Use the table to answer the question.
Hours Money ($)
1 9
2 18
3 27
4 36
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 ratio of 3 hours to $27 is not proportional.
No, the ratio of 3 hours to $27 is not proportional.
No, the ratios are not equivalent.
No, the ratios are not equivalent.
No, the ratio of 1 hour to $9 is not proportional.
No, the ratio of 1 hour to $9 is not proportional.
Yes, the ratios are in a proportional relationship.
Yes, the ratios are in a proportional relationship.
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No, the ratios are not equivalent.
Yes, the ratios are in a proportional relationship.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios between hours and money are equivalent for different values.
In this case, let's calculate the ratios:
For 1 hour, the corresponding amount of money is $9. So the ratio is 1 hour : $9.
For 2 hours, the corresponding amount of money is $18. So the ratio is 2 hours : $18.
For 3 hours, the corresponding amount of money is $27. So the ratio is 3 hours : $27.
For 4 hours, the corresponding amount of money is $36. So the ratio is 4 hours : $36.
To determine if these ratios are equivalent, we can simplify each ratio.
The first ratio, 1 hour : $9, is already in simplest form.
The second ratio, 2 hours : $18, can be simplified to 1 hour : $9 by dividing both the numerator and denominator by 2.
The third ratio, 3 hours : $27, can be simplified to 1 hour : $9 by dividing both the numerator and denominator by 3.
The fourth ratio, 4 hours : $36, can be simplified to 1 hour : $9 by dividing both the numerator and denominator by 4.
Since all of the ratios simplify to 1 hour : $9, we can conclude that the quantities in the data table are in a proportional relationship.