The tables below show the number of jumping jacks completed after a given period of time in minutes.
Kimberly
Time (min) 3, 8, 12, 16.
# Jumping jacks. 28, 58, 82, 106.
Katrina
Time (min) 2, 5, 12, 20.
# Jumping jacks. 16, 40, 96, 160.
Ther person showing a proportional relationship between time and # of jumping jacks. [enter answer]
Ther person doing the most jumping jacks per minute. [enter answer]
The person that did the most jumping jacks initially before the time started. [enter answer]
The person showing a proportional relationship between time and the number of jumping jacks is Katrina.
The person doing the most jumping jacks per minute is Kimberly.
The person that did the most jumping jacks initially before the time started is Kimberly.
The person showing a proportional relationship between time and the number of jumping jacks is Kimberly. This can be determined by calculating the rate of change (slope) between the time and the number of jumping jacks. In Kimberly's case, the rate of change is consistent at 9 jumping jacks per minute.
The person doing the most jumping jacks per minute is Katrina. This can be determined by comparing the numbers of jumping jacks divided by the corresponding time for each person. For Katrina, the jumping jacks per minute are as follows: 8 jumping jacks per minute (16 jumping jacks / 2 minutes), 8 jumping jacks per minute (40 jumping jacks / 5 minutes), 8 jumping jacks per minute (96 jumping jacks / 12 minutes), and 8 jumping jacks per minute (160 jumping jacks / 20 minutes).
The person that did the most jumping jacks initially before the time started cannot be determined based on the given information. The tables only provide the number of jumping jacks completed after a given period of time, not the initial number of jumping jacks before the time started.
To determine the answers, we need to analyze the given data.
The first question asks about the person showing a proportional relationship between time and the number of jumping jacks.
To find this, we need to compare the ratios of time to the number of jumping jacks for both Kimberly and Katrina. We can do this by dividing the number of jumping jacks by the time for each person.
For Kimberly:
3 minutes -> 28 jumping jacks -> ratio: 28/3 = 9.33 jumping jacks per minute
8 minutes -> 58 jumping jacks -> ratio: 58/8 = 7.25 jumping jacks per minute
12 minutes -> 82 jumping jacks -> ratio: 82/12 = 6.83 jumping jacks per minute
16 minutes -> 106 jumping jacks -> ratio: 106/16 = 6.63 jumping jacks per minute
For Katrina:
2 minutes -> 16 jumping jacks -> ratio: 16/2 = 8 jumping jacks per minute
5 minutes -> 40 jumping jacks -> ratio: 40/5 = 8 jumping jacks per minute
12 minutes -> 96 jumping jacks -> ratio: 96/12 = 8 jumping jacks per minute
20 minutes -> 160 jumping jacks -> ratio: 160/20 = 8 jumping jacks per minute
From the calculations, we can see that both Kimberly and Katrina have a proportional relationship between time and the number of jumping jacks. They both have a consistent ratio of 8 jumping jacks per minute.
Therefore, the answer to the first question is: Both Kimberly and Katrina show a proportional relationship between time and the number of jumping jacks.
Moving on to the second question, which asks about the person who did the most jumping jacks per minute.
To find this, we need to compare the ratios we calculated earlier for Kimberly and Katrina.
Kimberly had a maximum ratio of 9.33 jumping jacks per minute, while Katrina had a maximum ratio of 8 jumping jacks per minute.
Hence, Kimberly did the most jumping jacks per minute.
The answer to the second question is: Kimberly did the most jumping jacks per minute.
Now, let's look at the third question, which asks about the person who did the most jumping jacks initially before the time started.
To determine this, we need to analyze the number of jumping jacks at the beginning of the time period for both Kimberly and Katrina.
For Kimberly, the number of jumping jacks at the beginning was 28.
For Katrina, the number of jumping jacks at the beginning was 16.
Therefore, Kimberly did the most jumping jacks initially before the time started.
The answer to the third question is: Kimberly did the most jumping jacks initially before the time started.