Chapter 1.4, Problem 60E

(a)

To determine

The maximum and minimum voters who vote for Republican and Green.

Answer to Problem 60E

The maximum percentage of voter in republican and green is $44\%$ and $4\%$ and the minimum percentage of voters are $40\%$ and $0\%$

Explanation of Solution

Given information:

The data for the survey of voters is:

  

The possible error is survey is $\pm 2\%$

Calculation:

Consider the percentage of voter for republican from the given graph.

  $42\%$

Add $2\%$ to find the maximum percentage of voters.

  $42\%+2\%=44\%$

Subtract $2\%$ from the percentage of voters in republican to find the minimum percentage of voters.

  $42\%-2\%=40\%$

Consider the percentage of voter for green from the given graph.

  $2\%$

Add $2\%$ to find the maximum percentage of voters.

  $2\%+2\%=4\%$

Subtract $2\%$ from the percentage of voters in green to find the minimum percentage of voters.

  $2\%-2\%=0\%$

Hence, the maximum percentage of voter in republican and green is $44\%$ and $4\%$ and the minimum percentage of voters are $40\%$ and $0\%$

(b)

To determine

The absolute value equation of the above solution.

Answer to Problem 60E

The required equations are $\left|42-x\right|=2\%$ and $\left|2-x\right|=2\%$ .

Explanation of Solution

Given information:

The data for the side length of the square and the perimeter is:

  

The possible error is survey is $\pm 2\%$

Consider the result of maximum or minimum value of voters to be x .

Subtract x from the value of voters of republican and equate it with the modus of the error.

  $\left|42-x\right|=2\%$

Subtract x from the value of voters of green and equate it with the modus of the error.

  $\left|2-x\right|=2\%$

Hence, the required equations are $\left|42-x\right|=2\%$ and $\left|2-x\right|=2\%$ .

(c)

To determine

The candidate that can receive $44\%$ of the vote.

Answer to Problem 60E

The required equations are $\left|42-x\right|=2\%$ and $\left|2-x\right|=2\%$ .

Explanation of Solution

From the above equation it can be found that the maximum percentage of voter in republican and green is $44\%$

Hence, the candidate belong to the party republican.