To determine whether the tables represent proportional relationships and identify the constant of proportionality for each, we would typically look at the relationship between the number of pages in the books and the time it took each person to read those books.
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Proportional Relationships: A relationship is proportional if the ratio of the two quantities (in this case, time taken to read the number of pages) is constant for all the pairs in the table.
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Constant of Proportionality: This is defined as the ratio of the dependent variable (time) to the independent variable (number of pages). In other words, it is calculated as: \[ \text{Constant of proportionality} = \frac{\text{Time taken}}{\text{Number of pages}} \]
Without the specific tables:
If we had the number of pages and the time for Lucy and Britney explicitly laid out in tables, we could confirm which relationships are proportional by checking whether the ratios are the same for each person.
- If Lucy's times for each book divided by the number of pages she read yield the same number, then her table represents a proportional relationship.
- The same rule applies to Britney.
If the ratios differ for any pair or if they do not simplify to a consistent ratio, then that table would not represent a proportional relationship.
Answer Options:
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For Question 1:
- If Lucy's table shows consistent ratios, you'd select A or C (if both are consistent).
- If only Britney’s is consistent, you’d select B.
- If neither is consistent, you’d select D.
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For Question 2:
- You would calculate the constant of proportionality for both Lucy and Britney using the pages and times given.
- Based on those calculations, you would choose between options A, B, C, or D based on the constants found.
Conclusion
Without the actual data from the tables, I can't definitively guide you to the correct answers. You will need to analyze the tables accordingly. If you can share specific values from the tables, I could help you determine the correct responses!
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