Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

13th Edition

ISBN: 9780321869838

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen

Publisher: PEARSON

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Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known …

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosi…

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the prob…

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Textbook Question

Chapter A.4, Problem 36E

In Problems 35–42, imagine that the indicated “solutions” were given to you by a student whom you were tutoring in this class.

(A) Is the solution correct? If the solution is incorrect, explain what is wrong and how it can be corrected.

(B) Show a correct solution for each incorrect solution.

36. x 2 − 3 x − 3 x − 4 = x 2 − 3 x x = x − 3

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Chapter A.4, Problem 35E

Chapter A.4, Problem 37E

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1. 2. Show that the following are not logically equivalent by finding a counterexample: (p^q) →r and (db) V (d←d) Show that the following is not a contradiction by finding a counterexample: (pV-q) AqA (pv¬q Vr) 3. Here is a purported proof that (pq) ^ (q → p) = F: (db) v (bd) = (db) v (bd) =(qVp) A (g→p) = (¬¬q V ¬p) ^ (q→ p) (db) V (db) = =¬(a→p)^(a→p) = (gp) ^¬(a → p) =F (a) Show that (pq) ^ (q→p) and F are not logically equivalent by finding a counterex- ample. (b) Identify the error(s) in this proof and justify why they are errors. Justify the other steps with their corresponding laws of propositional logic.

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Chapter A.4 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

Ch. A.4 - Reduce each fraction to lowest terms....Ch. A.4 - Reduce each rational expression to lowest terms....Ch. A.4 - Prob. 3MP Ch. A.4 - Combine into a single fraction and reduce to...Ch. A.4 - Express as a simple fraction reduced to lowest...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - Prob. 3E Ch. A.4 - In Problems 122, perform the indicated operations...Ch. A.4 - Prob. 5E

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Solution Summary: The author explains that the given solution is incorrect, since it is impossible to cancel out 4 from both numerator and denominator. The solution cannot be reduced to the form x-3.

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Chapter A.4 Solutions