the tables below show the 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|
1. The person that did the most jumping jack initially before _____
2. The person doing the most jump jacks per minute ______
3. the person showing a proportional relationship between time and # of jumping jacks _____
A. neither
B. katrina
C. kimberly
D. both
1. The person that did the most jumping jacks initially before _____
To determine the person who did the most jumping jacks initially, we need to compare the number of jumping jacks they did at the same time point, which is at 3 minutes for both Kimberly and Katrina.
Number of jumping jacks at 3 minutes:
- Kimberly: 28
- Katrina: 16
So, Kimberly did the most jumping jacks initially.
2. The person doing the most jump jacks per minute ______
To determine the person who did the most jumping jacks per minute, we need to compare the rate of jumping jacks they did, which is calculated by dividing the number of jumping jacks by the time in minutes.
Rate of jumping jacks per minute:
- Kimberly:
- At 3 minutes: 28/3 = 9.33
- At 8 minutes: 58/8 = 7.25
- At 12 minutes: 82/12 = 6.83
- At 16 minutes: 106/16 = 6.63
- Katrina:
- At 2 minutes: 16/2 = 8
- At 5 minutes: 40/5 = 8
- At 12 minutes: 96/12 = 8
- At 20 minutes: 160/20 = 8
Both Kimberly and Katrina did an equal number of jumping jacks per minute, so the answer is: Both.
3. The person showing a proportional relationship between time and # of jumping jacks ______
To determine the person who shows a proportional relationship between time and the number of jumping jacks, we need to check if the ratio of jumping jacks to time remains constant.
Let's compare the ratios at different time points for Kimberly and Katrina:
- Kimberly:
- At 3 minutes: 28/3 = 9.33
- At 8 minutes: 58/8 = 7.25
- At 12 minutes: 82/12 = 6.83
- At 16 minutes: 106/16 = 6.63
- Katrina:
- At 2 minutes: 16/2 = 8
- At 5 minutes: 40/5 = 8
- At 12 minutes: 96/12 = 8
- At 20 minutes: 160/20 = 8
The ratios remain the same for both Kimberly and Katrina, indicating a proportional relationship between time and the number of jumping jacks. So, the answer is: Both.
are you sure?
Apologies for the errors in my previous response. Let me correct it.
1. The person that did the most jumping jacks initially before _____
To determine the person who did the most jumping jacks initially, we need to compare the number of jumping jacks they did at the same time point, which is at 3 minutes for both Kimberly and Katrina.
Number of jumping jacks at 3 minutes:
- Kimberly: 28
- Katrina: 16
So, Kimberly did the most jumping jacks initially.
2. The person doing the most jump jacks per minute ______
To determine the person who did the most jumping jacks per minute, we need to compare the rate of jumping jacks they did, which is calculated by dividing the number of jumping jacks by the time in minutes.
Rate of jumping jacks per minute:
- Kimberly:
- At 3 minutes: 28/3 = 9.33
- At 8 minutes: 58/8 = 7.25
- At 12 minutes: 82/12 = 6.83
- At 16 minutes: 106/16 = 6.63
Average rate of jumping jacks per minute: (9.33 + 7.25 + 6.83 + 6.63) / 4 = 7.51
- Katrina:
- At 2 minutes: 16/2 = 8
- At 5 minutes: 40/5 = 8
- At 12 minutes: 96/12 = 8
- At 20 minutes: 160/20 = 8
Average rate of jumping jacks per minute: (8 + 8 + 8 + 8) / 4 = 8
Both Kimberly and Katrina have an average rate of 8 jumping jacks per minute. So, the answer is: Both.
3. The person showing a proportional relationship between time and # of jumping jacks ______
To determine the person who shows a proportional relationship between time and the number of jumping jacks, we need to check if the ratio of jumping jacks to time remains constant.
Let's compare the ratios at different time points for Kimberly and Katrina:
- Kimberly:
- At 3 minutes: 28/3 = 9.33
- At 8 minutes: 58/8 = 7.25
- At 12 minutes: 82/12 = 6.83
- At 16 minutes: 106/16 = 6.63
- Katrina:
- At 2 minutes: 16/2 = 8
- At 5 minutes: 40/5 = 8
- At 12 minutes: 96/12 = 8
- At 20 minutes: 160/20 = 8
The ratios are not constant for both Kimberly and Katrina, as the values vary at different time points. So, the answer is: Neither.
Apologies for the confusion in my previous response.
To answer these questions, let's analyze the data for each person step-by-step:
1. To determine the person who did the most jumping jacks initially, compare the first data point for each person:
- Kimberly: 28 jumping jacks after 3 minutes.
- Katrina: 16 jumping jacks after 2 minutes.
Comparing these values, we can see that Kimberly did more jumping jacks initially.
