Determine if the quantities in the data table are in a proportional relationship. If they are not in a proportional relationship, indicate why.
No, the ratios of 3 hours to $27 is not proportional.
No, the ratio of 1 hour to $9 is not proportional.
No, the ratios are not equivalent.
Yes, the ratios are in a proportional relationship.
Yes, the quantities in the data table are in a proportional relationship.
To determine if the quantities in the data table are in a proportional relationship, we need to compare the ratios.
1) For the first statement, the ratio of 3 hours to $27 is 3:27, which can be simplified to 1:9. However, this ratio is not equivalent to the ratio of 1 hour to $9, which is 1:9. Therefore, the quantities are not in a proportional relationship.
2) For the second statement, the ratio of 1 hour to $9 is already simplified and is the same as the ratio given. Therefore, the quantities are in a proportional relationship.
Thus, the quantities in the data table are not in a proportional relationship except for the second statement.
To determine if the quantities in a data table are in a proportional relationship, we need to compare the ratios between the two quantities.
In this case, we have two tables where we compare the number of hours with the corresponding amount of money.
Table 1: 3 hours to $27
Table 2: 1 hour to $9
To check if these ratios are proportional, we divide the second quantity by the first quantity for each table.
For Table 1, we divide $27 by 3. The result is 9.
For Table 2, we divide $9 by 1. The result is also 9.
Since both ratios result in the same value (9), we can see that the quantities in Table 1 are in a proportional relationship. This means that for every 3 hours, there is $27, and we can write this relationship as 3:27.
However, in Table 2, the ratio between 1 hour and $9 is not proportional to the ratio in Table 1. This means that the quantities in Table 2 are not in a proportional relationship. We can write this relationship as 1:9.
So, to summarize:
- The ratios in Table 1 are proportional because the ratio is constant at 9.
- The ratios in Table 2 are not proportional as the ratio is not equal to that of Table 1.