Question
You are comparing the ratios 5:9 and 2:3 using the following tables. Finish the tables by filling in the missing values A and B. 5 9 10 18 15 27 2 3 4 6 A B Responses A = 8 and B = 9. A = 8 and B = 9 . - no response given A = 8 and B = 12. A = 8 and B = 12 . - no response given A = 5 and B = 7. A = 5 and B = 7 . - no response given A = 6 and B = 9.
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GPT-4o mini
To find the values of A and B that complete the tables based on the given ratios, we first need to analyze the ratios 5:9 and 2:3.
First, let's consider the table for the ratio 5:9:
- If we have 5, then 9 corresponds to a ratio factor of \( k = \frac{9}{5} \).
- For the values we see:
- If \( 5 \rightarrow 9 \) aligns with \( 10 \rightarrow 18 \) then \( 15 \rightarrow 27 \) follows that same multiplication factor.
To find A and B based on a consistent ratio:
1. For \( 5 \) corresponds to \( 9 \):
- \( \frac{5}{9} \)
Now looking at when \( A \) comes up as the corresponding element:
- If \( 2 \rightarrow 3 \) corresponds to \( 4 \rightarrow 6 \):
- Thus, we can deduce \( 8 \rightarrow B \). The value of A should hold the ratio with respect to either 5:9 or 2:3.
Now completing the ratios from the respective relationships based on their proportional growth:
### Completing the tables:
- **For 5:9**
- If we start from \( 5 \rightarrow 9 \)
- \( 10 \rightarrow 18 \)
- \( 15 \rightarrow 27 \)
- We must find A such that \( ? \rightarrow B \).
- The number must complete an equivalent proportion when we use the same multiplication factor.
### Finding values for A and B:
From 2:3:
- The general relationship has \( \frac{2}{3} \)
- If aligned for 8 in sequence of the proportion:
- \( 8 \rightrightarrow Y \)
### Now, simplify solving the assumption:
Using the consistent multiplicative integrities:
- If we cross-multiply per given ratio format:
- Have scenario style \( \frac{A}{B} = \frac{2}{3} => A = 2k , B = 3k \)
Followed by:
- To identify A:
- Relating where 8 belongs in this system retains
- Hence can proportion out \( B \) yields alignment.
Using:
1. \( A = 8 \)
2. Where establishing consistent checking finds via inspection:
3. B determines here from 3y where each would yield per growth:
- Fix historical find with values cross of type confirms.
### Conclusion:
- Thus A = 8 and B resolves into A=8, B=12
- Hence the correct fill-ins would confirm as:
- Responses: A = 8 and B = 12.
**Final values**:
- A = 8
- B = 12
First, let's consider the table for the ratio 5:9:
- If we have 5, then 9 corresponds to a ratio factor of \( k = \frac{9}{5} \).
- For the values we see:
- If \( 5 \rightarrow 9 \) aligns with \( 10 \rightarrow 18 \) then \( 15 \rightarrow 27 \) follows that same multiplication factor.
To find A and B based on a consistent ratio:
1. For \( 5 \) corresponds to \( 9 \):
- \( \frac{5}{9} \)
Now looking at when \( A \) comes up as the corresponding element:
- If \( 2 \rightarrow 3 \) corresponds to \( 4 \rightarrow 6 \):
- Thus, we can deduce \( 8 \rightarrow B \). The value of A should hold the ratio with respect to either 5:9 or 2:3.
Now completing the ratios from the respective relationships based on their proportional growth:
### Completing the tables:
- **For 5:9**
- If we start from \( 5 \rightarrow 9 \)
- \( 10 \rightarrow 18 \)
- \( 15 \rightarrow 27 \)
- We must find A such that \( ? \rightarrow B \).
- The number must complete an equivalent proportion when we use the same multiplication factor.
### Finding values for A and B:
From 2:3:
- The general relationship has \( \frac{2}{3} \)
- If aligned for 8 in sequence of the proportion:
- \( 8 \rightrightarrow Y \)
### Now, simplify solving the assumption:
Using the consistent multiplicative integrities:
- If we cross-multiply per given ratio format:
- Have scenario style \( \frac{A}{B} = \frac{2}{3} => A = 2k , B = 3k \)
Followed by:
- To identify A:
- Relating where 8 belongs in this system retains
- Hence can proportion out \( B \) yields alignment.
Using:
1. \( A = 8 \)
2. Where establishing consistent checking finds via inspection:
3. B determines here from 3y where each would yield per growth:
- Fix historical find with values cross of type confirms.
### Conclusion:
- Thus A = 8 and B resolves into A=8, B=12
- Hence the correct fill-ins would confirm as:
- Responses: A = 8 and B = 12.
**Final values**:
- A = 8
- B = 12
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