Therefore, the answer to question 1 is:
1. The person that did the most jumping jacks initially before Katrina is Kimberly.
2. To find the person doing the most jump jacks per minute, we can calculate the rate by dividing the total number of jumping jacks by the time in minutes:
- Kimberly:
- (58 - 28) jumping jacks / (8 - 3) minutes = 6 jumping jacks per minute
- (82 - 58) jumping jacks / (12 - 8) minutes = 6 jumping jacks per minute
- (106 - 82) jumping jacks / (16 - 12) minutes = 6 jumping jacks per minute
- Katrina:
- (40 - 16) jumping jacks / (5 - 2) minutes = 8 jumping jacks per minute
- (96 - 40) jumping jacks / (12 - 5) minutes = 10 jumping jacks per minute
- (160 - 96) jumping jacks / (20 - 12) minutes = 12 jumping jacks per minute
Comparing these rates, we can see that Katrina does the most jumping jacks per minute.
Therefore, the answer to question 2 is:
2. The person doing the most jump jacks per minute is Katrina.
3. To identify the person showing a proportional relationship between time and the number of jumping jacks, we need to check if the rate of increase in jumping jacks per minute is constant for each person.
- Kimberly:
- Rate from 3 to 8 minutes: 6 jumping jacks per minute
- Rate from 8 to 12 minutes: 6 jumping jacks per minute
- Rate from 12 to 16 minutes: 6 jumping jacks per minute
Since the rate is constant, Kimberly shows a proportional relationship between time and the number of jumping jacks.
- Katrina:
- Rate from 2 to 5 minutes: 8 jumping jacks per minute
- Rate from 5 to 12 minutes: 10 jumping jacks per minute
- Rate from 12 to 20 minutes: 12 jumping jacks per minute
Since the rate is not constant, Katrina does not show a proportional relationship between time and the number of jumping jacks.
Therefore, the answer to question 3 is:
3. The person showing a proportional relationship between time and the number of jumping jacks is Kimberly.
In summary:
A. Neither Kimberly nor Katrina did the most jumping jacks initially before Katrina.
B. Katrina does the most jumping jacks per minute.
C. Kimberly shows a proportional relationship between time and the number of jumping jacks.
D. Both Katrina and Kimberly do not show a proportional relationship between time and the number of jumping jacks.
To answer these questions, we need to analyze the data provided for Kimberly and Katrina.
1. The person that did the most jumping jacks initially before _____
To find out who did the most jumping jacks initially, we need to compare their data at the first time interval. In this case, the first time interval is 3 minutes for Kimberly and 2 minutes for Katrina. By comparing their respective number of jumping jacks at this time interval, we can determine who did the most initially.
Kimberly: 28 jumping jacks at 3 minutes
Katrina: 16 jumping jacks at 2 minutes
Comparing these values, we can see that Kimberly did more jumping jacks initially. Therefore, the answer is: C. Kimberly.
2. The person doing the most jump jacks per minute ______
To determine who did the most jumping jacks per minute, we need to calculate their respective rates of completing jumping jacks per minute. This can be done by dividing the total number of jumping jacks by the corresponding time for each person.
Kimberly:
- 28 jumping jacks in 3 minutes = 9.33 jumping jacks per minute
- 58 jumping jacks in 8 minutes = 7.25 jumping jacks per minute
- 82 jumping jacks in 12 minutes = 6.83 jumping jacks per minute
- 106 jumping jacks in 16 minutes = 6.63 jumping jacks per minute
Katrina:
- 16 jumping jacks in 2 minutes = 8 jumping jacks per minute
- 40 jumping jacks in 5 minutes = 8 jumping jacks per minute
- 96 jumping jacks in 12 minutes = 8 jumping jacks per minute
- 160 jumping jacks in 20 minutes = 8 jumping jacks per minute
Comparing these rates, we can see that both Kimberly and Katrina have the same rate of completing jumping jacks per minute, which is 8 jumping jacks per minute. Therefore, the answer is: D. both.
3. The person showing a proportional relationship between time and the number of jumping jacks _____
To determine who shows a proportional relationship between time and the number of jumping jacks, we need to examine the data points for each person. In a proportional relationship, the ratio of the number of jumping jacks to the time should remain constant.
Kimberly:
- Ratio at 3 minutes: 28/3 ≈ 9.33
- Ratio at 8 minutes: 58/8 ≈ 7.25
- Ratio at 12 minutes: 82/12 ≈ 6.83
- Ratio at 16 minutes: 106/16 ≈ 6.63
Katrina:
- Ratio at 2 minutes: 16/2 = 8
- Ratio at 5 minutes: 40/5 = 8
- Ratio at 12 minutes: 96/12 = 8
- Ratio at 20 minutes: 160/20 = 8
Comparing these ratios, we can see that both Kimberly and Katrina show a constant ratio between the number of jumping jacks and time. Therefore, the answer is: D. both.