Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
13th Edition
ISBN: 9780321945525
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
Publisher: PEARSON
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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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Chapter 9.2, Problem 58E

Insurance. Repeat Problems 61 if 40 % of preferred customers are moved to the satisfactory category each year, and all other information remains the same.

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Q.1) Classify the following statements as a true or false statements: Q a. A simple ring R is simple as a right R-module. b. Every ideal of ZZ is small ideal. very den to is lovaginz c. A nontrivial direct summand of a module cannot be large or small submodule. d. The sum of a finite family of small submodules of a module M is small in M. e. The direct product of a finite family of projective modules is projective f. The sum of a finite family of large submodules of a module M is large in M. g. Zz contains no minimal submodules. h. Qz has no minimal and no maximal submodules. i. Every divisible Z-module is injective. j. Every projective module is a free module. a homomorp cements Q.4) Give an example and explain your claim in each case: a) A module M which has a largest proper submodule, is directly indecomposable. b) A free subset of a module. c) A finite free module. d) A module contains no a direct summand. e) A short split exact sequence of modules.
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Chapter 9 Solutions

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

Ch. 9.1 - (A) Refer to the transition diagram in Figure 1....Ch. 9.1 - Refer to Example 4. States D and G are referred to...Ch. 9.1 - An insurance company classifies drivers as...Ch. 9.1 - Find P4 and use it to find S4 for AAP=AA.8.2.3.7...Ch. 9.1 - Use P8 and a graphing calculator to find S8 for P...Ch. 9.1 - Refer to Example 4. At the end of each year the...Ch. 9.1 - In Problems 1-8, find the matrix product, if it is...Ch. 9.1 - In Problems 1-8, find the matrix product, if it is...Ch. 9.1 - In Problems 1-8, find the matrix product, if it is...Ch. 9.1 - In Problems 1-8, find the matrix product, if it is...
Ch. 9.1 - In Problems 1-8, find the matrix product, if it is...Ch. 9.1 - In Problems 1-8, find the matrix product, if it is...Ch. 9.1 - In Problems 1-8, find the matrix product, if it is...Ch. 9.1 - In Problems 1-8, find the matrix product, if it is...Ch. 9.1 - Prob. 9ECh. 9.1 - Prob. 10ECh. 9.1 - Prob. 11ECh. 9.1 - In Problems 9-12, find S1 for the indicated...Ch. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - In problems 17-20, use the transition diagram to...Ch. 9.1 - Prob. 21ECh. 9.1 - Prob. 22ECh. 9.1 - Prob. 23ECh. 9.1 - Prob. 24ECh. 9.1 - In Problems 37-44, could the given matrix be the...Ch. 9.1 - In Problems 37-44, could the given matrix be the...Ch. 9.1 - In Problems 37-44, could the given matrix be the...Ch. 9.1 - In Problems 37-44, could the given matrix be the...Ch. 9.1 - In Problems 37-44, could the given matrix be the...Ch. 9.1 - Prob. 30ECh. 9.1 - In Problems 37-44, could the given matrix be the...Ch. 9.1 - In Problems 37-44, could the given matrix be the...Ch. 9.1 - In Problems 45-50, is there a unique way of...Ch. 9.1 - In Problems 45-50, is there a unique way of...Ch. 9.1 - In Problems 45-50, is there a unique way of...Ch. 9.1 - In Problems 45-50, is there a unique way of...Ch. 9.1 - In Problems 45-50, is there a unique way of...Ch. 9.1 - In Problems 45-50, is there a unique way of...Ch. 9.1 - In Problems 51-56, are there unique values of a,b,...Ch. 9.1 - In Problems 51-56, are there unique values of a,b,...Ch. 9.1 - In Problems 51-56, are there unique values of a,b,...Ch. 9.1 - Prob. 42ECh. 9.1 - In Problems 51-56, are there unique values of a,b,...Ch. 9.1 - Prob. 44ECh. 9.1 - In Problems 57-60, use the given information to...Ch. 9.1 - A Markov chain has two states, A and B. The...Ch. