use the table to answer the question.
Hours / Money
H:1 M:9
H:2 M:18
H:3 M:27
H:4 M:36
determine if the quantity is in the data table are in a proportional relationship period if they are not in a proportional relationship, indicate why.
A no, the ratio of 1 hour to $9 is not proportional.
B no, the ratios are not equivalent.
C yes, the ratios are in a proportional relationship.
D no, the ratio of 3 hours to $27 is not proportional.
C yes, the ratios are in a proportional relationship.
The correct answer is C: yes, the ratios are in a proportional relationship.
To determine if the quantities in the data table are in a proportional relationship, we can examine the ratios between the hours and the money.
For example, if we take the ratio of 1 hour to $9, we get 1:9. If we double the number of hours to 2, we also double the amount of money to $18, resulting in a ratio of 2:18.
Similarly, for 3 hours we have $27, which gives us a ratio of 3:27.
We can see that in both cases, when we increase the hours by a factor of 3, the money also increases by a factor of 3. Hence, the ratios are proportional, and the correct answer is C.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios between the hours and money amounts are the same for all values.
Let's calculate the ratios for each row in the table:
For the first row:
- The ratio of 1 hour to $9 is 1:9
For the second row:
- The ratio of 2 hours to $18 is 2:18, which simplifies to 1:9 (same as the first row)
For the third row:
- The ratio of 3 hours to $27 is 3:27, which simplifies to 1:9 (same as the first and second rows)
For the fourth row:
- The ratio of 4 hours to $36 is 4:36, which simplifies to 1:9 (same as all previous rows)
From the calculations, we can see that all the ratios of hours to money are the same, specifically 1:9. Therefore, the quantities in the data table are in a proportional relationship.
The correct answer is C: yes, the ratios are in a proportional relationship.