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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 answers

To analyze the data provided for Kimberly and Katrina, we can look at the progression of the number of jumping jacks completed over time and determine the rates of performance for both individuals.

Kimberly's Data:

| Time (min) | # Jumping Jacks | |------------|------------------| | 3 | 28 | | 8 | 58 | | 12 | 82 | | 16 | 106 |

Observations:

  • From 3 to 8 minutes:

    • Increase = 58 - 28 = 30 jumping jacks
    • Time increase = 8 - 3 = 5 minutes
    • Rate = 30 / 5 = 6 jumping jacks/min

  • From 8 to 12 minutes:

    • Increase = 82 - 58 = 24 jumping jacks
    • Time increase = 12 - 8 = 4 minutes
    • Rate = 24 / 4 = 6 jumping jacks/min

  • From 12 to 16 minutes:

    • Increase = 106 - 82 = 24 jumping jacks
    • Time increase = 16 - 12 = 4 minutes
    • Rate = 24 / 4 = 6 jumping jacks/min

Kimberly consistently completes 6 jumping jacks per minute.

Katrina's Data:

| Time (min) | # Jumping Jacks | |------------|------------------| | 2 | 16 | | 5 | 40 | | 12 | 96 | | 20 | 160 |

Observations:

  • From 2 to 5 minutes:

    • Increase = 40 - 16 = 24 jumping jacks
    • Time increase = 5 - 2 = 3 minutes
    • Rate = 24 / 3 = 8 jumping jacks/min

  • From 5 to 12 minutes:

    • Increase = 96 - 40 = 56 jumping jacks
    • Time increase = 12 - 5 = 7 minutes
    • Rate = 56 / 7 = 8 jumping jacks/min

  • From 12 to 20 minutes:

    • Increase = 160 - 96 = 64 jumping jacks
    • Time increase = 20 - 12 = 8 minutes
    • Rate = 64 / 8 = 8 jumping jacks/min

Katrina consistently completes 8 jumping jacks per minute.

Summary:

  • Kimberly: 6 jumping jacks/min
  • Katrina: 8 jumping jacks/min

Katrina is performing at a higher rate than Kimberly based on the provided data.

The person doing the most jumping jacks per minute [_]
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 [_]

Let's fill in the blanks based on the analyses of Kimberly and Katrina's data:

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

    • Katrina

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

    • Both Kimberly and Katrina show a consistent rate of jumping jacks over their respective time intervals, but since the increases are uniform for Katrina's dataset, we can say Katrina shows a more clear proportional relationship.

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

    • Neither person has a value before time started in the given data, but at the lowest point of available data:
    • At time 0 for both, we assume they both started at 0 jumping jacks. However, if we look at their first data points:
      • Kimberly had her first data point at 3 minutes with 28 jumping jacks.
      • Katrina had her first data point at 2 minutes with 16 jumping jacks.
    • Since Kimberly's initial data (3 min, 28 JJs) is greater than Katrina's initial data (2 min, 16 JJs), we can say Kimberly did more jumping jacks at her first observation.

Final Answers:

  1. The person doing the most jumping jacks per minute: Katrina
  2. The person showing a proportional relationship between time and # of jumping jacks: Katrina
  3. The person that did the most jumping jacks initially before the time started: Kimberly