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Problems 61-70 refer to the following transition...Ch. 9.1 - Problems 61-70 refer to the following transition...Ch. 9.1 - Problems 61-70 refer to the following transition...Ch. 9.1 - Problems 61-70 refer to the following transition...Ch. 9.1 - Prob. 53ECh. 9.1 - Problems 61-70 refer to the following transition...Ch. 9.1 - Prob. 55ECh. 9.1 - Prob. 56ECh. 9.1 - Problems 61-70 refer to the following transition...Ch. 9.1 - Problems 61-70 refer to the following transition...Ch. 9.1 - In Problems 71-74, given the transition matrix P...Ch. 9.1 - In Problems 71-74, given the transition matrix P...Ch. 9.1 - In Problems 71-74, given the transition matrix P...Ch. 9.1 - In Problems 71-74, given the transition matrix P...Ch. 9.1 - A Markov chain with two states has transition...Ch. 9.1 - Repeat Problem 75 if the initial-state matrix is...Ch. 9.1 - Prob. 65ECh. 9.1 - Prob. 66ECh. 9.1 - Prob. 67ECh. 9.1 - Prob. 68ECh. 9.1 - Prob. 69ECh. 9.1 - Prob. 70ECh. 9.1 - Given the transition matrix...Ch. 9.1 - Prob. 72ECh. 9.1 - Show that if P=a1a1bb is probability matrix, then...Ch. 9.1 - Show that if P=a1a1bbandS=c1c are probability...Ch. 9.1 - Use a graphing calculator and the formula Sk =...Ch. 9.1 - Use a graphing calculator and the formula Sk=S0Pk...Ch. 9.1 - Use a graphing calculator and the formula Sk=S0Pk...Ch. 9.1 - Use a graphing calculator and the formula Sk=S0Pk...Ch. 9.1 - Scheduling. An outdoor restaurant in a summer...Ch. 9.1 - Scheduling. Repeat Problem 85 if the probability...Ch. 9.1 - Advertising. A television advertising campaign is...Ch. 9.1 - Car rental. A car rental agency has facilities at...Ch. 9.1 - Homeowner's insurance. In a given city, the market...Ch. 9.1 - Service contracts. A small community has two...Ch. 9.1 - Travel agent training. A chain of travel agencies...Ch. 9.1 - Welder training. All welders in a factory begin as...Ch. 9.1 - Health plans. A midwestern university offers its...Ch. 9.1 - Dental insurance. Refer to Problem 93. During the...Ch. 9.1 - Housing trends. The 2000 census reported that 41.9...Ch. 9.1 - Housing trends. The 2000 census reported that 66.4...Ch. 9.2 - (A) Suppose that the toothpaste company started...Ch. 9.2 - Which of the following matrices are regular? (A)...Ch. 9.2 - The transition matrix for a Markov chain is...Ch. 9.2 - Refer to Matched Problem 1 in Section 9.1, where...Ch. 9.2 - A mail-order company classifies its customers as...Ch. 9.2 - Repeat Example 5 for P=.3.6.1.2.3.5.1.2.7Ch. 9.2 - In Problems 1-8. without using a calculator, find...Ch. 9.2 - In Problems 1-8. without using a calculator, find...Ch. 9.2 - In Problems 1-8. without using a calculator, find...Ch. 9.2 - In Problems 1-8. without using a calculator, find...Ch. 9.2 - In Problems 1-8. without using a calculator, find...Ch. 9.2 - In Problems 1-8. without using a calculator, find...Ch. 9.2 - In Problems 1-8. without using a calculator, find...Ch. 9.2 - In Problems 1-8. without using a calculator, find...Ch. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Prob. 16ECh. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - In Problems 9-22, could the given matrix be the...Ch. 9.2 - For each transition matrix P in Problems 23-30,...Ch. 9.2 - For each transition matrix P in Problems 23-30,...Ch. 9.2 - For each transition matrix P in Problems 23-30,...Ch. 9.2 - For each transition matrix P in Problems 23-30,...Ch. 9.2 - For each transition matrix P in Problems 23-30,...Ch. 9.2 - For each transition matrix P in Problems 23-30,...Ch. 9.2 - For each transition matrix P in Problems 23-30,...Ch. 9.2 - For each transition matrix P in Problems 23-30,...Ch. 9.2 - In Problems 35-40, discuss the validity of each...Ch. 9.2 - In Problems 35-40, discuss the validity of each...Ch. 9.2 - In Problems 35-40, discuss the validity of each...Ch. 9.2 - In Problems 35-40, discuss the validity of each...Ch. 9.2 - In Problems 35-40, discuss the validity of each...Ch. 9.2 - In Problems 35-40, discuss the validity of each...Ch. 9.2 - In Problems 41-44, approximate the stationary...Ch. 9.2 - In Problems 41-44, approximate the