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In a certain city the proportions of voters in each age group who are registered as Democrats, Republicans, or Independents are given by the following matrix. Age 18-30 31-50 Over 50 Democrat 0.30 0.60 0.50 Republican 0.50 0.35 0.25 = A Independent 0.20 0.05 0.25 The next matrix gives the distribution, by age and sex, of the voting population of this city. Male Female 18-30 5,000 6,000 Age 31-50 10,000 12,000 = B Over 50 12,000 15,000 For this problem, let's make the (highly unrealistic) assumption that within each age group, political preference is not related to gender. That is, the percentage of Demo- crat males in the 18-30 group, for example, is the same as the percentage of Demo- crat females in this group. (a) Calculate the product AB. (b) How many males are registered as Democrats in this city? (c) How many females are registered as Republicans?

In a certain city the proportions of voters in each age group who are registered as Democrats, Republicans, or Independents are given by the following matrix. Age 18-30 31-50 Over 50 Democrat 0.30 0.60 0.50 Republican 0.50 0.35 0.25 = A Independent 0.20 0.05 0.25 The next matrix gives the distribution, by age and sex, of the voting population of this city. Male Female 18-30 5,000 6,000 Age 31-50 10,000 12,000 = B Over 50 12,000 15,000 For this problem, let's make the (highly unrealistic) assumption that within each age group, political preference is not related to gender. That is, the percentage of Demo- crat males in the 18-30 group, for example, is the same as the percentage of Demo- crat females in this group. (a) Calculate the product AB. (b) How many males are registered as Democrats in this city? (c) How many females are registered as Republicans?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 41EQ
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In a certain city the proportions of voters in each age group who are registered as Democrats, Republicans, or Independents are given by the following matrix. Age 18-30 31-50 Over 50 Democrat 0.30 0.60 0.50 Republican 0.50 0.35 0.25 = A Independent 0.20 0.05 0.25 The next matrix gives the distribution, by age and sex, of the voting population of this city. Male Female 18-30 5,000 6,000 Age 31-50 10,000 12,000 = B Over 50 12,000 15,000 For this problem, let's make the (highly unrealistic) assumption that within each age group, political preference is not related to gender. That is, the percentage of Demo- crat males in the 18-30 group, for example, is the same as the percentage of Demo- crat females in this group. (a) Calculate the product AB. (b) How many males are registered as Democrats in this city? (c) How many females are registered as Republicans?
Transcribed Image Text:In a certain city the proportions of voters in each age group who are registered as Democrats, Republicans, or Independents are given by the following matrix. Age 18-30 31-50 Over 50 Democrat 0.30 0.60 0.50 Republican 0.50 0.35 0.25 = A Independent 0.20 0.05 0.25 The next matrix gives the distribution, by age and sex, of the voting population of this city. Male Female 18-30 5,000 6,000 Age 31-50 10,000 12,000 = B Over 50 12,000 15,000 For this problem, let's make the (highly unrealistic) assumption that within each age group, political preference is not related to gender. That is, the percentage of Demo- crat males in the 18-30 group, for example, is the same as the percentage of Demo- crat females in this group. (a) Calculate the product AB. (b) How many males are registered as Democrats in this city? (c) How many females are registered as Republicans?
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