Question

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 showing a proportional relationship between time and # of jumping jacks The person that did the most jumping jacks initially before the time started The person doing the most jumping jacks per minute

Answer 1

To analyze the data provided in the tables for Kimberly and Katrina, let's look at each person's performance in terms of the relationships and metrics mentioned in the question:

1. Proportional Relationship: A proportional relationship means that as one variable increases, the other variable increases at a constant rate. To find this, we can calculate the ratio of jumping jacks to time for each person.

   • Kimberly:
     • 3 minutes → 28 jumping jacks → 28/3 ≈ 9.33
     • 8 minutes → 58 jumping jacks → 58/8 = 7.25
     • 12 minutes → 82 jumping jacks → 82/12 ≈ 6.83
     • 16 minutes → 106 jumping jacks → 106/16 = 6.625
   • Katrina:
     • 2 minutes → 16 jumping jacks → 16/2 = 8
     • 5 minutes → 40 jumping jacks → 40/5 = 8
     • 12 minutes → 96 jumping jacks → 96/12 = 8
     • 20 minutes → 160 jumping jacks → 160/20 = 8

   Katrina has a constant ratio of jumping jacks to time—8 jumping jacks per minute—indicating a proportional relationship.

2. Most Jumping Jacks Initially: The initial jumping jacks completed in relation to the starting time.

   • Kimberly's first entry (3 minutes) has 28 jumping jacks.
   • Katrina's first entry (2 minutes) has 16 jumping jacks.

   Kimberly completed the most jumping jacks initially before the time started.

3. Most Jumping Jacks per Minute: To find out who did the most jumping jacks per minute, we will compare their rates of completion:

   • Kimberly's averages are calculated above and drew varying results, ranging around 6.6 to 9.33.
   • Katrina has consistently 8 jumps per minute.

   At her maximum, Kimberly completed approximately 9.33 jumping jacks per minute during the first duration.

Now we can summarize the responses:

• Person showing a proportional relationship between time and # of jumping jacks: Katrina
• Person that did the most jumping jacks initially before the time started: Kimberly
• Person doing the most jumping jacks per minute: Kimberly

You can now input the responses accordingly.