stationary...Ch. 9.2 - In Problems 41-44, approximate the stationary...Ch. 9.2 - In Problems 41-44, approximate the stationary'...Ch. 9.2 - A red urn contains 2 red marbles and 3 blue...Ch. 9.2 - Repeat Problem 45 if the red urn contains 5 red...Ch. 9.2 - Given the transition matrix P=0110 A) Discuss the...Ch. 9.2 - Given the transition matrix P=001100010 (A)...Ch. 9.2 - The transition matrix for a Markov chain is...Ch. 9.2 - The transition matrix for a Markov chain is...Ch. 9.2 - Problems 51 and 52 require the use of a graphing...Ch. 9.2 - Problems 51 and 52 require the use of a graphing...Ch. 9.2 - The transition matric for a Markov chain is...Ch. 9.2 - The transition matric for a Markov chain is...Ch. 9.2 - Transportation. Most railroad cars are owned by...Ch. 9.2 - Transportation. The railroad in Problem 55 also...Ch. 9.2 - Labor force. Table 1 gives the percentage of the...Ch. 9.2 - Home ownership. The U.S. Census Bureau published...Ch. 9.2 - Market share. Consumers can choose between three...Ch. 9.2 - Market share. Consumers in a certain area can...Ch. 9.2 - Insurance. An auto insurance company classifies...Ch. 9.2 - Insurance. Repeat Problems 61 if 40 of preferred...Ch. 9.2 - Problems 63 and 64 require the use of a graphing...Ch. 9.2 - Problems 63 and 64 require the use of a graphing...Ch. 9.2 - Genetics. A given plant species has red, pink, or...Ch. 9.2 - Gene mutation. Suppose that a gene in a chromosome...Ch. 9.2 - Rapid transit. A new rapid transit system has just...Ch. 9.2 - Politics: filibuster. The Senate is in the middle...Ch. 9.2 - The population center of the 48 contiguous states...Ch. 9.2 - The population center of the 48 contiguous states...Ch. 9.3 - (A) For the initial-state matrix S0=abc, find the...Ch. 9.3 - Determine whether each statement is true or false....Ch. 9.3 - Identify any absorbing states for the following...Ch. 9.3 - Use a transition diagram to determine whether P is...Ch. 9.3 - Repeat Example 3 if 10 of farmers sell to company...Ch. 9.3 - Repeat Example 4 for the standard form P found in...Ch. 9.3 - Repeat Example 5 for the following transition...Ch. 9.3 - In problems 1-6, identify the absorbing states in...Ch. 9.3 - In Problems 1-6, identify the absorbing states in...Ch. 9.3 - In Problems 1-6, identify the absorbing states in...Ch. 9.3 - In Problems 1-6, identify the absorbing states in...Ch. 9.3 - In Problems 1-6, identify the absorbing states in...Ch. 9.3 - In Problems 1-6, identify the absorbing states in...Ch. 9.3 - In Problems 7-10, identify the absorbing states...Ch. 9.3 - In Problems 7-10, identify the absorbing states...Ch. 9.3 - In Problems 7-10, identify the absorbing states...Ch. 9.3 - In Problems 7-10, identify the absorbing states...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 11-20, could the given matrix be the...Ch. 9.3 - In Problems 21-24.find a standard form for the...Ch. 9.3 - In Problems 21-24.find a standard form for the...Ch. 9.3 - In Problems 21-24.find a standard form for the...Ch. 9.3 - In Problems 21-24.find a standard form for the...Ch. 9.3 - In Problems 25-28, find a standard form for the...Ch. 9.3 - In Problems 25-28, find a standard form for the...Ch. 9.3 - In Problems 25-28, find a standard form for the...Ch. 9.3 - In Problems 25-28, find a standard form for the...Ch. 9.3 - In Problems 29-34, find the limiting matrix for...Ch. 9.3 - In Problems 29-34, find the limiting matrix for...Ch. 9.3 - In Problems 29-34, find the limiting matrix for...Ch. 9.3 - In Problems 29-34, find the limiting matrix for...Ch. 9.3 - In Problems 29-34, find the limiting matrix for...Ch. 9.3 - In Problems 29-34, find the limiting matrix for...Ch. 9.3 - Problems 35-40 refer to the matrices in Problems...Ch. 9.3 - Problems 35-40 refer to the matrices in Problems...Ch. 9.3 - Problems 35-40 refer to the matrices in Problems...Ch. 9.3 - Problems 35-40 refer to the matrices in Problems...Ch. 9.3 - Problems 35-40 refer to the matrices in Problems...Ch. 9.3 - Problems 35-40 refer to the matrices in Problems...Ch. 9.3 - In Problems 41-48, discuss the validity