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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)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The person that did the most jumping jacks initially before the time started
The person doing the most jumping jacks per minute
The person showing a proportional relationship between time and # of jumping jacks

1 answer

To analyze the information provided for Kimberly and Katrina, we can establish the following responses based on the data shared:

  1. The person that did the most jumping jacks initially before the time started: This information isn’t directly available from the tables because they only show the number of jumping jacks completed at specific time intervals. Therefore, we cannot determine who did the most jumping jacks initially.

  2. The person doing the most jumping jacks per minute: To calculate this, we will find the average rate of jumping jacks per minute for each individual.

    • Kimberly:

      • From 3 min to 8 min: (58 - 28) / (8 - 3) = 30 / 5 = 6 jacks/min
      • From 8 min to 12 min: (82 - 58) / (12 - 8) = 24 / 4 = 6 jacks/min
      • From 12 min to 16 min: (106 - 82) / (16 - 12) = 24 / 4 = 6 jacks/min

      Average for Kimberly: 6 jacks/min

    • Katrina:

      • From 2 min to 5 min: (40 - 16) / (5 - 2) = 24 / 3 = 8 jacks/min
      • From 5 min to 12 min: (96 - 40) / (12 - 5) = 56 / 7 ≈ 8 jacks/min
      • From 12 min to 20 min: (160 - 96) / (20 - 12) = 64 / 8 = 8 jacks/min

      Average for Katrina: 8 jacks/min

    So, Katrina is doing more jumping jacks per minute.

  3. The person showing a proportional relationship between time and # of jumping jacks: A proportional relationship would mean that the number of jumping jacks per given time is consistent throughout the intervals.

    • For Katrina, we see consistent rates (8 jacks/min), which implies a proportional relationship in her data.
    • For Kimberly, the rate of jumping jacks changes per interval (6 jacks/min), indicating it is not proportional.

Conclusion:

  • The person that did the most jumping jacks initially before the time started: Cannot determine from the data provided.
  • The person doing the most jumping jacks per minute: Katrina
  • The person showing a proportional relationship between time and # of jumping jacks: Katrina