Explanation Definition: A permutation is an ordering of distinct objects. If we select r different objects from a set of n objects, and arrange them in order, this is called a permutation of n objects taken r at a time. The number of permutations of n objects taken r at a time is denoted by P ( n , r ) . Formula for computing P ( n , r ) = n ! ( n − r ) ! Calculation: Given, The editorial staff of Oprah’s O Magazine is reviewing 17 articles expect that in addition to choosing the stories, the editorial staff must also decide in order the stories will appear. For get the number of ways we use the permutation P ( 17 , 8 ) Using the formula for permutation, P ( n , r ) = n ! ( n − r ) ! P ( 17 , 8 ) = 17 ! ( 17 − 8 ) !

MYLAB MATH WITH PEARSON ETEXT FOR MATHEM

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ISBN: 9780136470137

Author: Pirnot

Publisher: PEARSON

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Chapter 12.3, Problem 47E

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The number of years would it take to write all possible lists of eight articles.

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Chapter 12.3, Problem 46E

Chapter 12.3, Problem 48E

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Proof: LN⎯⎯⎯⎯⎯LN¯ divides quadrilateral KLMN into two triangles. The sum of the angle measures in each triangle is ˚, so the sum of the angle measures for both triangles is ˚. So, m∠K+m∠L+m∠M+m∠N=m∠K+m∠L+m∠M+m∠N=˚. Because ∠K≅∠M∠K≅∠M and ∠N≅∠L, m∠K=m∠M∠N≅∠L, m∠K=m∠M and m∠N=m∠Lm∠N=m∠L by the definition of congruence. By the Substitution Property of Equality, m∠K+m∠L+m∠K+m∠L=m∠K+m∠L+m∠K+m∠L=°,°, so (m∠K)+ m∠K+ (m∠L)= m∠L= ˚. Dividing each side by gives m∠K+m∠L=m∠K+m∠L= °.°. The consecutive angles are supplementary, so KN⎯⎯⎯⎯⎯⎯∥LM⎯⎯⎯⎯⎯⎯KN¯∥LM¯ by the Converse of the Consecutive Interior Angles Theorem. Likewise, (m∠K)+m∠K+ (m∠N)=m∠N= ˚, or m∠K+m∠N=m∠K+m∠N= ˚. So these consecutive angles are supplementary and KL⎯⎯⎯⎯⎯∥NM⎯⎯⎯⎯⎯⎯KL¯∥NM¯ by the Converse of the Consecutive Interior Angles Theorem. Opposite sides are parallel, so quadrilateral KLMN is a parallelogram.

Chapter 12 Solutions

MYLAB MATH WITH PEARSON ETEXT FOR MATHEM

Ch. 12.1 - In Exercises 14, you are selecting from the set...Ch. 12.1 - In Exercises 14, you are selecting from the set...Ch. 12.1 - In Exercises 14, you are selecting from the set...Ch. 12.1 - In Exercises 14, you are selecting from the set...Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E Ch. 12.1 - How many different two-digit numbers can you form...Ch. 12.1 - How many different two-digit numbers can you form...

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The number of years would it take to write all possible lists of eight articles.

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The number of years would it take to write all possible lists of eight articles.