To determine if there is a proportional relationship between the "Hours biked" and "Miles traveled," we need to check if the ratios of miles per hour (miles traveled divided by hours biked) are equivalent for each entry in the data table.
Let's assume the "Hours biked" in your data is as follows:
- 1 hour - 12 miles
- 2 hours - 26 miles
- 3 hours - 30 miles
- 4 hours - 48 miles
Now, let's calculate the ratios (miles per hour):
- For the first data point: \( \frac{12 \text{ miles}}{1 \text{ hour}} = 12 \text{ miles/hour} \)
- For the second data point: \( \frac{26 \text{ miles}}{2 \text{ hours}} = 13 \text{ miles/hour} \)
- For the third data point: \( \frac{30 \text{ miles}}{3 \text{ hours}} = 10 \text{ miles/hour} \)
- For the fourth data point: \( \frac{48 \text{ miles}}{4 \text{ hours}} = 12 \text{ miles/hour} \)
Now we have the following ratios:
- 12 miles/hour
- 13 miles/hour
- 10 miles/hour
- 12 miles/hour
Since the ratios are not all the same, we can conclude:
D) No, not all of the ratios are proportional or have equivalents.
Thus, the quantities in the data table do not have a proportional relationship.