a. To determine which person is doing more jumping jacks per second, we need to calculate the jacks per second for each person. The jacks per second is found by dividing the number of jumping jacks by the time in seconds.
For Kimberly:
3 seconds - 17 jumping jacks, so 17 jacks / 3 sec = 5.67 jacks/sec
8 seconds - 37 jumping jacks, so 37 jacks / 8 sec = 4.63 jacks/sec
12 seconds - 53 jumping jacks, so 53 jacks / 12 sec = 4.42 jacks/sec
16 seconds - 69 jumping jacks, so 69 jacks / 16 sec = 4.31 jacks/sec
For Katrina:
2 seconds - 10 jumping jacks, so 10 jacks / 2 sec = 5 jacks/sec
5 seconds - 25 jumping jacks, so 25 jacks / 5 sec = 5 jacks/sec
12 seconds - 60 jumping jacks, so 60 jacks / 12 sec = 5 jacks/sec
20 seconds - 100 jumping jacks, so 100 jacks / 20 sec = 5 jacks/sec
From the calculations, we can see that both Kimberly and Katrina are doing the same number of jumping jacks per second, which is 5 jacks/sec.
b. To determine which person had done more jumping jacks initially before the timer started, we need to look at the first data point for each person.
For Kimberly, the first data point is at 3 seconds, and she completed 17 jumping jacks.
For Katrina, the first data point is at 2 seconds, and she completed 10 jumping jacks.
Therefore, Kimberly had done more jumping jacks initially before the timer started.
c. To determine which person shows a proportional relationship between time and jumping jacks, we need to compare the ratios of jumping jacks to time for each person. If the ratios are constant, then there is a proportional relationship.
For Kimberly:
17 jacks / 3 sec = 5.67 jacks/sec
37 jacks / 8 sec = 4.63 jacks/sec
53 jacks / 12 sec = 4.42 jacks/sec
69 jacks / 16 sec = 4.31 jacks/sec
The ratios for Kimberly are not constant, indicating that there is no proportional relationship.
For Katrina:
10 jacks / 2 sec = 5 jacks/sec
25 jacks / 5 sec = 5 jacks/sec
60 jacks / 12 sec = 5 jacks/sec
100 jacks / 20 sec = 5 jacks/sec
The ratios for Katrina are constant, indicating that there is a proportional relationship between time and jumping jacks for Katrina.
The tables below show the number of jumping jacks completed after a given period of time in seconds. Kimberly: Time (seconds) Jumping Jacks 3 17 8 37 12 53 16 69 Katrina: Time (seconds) Jumping Jacks 2 10 5 25 12 60 20 100(3 points) a. Which person is doing more jumping jacks per second? b. Which person had done more jumping jacks initially before the timer started? c. Which person shows a proportional relationship?
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