At the end of a certain year, the four organizations ranking 5 through 8 in home Internet users in the United States were eBay, the U.S. Government, Amazon, and Lycos, with a combined audience of 112 million users. Taking x to be the eBay audience in millions, y the U.S. Government audience in millions, z the Amazon audience in millions, and u the Lycos audience in millions, it was observed that

At the end of a certain year, the four organizations ranking 5 through 8 in home Internet users in the United States were eBay, the U.S. Government, Amazon, and Lycos, with a combined audience of 112 million users. Taking x to be the eBay audience in millions, y the U.S. Government audience in millions, z the Amazon audience in millions, and u the Lycos audience in millions, it was observed that

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2
At the end of a certain year, the four organizations ranking 5 through 8 in home Internet users in the United States were eBay, the U.S. Government, Amazon, and Lycos, with a combined audience of 112 million users. Taking x to be the eBay audience in millions, y the U.S. Government audience in millions, z the Amazon audience in millions, and u the Lycos audience in millions, it was observed that y - z = z -u x - y = 3(y - u) + 17and x - y + z - u = 24 How large was the audience of each of the four companies at the end of that year? eBay= ______ millionU.S. Government= ______ millionAmazon million= ______ millionLycos million= ______ million
At the end of a certain year, the four organizations ranking 5 through 8 in home Internet users in the United States were eBay, the U.S. Government, Amazon, and Lycos, with a combined audience of 112 million users. Taking x to be the eBay audience in millions, y the U.S. Government audience in millions, z the Amazon audience in millions, and u the Lycos audience in millions, it was observed that y − z = z − u x − y = 3(y − u) + 13 x − y + z − u = 20.
At the end of a certain year, the four organizations ranking 5 through 8 in home Internet users in the United States were eBay, the U.S. Government, Amazon, and Lycos, with a combined audience of 112 million users. Taking x to be the eBay audience in millions, y the U.S. Government audience in millions, z the Amazon audience in millions, and u the Lycos audience in millions, it was observed that y − z = z − u x − y = 3(y − u) + 7 and   x − y + z − u = 28. How large was the audience of each of the four organizations at the end of that year? eBay millionU.S. Government millionAmazon millionLycos million
At the end of a certain year, the four organizations ranking 5 through 8 in home Internet users in the United States were eBay, the U.S. Government, Amazon, and Lycos, with a combined audience of 112 million users. Taking x to be the eBay audience in millions, y the U.S. Government audience in millions, z the Amazon audience in millions, and u the Lycos audience in millions, it was observed that y − z = z − u x − y = 3(y − u) + 21 and   x − y + z − u = 28. How large was the audience of each of the four organizations at the end of that year? eBay ____ million U.S. Government _____ million Amazon ____ million Lycos ____ million
At the end of a certain year, the four organizations ranking 5 through 8 in home Internet users in the United States were eBay, the U.S. Government, Amazon, and Lycos, with a combined audience of 112 million users. Taking x to be the eBay audience in millions, y the U.S. Government audience in millions, z the Amazon audience in millions, and u the Lycos audience in millions, it was observed that y − z = z − u x − y = 3(y − u) + 1 and   x − y + z − u = 8. How large was the audience of each of the four organizations at the end of that year? eBay, U.S. Government, Amazon, Lycos
In a certain company, the salary of men can take the values of 1,000,000, 1,500,000, 2,000,000 and 2,500,000. Women can enjoy the following salaries: 500,000, 1,000,000, 1,500,000 and 2,000,000. Assuming that the percentage of men earning each of the values is the same, and the same relative to women, and that men's wages are independent of women's wages, what is the probability that a couple, chosen at random, together, earn between 2,000,000 and 3,500,000 (included)?
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Three market leaders in homeowners insurance in a state are State Farm, American Family Insurance Group, and Allstate. Based on data from a certain year, two relationships between the homeowners insurance percentage market shares are found to be as given below, where x, y, z, and w are the percentages of the market held by State Farm, American Family, Allstate, and other companies, respectively. x = −86 + 5y + z z = 18− 2y + w Given that the four groups account for the entire market, obtain a third equation relating x, y, z, and w, and solve the associated system of three linear equations to show how the market shares of State Farm, American Family, and Allstate depend on the share held by other companies. (Express your answer in terms of w, where x = x(w), y = y(w), and z = z(w).) (x, y, z) =
Three market leaders in homeowners insurance in a state are State Farm, American Family Insurance Group, and Allstate. Based on data from a certain year, two relationships between the homeowners insurance percentage market shares are found to be as given below, where x, y, z, and w are the percentages of the market held by State Farm, American Family, Allstate, and other companies, respectively. x = −54 + 5y + z z = 9 − 2y + w Given that the four groups account for the entire market, obtain a third equation relating x, y, z, and w, and solve the associated system of three linear equations to show how the market shares of State Farm, American Family, and Allstate depend on the share held by other companies. (Express your answer in terms of w, where x = x(w), y = y(w), and z = z(w).) (x, y, z) = Which of the three companies' market share is most affected by the share held by other companies?
Three market leaders in homeowners insurance in a state are State Farm, American Family Insurance Group, and Allstate. Based on data from a certain year, two relationships between the homeowners insurance percentage market shares are found to be as given below, where x, y, z, and w are the percentages of the market held by State Farm, American Family, Allstate, and other companies, respectively. x = −60 + 5y + z z = 11 − 2y + w Given that the four groups account for the entire market, obtain a third equation relating x, y, z, and w, and solve the associated system of three linear equations to show how the market shares of State Farm, American Family, and Allstate depend on the share held by other companies. (Express your answer in terms of w, where x = x(w), y = y(w), and z = z(w).)
Internet Audience At the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that z − u = 3(x − y) + 16 x + y = 44 + z + u and x − y + z − u = 40. How large was the audience of each of the four companies at the end of that year?