73. Winning a Lottery Lotto America is a multistate lottery in which 5 red balls from a drum with 52 balls numbered from 1 to 52 and 1 star ball from a drum with 10 balls are selected. For a $1 ticket, players get one chance at winning the grand prize by matching all 6 numbers. What is the probability of selecting the winning numbers on a $1 play? 74. Challenge Problem If 3 six-sided dice are tossed, find the probability that exactly 2 dice have the same reading. 70. The faculty of the mathematics department at Valencia College is composed of 4 women and 9 men. Of the 4 women, 2 are under age 40, and of the 9 men, 3 are under age 40. Find the probability that a randomly selected faculty member is: (a) A woman or under age 40 (b) A man or over age 40 71. Birthday Problem What is the probability that at least 2 people in a group of 12 people have the same birthday? Assume that there are 365 days in a year. 72. Birthday Problem What is the probability that at least 2 people in a group of 35 people have the same birthday? Assume that there are 365 days in a year. Problems 75–84 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for subsequent sections, a final exam, or later courses such as calculus. Retain Your Knowledge 75. To graph ( ) = + − g x x 2 3, shift the graph of ( ) = f x x number units left right / and then number units . up down / 76. Find the rectangular coordinates of the point whose polar coordinates are π ( ) 6, 2 3 . 77. Solve: ( ) + = x log 3 2 5 78. Solve the given system using matrices. + + = − + = + + =− ⎧ ⎨ ⎪⎪ ⎪⎪ ⎩ ⎪⎪ ⎪⎪ x y z x y z x y z 3 2 1 2 2 5 5 3 2 9 79. Evaluate: − − − 7 6 3 8 0 5 6 4 2 80. Simplify: − + 108 147 363 81. José drives 60 miles per hour to his friend’s house and 40 miles per hour on the way back. What is his average speed? 82. Find the 85th term of the sequence … 5, 12, 19, 26, . 83. Find the area bounded by the graphs of = − + = + y x y x 4, 3 5 12 5 , and = − − y x 16 . 2 84. Find the partial fraction decomposition: − + − x x x 7 5 30 8 2 3 Chapter Review Things to Know Counting Formula (p. 912) ( ) ( ) ( ) ( ) ∪ = + − ∩ nAB nA nB nAB Addition Principle of Counting (p. 912) If ∩ = ∅ A B , then ( ) ( ) ( ) ∪ = + n A B n A n B . Multiplication Principle of Counting (p. 914) If a task consists of a sequence of choices in which there are p selections for the first choice, q selections for the second choice, and so on, the task of making these selections can be done in p q ⋅ ⋅ different ways. Permutation (p. 917) An ordered arrangement of r objects chosen from n objects Number of permutations: Distinct, with repetition (p. 917) nr The n objects are distinct (different), and repetition is allowed in the selection of r of them. Number of permutations: Distinct, without repetition (p. 919) P n r n n n r n n r , 1 1 ! ! ( ) ( ) ( ) [ ] ( ) = − ⋅ ⋅ − − = − The n objects are distinct (different), and repetition is not allowed in the selection of r of them, where ≤ r n. Combination (p. 920) An arrangement, without regard to order, of r objects selected from n distinct objects, where ≤ r n Chapter Review 935
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