To solve this problem, we need to calculate and match the given ratios with the appropriate descriptions. We'll use the given percentages to determine the ratios and then provide the matching.
1. Ratio of 6th graders who have a sibling to 6th graders who do not have a sibling:
Given: [tex]\(90\%\)[/tex] of the 6th graders have a sibling.
This means [tex]\(10\%\)[/tex] of the 6th graders do not have a sibling.
The ratio can be expressed as:
[tex]\[ \text{Ratio} = \frac{90}{10} = 9:1 \][/tex]
2. Ratio of 6th graders who have a sibling to the total number of 6th graders:
Given: [tex]\(90\%\)[/tex] of the 6th graders have a sibling.
The ratio can be expressed as:
[tex]\[ \text{Ratio} = \frac{90}{100} = 0.9 \][/tex]
3. Ratio of 8th graders on the soccer team to 8th graders not on the soccer team:
Given: [tex]\(10\%\)[/tex] of the 8th graders are on the soccer team.
This means [tex]\(90\%\)[/tex] of the 8th graders are not on the soccer team.
The ratio can be expressed as:
[tex]\[ \text{Ratio} = \frac{10}{90} = \frac{1}{9} \approx 0.1 \][/tex]
Given that we need to match ratios with descriptions, let's formalize this into our matching:
- (A) The ratio of 6th graders who have a sibling to 6th graders who do not have a sibling is [tex]\(9:1\)[/tex].
- (B) The ratio of 6th graders who do not have a sibling to 6th graders who have a sibling is [tex]\(1:9\)[/tex], which we derived as the inverse of (A).
- (C) The ratio of 6th graders who have a sibling to the total number of 6th graders is [tex]\(0.9\)[/tex].
- (E) The ratio of 8th graders on the soccer team to 8th graders not on the soccer team is [tex]\(0.1\)[/tex].
- (F) The ratio of 8th graders not on the soccer team to 8th graders on the soccer team is [tex]\(10:1\)[/tex], which is the inverse of (E).
So, the correct matches are:
- The ratio of 6th graders who have a sibling to 6th graders who do not have a sibling: (A)
- The ratio of 6th graders who do not have a sibling to 6th graders who have a sibling: (B)
- The ratio of 6th graders who have a sibling to the total number of 6th graders: (C)
- The ratio of 8th graders on the soccer team to 8th graders not on the soccer team: (E)
- The ratio of 8th graders not on the soccer team to 8th graders on the soccer team: (F)
