Question

Hours biked. Miles travel
1. 12
2. 26
3. 30
4. 48

Determine if the quantities in the data table are in proportional relationship if they do not have a proportional relationship indicate why a yes the data table has a proportional relationship be no you can't back 12 miles an hour see no none of the ratios have equivalents Dee no not all of the ratios are proportional or have equivalents

Answer 1

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. 1 hour - 12 miles
2. 2 hours - 26 miles
3. 3 hours - 30 miles
4. 4 hours - 48 miles

Now, let's calculate the ratios (miles per hour):

1. For the first data point: \( \frac{12 \text{ miles}}{1 \text{ hour}} = 12 \text{ miles/hour} \)
2. For the second data point: \( \frac{26 \text{ miles}}{2 \text{ hours}} = 13 \text{ miles/hour} \)
3. For the third data point: \( \frac{30 \text{ miles}}{3 \text{ hours}} = 10 \text{ miles/hour} \)
4. 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.