.4 used all three methods.1[removed][removed][removed]students    5.             Question PartPoints12345678–/0.36–/0.36–/0.36–/0.36–/0.36–/0.36–/0.36–/0.36Total–/2.88Give the numbers of elements in the regions marked I, II, III, IV, V, VI, VII, VIII in the figure.|U| = 230, |A| = 30, |B| = 12, |C| = 20 |A∩B| = 2, |A∩C| = 3, |B∩C| = 3, |A∩B∩C| = 1| I |=1[removed][removed][removed]| II |=2[removed][removed][removed]| III |=3[removed][removed][removed]| IV |=4[removed][removed][removed]| V |=5[removed][removed][removed]| VI |=6[removed][removed][removed]| VII |=7[removed][removed][removed]| VIII |=8[removed][removed][removed] 6. Evaluate the expression.[removed](11/4)(6/5)(3/1) 7.A club consists of 16 men and 19 women. In how many ways can they choose a president, vice president, treasurer, and secretary, along with an advisory committee of six people? (Round the answer to five decimal places.)1[removed][removed] 1011 ways8.

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