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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

25-42 ■ Probability These exercises involve probability.

Divisors of a Number Let =   3 , 600 , 000 . (Note that =   2 7 3 2 5 5 .)

(a) How many divisors does N have?

(b) How many even divisors does N have?

(c) How many divisors of N are multiples of 6 ?

(d) What is the probability that a randomly chosen divisor of N is even?

To determine

(a)

To find:

The number of divisors of N.

Explanation

Given:

The number is

N=3600000=(27)(32)(55)

Approach:

The total number of divisors of a number N=Aa×Bb×Cc× is given by,

d=(a+1)(b+1)(c+1) ..

To determine

(b)

To find:

The number of even divisors of N.

To determine

(c)

To find:

The number of divisors N that are multiples of 6.

To determine

(d)

To find:

The probability that a randomly chosen divisor of N is even.

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Chapter 14 Solutions

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