use the table to answer the question.
Hours Biked: 1 Miles Traveled: 12
Hours Biked: 2 Miles Traveled: 26
Hours Biked: 3 Miles Traveled: 30
Hours Biked: 4 Miles Traveled: 48
determine if the quantity is in the data table or in a proportional relationship. if they do not have a proportional relationship, indicate why
A no, you can't bike 12 miles in an hour
B yes, this data table has a proportional relationship.
C no, none of the ratios have equivalence
D no, not all of the ratios are proportional or have equivalence
D no, not all of the ratios are proportional or have equivalence
To determine if the quantities have a proportional relationship, we can compare the ratios of miles traveled to hours biked.
For the given data:
1 hour of biking corresponds to 12 miles
2 hours of biking corresponds to 26 miles
3 hours of biking corresponds to 30 miles
4 hours of biking corresponds to 48 miles
We can calculate the ratios of miles to hours for each pair of data points:
1/12 = 0.0833
2/26 ≈ 0.0769
3/30 = 0.1
4/48 = 0.0833
Since the ratios do not have equivalence (i.e., they are not the same value), the quantities do not have a proportional relationship.
Therefore, the correct answer is D) no, not all of the ratios are proportional or have equivalence.
To determine if the quantities in the data table have a proportional relationship, we need to check if the ratios of miles traveled to hours biked are equivalent for each pair of values.
Let's calculate the ratios for each pair:
For the first pair:
Ratio = Miles Traveled / Hours Biked
Ratio = 12 / 1
Ratio = 12
For the second pair:
Ratio = Miles Traveled / Hours Biked
Ratio = 26 / 2
Ratio = 13
For the third pair:
Ratio = Miles Traveled / Hours Biked
Ratio = 30 / 3
Ratio = 10
For the fourth pair:
Ratio = Miles Traveled / Hours Biked
Ratio = 48 / 4
Ratio = 12
Looking at the ratios, we can see that they are not all equivalent. For a proportional relationship, each ratio should be the same. Since the ratios in this data table are not constant, we can conclude that the quantities do not have a proportional relationship.
Therefore, the correct answer is D) no, not all of the ratios are proportional or have equivalence.