of each...Ch. 9.3 - In Problems 41-48, discuss the validity of each...Ch. 9.3 - In Problems 41-48, discuss the validity of each...Ch. 9.3 - In Problems 41-48, discuss the validity of each...Ch. 9.3 - In Problems 41-48, discuss the validity of each...Ch. 9.3 - In Problems 41-48, discuss the validity of each...Ch. 9.3 - In Problems 41-48, discuss the validity of each...Ch. 9.3 - In Problems 41-48, discuss the validity of each...Ch. 9.3 - In Problems 49-52, use a graphing calculator to...Ch. 9.3 - In Problems 49-52, use a graphing calculator to...Ch. 9.3 - In Problems 49-52, use a graphing calculator to...Ch. 9.3 - In Problems 49-52, use a graphing calculator to...Ch. 9.3 - The following matrix P is a nonstandard transition...Ch. 9.3 - Repeat Problem 53 for...Ch. 9.3 - Verify the results in Problem 53 by computing Pk...Ch. 9.3 - Verify the results in Problem 54 by computing Pk...Ch. 9.3 - Show that S=x1x0,0x1, is a stationary matrix for...Ch. 9.3 - Show that S=x1x00,0x1, is a stationary matrix for...Ch. 9.3 - An absorbing Markov chain has the following matrix...Ch. 9.3 - Refer to the matrices P and Q of Problem 59. For k...Ch. 9.3 - Loans. A credit union classifies car loans into...Ch. 9.3 - Employee training. A chain of car muffler and...Ch. 9.3 - Marketing. Three electronics firms are...Ch. 9.3 - Pensions. Once a year company employees are given...Ch. 9.3 - Medicine. After bypass surgery, patients are...Ch. 9.3 - Medicine. The study discussed in Problem 65 also...Ch. 9.3 - Psychology. A rat is placed in room F or room B of...Ch. 9.3 - Psychology. Repeat Problem 67 if the exit from...Ch. 9 - Given the transition matrix P and initial-state...Ch. 9 - In Problems 2-6, P is a transition matrix for a...Ch. 9 - In Problems 2-6, P is a transition matrix for a...Ch. 9 - In Problems 2-6, P is a transition matrix for a...Ch. 9 - In Problems 2-6, P is a transition matrix for a...Ch. 9 - Prob. 6RECh. 9 - In Problems 7-10, write a transition matrix for...Ch. 9 - In Problems 7-10, write a transition matrix for...Ch. 9 - In Problems 7-10, write a transition matrix for...Ch. 9 - In Problems 7-10, write a transition matrix for...Ch. 9 - A Markov chain has three states, A,B, and C. The...Ch. 9 - Given the transition matrix ABP=AB.4.6.9.1 find...Ch. 9 - In Problems 13 and 14. solve the equation SP=S to...Ch. 9 - In Problems 13 and 14. solve the equation SP=S to...Ch. 9 - In Problems 15 and 16, find the limiting matrix...Ch. 9 - In Problems 15 and 16, find the limiting matrix...Ch. 9 - In Problems 17-20, use a graphing calculator to...Ch. 9 - In Problems 17-20, use a graphing calculator to...Ch. 9 - In Problems 17-20, use a graphing calculator to...Ch. 9 - In Problems 17-20, use a graphing calculator to...Ch. 9 - Find a standard form for the absorbing Markov...Ch. 9 - In Problems 22 and 23, determine the long-run...Ch. 9 - In Problems 22 and 23, determine the long-run...Ch. 9 - Let P be a 22 transition matrix for a Markov...Ch. 9 - Let P be a 33 transition matrix for a Markov...Ch. 9 - A red urn contains 2 red marbles, 1 blue marble,...Ch. 9 - Repeat Problem 26 if the blue and green marbles...Ch. 9 - Show that S=xyz0, where 0x1, 0y1, 0z1, and...Ch. 9 - In problems 29-35, either give an example of a...Ch. 9 - In problems 29-35, either give an example of a...Ch. 9 - In problems 29-35, either give an example of a...Ch. 9 - In problems 29-35, either give an example of a...Ch. 9 - In problems 29-35, either give an example of a...Ch. 9 - In problems 29-35, either give an example of a...Ch. 9 - In problems 29-35, either give an example of a...Ch. 9 - In Problems 36 and 37, use a graphing calculator...Ch. 9 - In Problems 36 and 37, use a graphing calculator...Ch. 9 - Product switching. A company's brand X has 20 of...Ch. 9 - Marketing. Recent technological advances have led...Ch. 9 - Prob. 40RECh. 9 - Employee training. In order to become a fellow of...Ch. 9 - Genetics. A given plant species has red, pink, or...Ch. 9 - Smoking. Table 2 gives the percentage of U.S....

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