8. The tables below show the number of jumping jacks completed after a given period of time in minutes. KimberlyTime (min) # Jumping Jacks3 288 5812 8216 106KatrinaTime (min) # Jumping Jacks2 165 4012 9620 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 startedThe person doing the most jumping jacks per minuteThe person showing a proportional relationship between time and # of jumping jacksKatrinaNeitherBothKimberly

Answer 1

To analyze the performance of Kimberly and Katrina in terms of jumping jacks completed, we can break down the specific points of comparison:

1. The person that did the most jumping jacks initially before the time started:

   • The initial count from both tables is zero since both start at the time (0 minutes) with zero jumping jacks. Therefore, the correct response is Neither.

2. The person doing the most jumping jacks per minute:

   • To find the jumping jacks per minute for each person, we can calculate the rate from the data provided:

     • Kimberly:

       • 3 min: 28 JJs → 9.33 JJs/min (28/3)
       • 8 min: 58 JJs → 7.25 JJs/min (58/8)
       • 12 min: 82 JJs → 6.83 JJs/min (82/12)
       • 16 min: 106 JJs → 6.63 JJs/min (106/16)

     • The highest rate for Kimberly is 9.33 JJs/min.

     • Katrina:

       • 2 min: 16 JJs → 8 JJs/min (16/2)
       • 5 min: 40 JJs → 8 JJs/min (40/5)
       • 12 min: 96 JJs → 8 JJs/min (96/12)
       • 20 min: 160 JJs → 8 JJs/min (160/20)

     • The rate for Katrina is consistently 8 JJs/min.

   • Comparing the highest rates, Kimberly has the highest rate of 9.33 JJs/min. So the response is Kimberly.

3. The person showing a proportional relationship between time and # of jumping jacks:

   • A proportional relationship means that as time increases, the number of jumping jacks increases at a constant rate.
   • Looking at the data points:
     • Kimberly does not show a constant increase in the number of jumping jacks per minute.
     • Katrina has consistent rates of 8 JJs/min throughout all time intervals, indicating a proportional relationship.
   • Therefore, the response is Katrina.

Final responses:

1. The person that did the most jumping jacks initially before the time started: Neither
2. The person doing the most jumping jacks per minute: Kimberly
3. The person showing a proportional relationship between time and # of jumping jacks: Katrina