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.
A: no the ratio of 1 hour to 9 is not proportional
B: no the ratio of 3 hours to 27 is not proportional
C: yes the ratios are in a proportional relationship
D: no the ratios are not equivalent
C: yes the ratios are in a proportional relationship. The ratio of hours to money is consistent, with each hour corresponding to $9. As the number of hours increases by 1, the amount of money also increases by $9, indicating 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 remain constant.
Let's calculate the ratios for each hour:
For hour 1: money/hours = 9/1 = 9
For hour 2: money/hours = 18/2 = 9
For hour 3: money/hours = 27/3 = 9
For hour 4: money/hours = 36/4 = 9
As we can see, the ratio between money and hours remains constant at 9 for each hour. This means that the quantities in the data table are in a proportional relationship.
Therefore, 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 check if the ratios between the hours and money are constant.
Let's calculate the ratios for each set of hours and money:
- For 1 hour to 9 money: 1/9 = 0.111
- For 2 hours to 18 money: 2/18 = 0.111
- For 3 hours to 27 money: 3/27 = 0.111
- For 4 hours to 36 money: 4/36 = 0.111
Since the ratios are all equal to 0.111, the quantities in the data table are in a proportional relationship. Therefore, the correct answer is:
C: Yes, the ratios are in a proportional relationship.