Answer :
Let's carefully calculate the required relative frequencies for Republican and Democratic residents of County 1, as well as the total percentages for the entire group of counties. We'll express our answers to the nearest tenth of a percent.
### Step 1: Calculate the Percentage of Republican Residents in County 1
First, consider the number of Republican residents in County 1:
- Republican residents in County 1: [tex]\( 2,470 \)[/tex]
Total population in County 1:
- Total population in County 1: [tex]\( 6,520 \)[/tex]
To find the percentage of Republican residents in County 1, we use the formula:
[tex]\[ \text{Republican Percentage in County 1} = \left( \frac{\text{Republican residents in County 1}}{\text{Total population in County 1}} \right) \times 100 \][/tex]
[tex]\[ = \left( \frac{2470}{6520} \right) \times 100 \approx 37.9\% \][/tex]
Thus, the percentage of Republican residents in County 1 is [tex]\( \mathbf{37.9\%} \)[/tex].
### Step 2: Calculate the Percentage of Democratic Residents in County 1
Next, consider the number of Democratic residents in County 1:
- Democratic residents in County 1: [tex]\( 4,050 \)[/tex]
To find the percentage of Democratic residents in County 1, we use the formula:
[tex]\[ \text{Democratic Percentage in County 1} = \left( \frac{\text{Democratic residents in County 1}}{\text{Total population in County 1}} \right) \times 100 \][/tex]
[tex]\[ = \left( \frac{4050}{6520} \right) \times 100 \approx 62.1\% \][/tex]
Thus, the percentage of Democratic residents in County 1 is [tex]\( \mathbf{62.1\%} \)[/tex].
### Step 3: Calculate the Total Percentage of Republican Residents
Consider the total number of Republican residents in all three counties:
- Total Republican residents: [tex]\( 14,430 \)[/tex]
Total population in all three counties:
- Total population: [tex]\( 24,505 \)[/tex]
To find the total percentage of Republican residents, we use the formula:
[tex]\[ \text{Total Republican Percentage} = \left( \frac{\text{Total Republican residents}}{\text{Total population}} \right) \times 100 \][/tex]
[tex]\[ = \left( \frac{14430}{24505} \right) \times 100 \approx 58.9\% \][/tex]
Thus, the total percentage of Republican residents is [tex]\( \mathbf{58.9\%} \)[/tex].
### Step 4: Calculate the Total Percentage of Democratic Residents
Finally, consider the total number of Democratic residents in all three counties:
- Total Democratic residents: [tex]\( 10,075 \)[/tex]
To find the total percentage of Democratic residents, we use the formula:
[tex]\[ \text{Total Democratic Percentage} = \left( \frac{\text{Total Democratic residents}}{\text{Total population}} \right) \times 100 \][/tex]
[tex]\[ = \left( \frac{10075}{24505} \right) \times 100 \approx 41.1\% \][/tex]
Thus, the total percentage of Democratic residents is [tex]\( \mathbf{41.1\%} \)[/tex].
### Summary
- Republican residents of County 1: [tex]\( 37.9\% \)[/tex]
- Democratic residents of County 1: [tex]\( 62.1\% \)[/tex]
- Total Republican residents: [tex]\( 58.9\% \)[/tex]
- Total Democratic residents: [tex]\( 41.1\% \)[/tex]
### Step 1: Calculate the Percentage of Republican Residents in County 1
First, consider the number of Republican residents in County 1:
- Republican residents in County 1: [tex]\( 2,470 \)[/tex]
Total population in County 1:
- Total population in County 1: [tex]\( 6,520 \)[/tex]
To find the percentage of Republican residents in County 1, we use the formula:
[tex]\[ \text{Republican Percentage in County 1} = \left( \frac{\text{Republican residents in County 1}}{\text{Total population in County 1}} \right) \times 100 \][/tex]
[tex]\[ = \left( \frac{2470}{6520} \right) \times 100 \approx 37.9\% \][/tex]
Thus, the percentage of Republican residents in County 1 is [tex]\( \mathbf{37.9\%} \)[/tex].
### Step 2: Calculate the Percentage of Democratic Residents in County 1
Next, consider the number of Democratic residents in County 1:
- Democratic residents in County 1: [tex]\( 4,050 \)[/tex]
To find the percentage of Democratic residents in County 1, we use the formula:
[tex]\[ \text{Democratic Percentage in County 1} = \left( \frac{\text{Democratic residents in County 1}}{\text{Total population in County 1}} \right) \times 100 \][/tex]
[tex]\[ = \left( \frac{4050}{6520} \right) \times 100 \approx 62.1\% \][/tex]
Thus, the percentage of Democratic residents in County 1 is [tex]\( \mathbf{62.1\%} \)[/tex].
### Step 3: Calculate the Total Percentage of Republican Residents
Consider the total number of Republican residents in all three counties:
- Total Republican residents: [tex]\( 14,430 \)[/tex]
Total population in all three counties:
- Total population: [tex]\( 24,505 \)[/tex]
To find the total percentage of Republican residents, we use the formula:
[tex]\[ \text{Total Republican Percentage} = \left( \frac{\text{Total Republican residents}}{\text{Total population}} \right) \times 100 \][/tex]
[tex]\[ = \left( \frac{14430}{24505} \right) \times 100 \approx 58.9\% \][/tex]
Thus, the total percentage of Republican residents is [tex]\( \mathbf{58.9\%} \)[/tex].
### Step 4: Calculate the Total Percentage of Democratic Residents
Finally, consider the total number of Democratic residents in all three counties:
- Total Democratic residents: [tex]\( 10,075 \)[/tex]
To find the total percentage of Democratic residents, we use the formula:
[tex]\[ \text{Total Democratic Percentage} = \left( \frac{\text{Total Democratic residents}}{\text{Total population}} \right) \times 100 \][/tex]
[tex]\[ = \left( \frac{10075}{24505} \right) \times 100 \approx 41.1\% \][/tex]
Thus, the total percentage of Democratic residents is [tex]\( \mathbf{41.1\%} \)[/tex].
### Summary
- Republican residents of County 1: [tex]\( 37.9\% \)[/tex]
- Democratic residents of County 1: [tex]\( 62.1\% \)[/tex]
- Total Republican residents: [tex]\( 58.9\% \)[/tex]
- Total Democratic residents: [tex]\( 41.1\% \)[/tex]
