7. The tables below show the number of jumping jacks completed after a given period of time in minutes.
Kimberly
Time (min) # Jumping Jacks
3 28
8 58
12 82
16 106
Katrina
Time (min) # Jumping Jacks
2 16
5 40
12 96
20 160
(3 points)
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The person showing a proportional relationship between time and # of jumping jacks - Response area
The person that did the most jumping jacks initially before the time started - Response area
The person doing the most jumping jacks per minute - Response area
The person showing a proportional relationship between time and # of jumping jacks - Katrina
The person that did the most jumping jacks initially before the time started - Kimberly
The person doing the most jumping jacks per minute - Katrina
The person showing a proportional relationship between time and # of jumping jacks - Kimberly
The person that did the most jumping jacks initially before the time started - Kimberly
The person doing the most jumping jacks per minute - Katrina
To determine the person showing a proportional relationship between time and the number of jumping jacks, we need to analyze the data for each person.
Kimberly's data:
Time (min) - # Jumping Jacks
3 - 28
8 - 58
12 - 82
16 - 106
Katrina's data:
Time (min) - # Jumping Jacks
2 - 16
5 - 40
12 - 96
20 - 160
A proportional relationship means that as the time increases, the number of jumping jacks also increases at a constant rate. To verify this, we can calculate the jumping jacks per minute for each person by dividing the number of jumping jacks by the time in minutes.
Kimberly's jumping jacks per minute:
for 3 minutes: 28 / 3 = 9.333
for 8 minutes: 58 / 8 = 7.25
for 12 minutes: 82 / 12 = 6.833
for 16 minutes: 106 / 16 = 6.625
Katrina's jumping jacks per minute:
for 2 minutes: 16 / 2 = 8
for 5 minutes: 40 / 5 = 8
for 12 minutes: 96 / 12 = 8
for 20 minutes: 160 / 20 = 8
Therefore, both Kimberly and Katrina have a proportional relationship between time and the number of jumping jacks, as their jumping jacks per minute values remain constant.
To determine which person did the most jumping jacks initially before the time started, we need to compare the number of jumping jacks when time is 0. Unfortunately, the given data does not provide information on the number of jumping jacks before the time starts. Thus, we cannot determine who did the most jumping jacks initially.
To identify the person doing the most jumping jacks per minute, we can compare the jumping jacks per minute values calculated above.
Kimberly's jumping jacks per minute values:
9.333, 7.25, 6.833, 6.625
Katrina's jumping jacks per minute values:
8, 8, 8, 8
Since Kimberly's highest jumping jacks per minute value is 9.333, and Katrina's highest jumping jacks per minute value is 8, Kimberly is the person doing the most jumping jacks per minute.
To summarize:
- Both Kimberly and Katrina show a proportional relationship between time and the number of jumping jacks.
- We cannot determine who did the most jumping jacks initially before the time started.
- Kimberly is the person doing the most jumping jacks per minute.