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Chapter 6: Problem 18
Of 100 clock radios with digital tuners and/or CD players sold recently in a department store, 70 had digital tuners and 90 had CD players. How many radios had both digital tuners and CD players?
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Results of a Department of Education survey of SAT test scores in 22 states showed that 10 states had an average composite SAT score of at least 1000 during the past 3 yr. 15 states had an increase of at least 10 points in the average composite SAT score during the past 3 yr. 8 states had both an average composite SAT score of at least 1000 and an increase in the average composite SAT score of at least 10 points during the past 3 yr. a. How many of the 22 states had composite SAT scores of less than 1000 and showed an increase of at least 10 points over the 3 -yr period? b. How many of the 22 states had composite SAT scores of at least 1000 and did not show an increase of at least 10 points over the 3 -yr period?
Let \(A\) and \(B\) be subsets of a universal set \(U\) and suppose \(n(U)=200, n(A)=100, n(B)=80\), and \(n(A \cap B)=\) 40. Compute: a. \(n\left(A^{c} \cap B\right)\) b. \(n\left(B^{\circ}\right)\) c. \(n\left(A^{e} \cap B^{n}\right)\)
A survey of 100 college students who frequent the reading lounge of a university revealed the following results: 40 read Time. 30 read Newsweek. 25 read U.S. News \& World Report. 15 read Time and Newsweek. 12 read Time and U.S. News \& World Report. 10 read Newsweek and U.S. News \& World Report. 4 read all three magazines. How many of the students surveyed read a. At least one of these magazines? b. Exactly one of these magazines? c. Exactly two of these magazines? d. None of these magazines?
Let \(U=\\{1,2,3,4,5,6,7,8,9,10\\}\) \(A=\\{1,3,5,7,9\\}, B=\\{2,4,6,8,10\\}\), and \(C=\\{1,2,4\) \(5,8,9\\}\). List the elements of each set. a. \(C \cap C^{c}\) b. \((A \cap C)^{c}\) c. \(A \cup(B \cap C)\)
a. How many seven-digit telephone numbers are possible if the first digit must be nonzero? b. How many direct-dialing numbers for calls within the United States and Canada are possible if each number consists of a 1 plus a three-digit area code (the first digit of which must be nonzero) and a number of the type described in part (a)?
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