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Determine if the quantities in the data table are in a proportional relationship. If they are not in a proportional relationship, indicate why.

(1 point)
Responses

No, the ratios are not equivalent.
No, the ratios are not equivalent.

No, the ratio 6 : 78 is not proportional to the other ratios.
No, the ratio 6 : 78 is not proportional to the other ratios.

Yes, the data table has a proportional relationship.
Yes, the data table has a proportional relationship.

No, the table does not count consecutively.

3 answers

To determine if the quantities in a data table are in a proportional relationship, we need to check if the ratios of corresponding values are equivalent. Proportional relationships can be represented by the equation \( \frac{y_1}{x_1} = \frac{y_2}{x_2} = \frac{y_3}{x_3} = \ldots \) for all pairs of values in the table.

If there is one remainder ratio that does not match the others, then the quantities do not have a proportional relationship.

Given the response options and the fact that we don't have the actual data or ratios from the table, you would likely choose one of the responses based on the information about the ratios.

  1. "No, the ratios are not equivalent." - This indicates that some ratios do not match.
  2. "No, the ratio 6:78 is not proportional to the other ratios." - This specifies that this particular ratio is not equivalent to the others.
  3. "Yes, the data table has a proportional relationship." - This confirms all ratios are equivalent.
  4. "No, the table does not count consecutively." - This indicates a misunderstanding of proportionality, as counting consecutively doesn't impact whether ratios are equivalent.

To conclude, if you have already checked the ratios and found that not all of them are the same, you would respond according to those observations. If the ratio of 6:78 is indeed different from others, you would choose the second response.

so what's the answer

Without the specific data table to analyze the ratios, I cannot provide a definitive answer regarding whether the quantities are in a proportional relationship. However, if one of the stated responses applies to your findings, you should choose accordingly.

  • If you find that some ratios do not match each other, select: “No, the ratios are not equivalent.”
  • If you specifically identify that the ratio 6:78 does not match others, select: “No, the ratio 6 : 78 is not proportional to the other ratios.”
  • If all ratios are equivalent, select: “Yes, the data table has a proportional relationship.”
  • If the arrangement does not affect the ratios being equivalent, the option about counting consecutively could be disregarded.

Based on common responses seen in similar scenarios, if the specific ratio 6:78 stands out as not matching others, the second option would generally be the most appropriate. Therefore, if that applies, the answer would be:

“No, the ratio 6 : 78 is not proportional to the other ratios.”

However, please verify this against your actual data!