Contemporary Mathematics for Business & Consumers

8th Edition

ISBN: 9781305585447

Author: Robert Brechner, Geroge Bergeman

Publisher: Cengage Learning

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…

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Textbook Question

Chapter 6.II, Problem 13TIE

Solve the following for the base. Round to hundredths or the nearest cent when necessary.

a. In a machine shop. 35% of the motor repairs are for broken shafts. If 126 motors had broken shafts last month, how many total motors were repaired?

b. At Office Mart. 75% of the copy paper sold is letter size. If 3.420 reams of letter size were sold, how many total reams of copy paper were sold?

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Chapter 6.II, Problem 12TIE

Chapter 6.II, Problem 1RE

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6. Let, for p = (0, 1), and xe R. X be a random variable defined as follows: P(X=-x) = P(X = x)=p. P(X=0)= 1-2p. Show that there is equality in Chebyshev's inequality for X. This means that Chebyshev's inequality, in spite of being rather crude, cannot be improved without additional assumptions.

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8. Recall, from Sect. 2.16.4, the likelihood ratio statistic, Ln, which was defined as a product of independent, identically distributed random variables with mean 1 (under the so-called null hypothesis), and the, sometimes more convenient, log-likelihood, log L, which was a sum of independent, identically distributed random variables, which, however, do not have mean log 1 = 0. (a) Verify that the last claim is correct, by proving the more general statement, namely that, if Y is a non-negative random variable with finite mean, then E(log Y) log(EY). (b) Prove that, in fact, there is strict inequality: E(log Y) < log(EY), unless Y is degenerate. (c) Review the proof of Jensen's inequality, Theorem 5.1. Generalize with a glimpse on (b).

Chapter 6 Solutions

Contemporary Mathematics for Business & Consumers

Ch. 6.I - Convert the following percents to decimals. a. 27%...Ch. 6.I - Convert the following decimals or whole numbers to...Ch. 6.I - Prob. 3TIE Ch. 6.I - Prob. 4TIE Ch. 6.I - Convert the following percents to decimals. 1. Ch. 6.I - Prob. 2RE Ch. 6.I - Prob. 3RE Ch. 6.I - Prob. 4RE Ch. 6.I - Prob. 5RE Ch. 6.I - Prob. 6RE

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Solution Summary: The author explains how to calculate the total number of motors that were repaired last month.

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