graphing linear equations review
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
the person doing the most jumping jacks _
the person that did the most jumping hacks initially before the time started _
the person showing a proportional relationship between time and # of jumping jacks _
katrina kimberly neither both
Based on the given tables:
- The person doing the most jumping jacks is Kimberly. As the time increases, the number of jumping jacks completed also increases consistently for Kimberly.
- The person that did the most jumping jacks initially before the time started cannot be determined from the given information as it does not specify the number of jumping jacks at time 0.
- Neither Katrina nor Kimberly shows a proportional relationship between time and number of jumping jacks.
To determine the person who did the most jumping jacks, you need to compare the maximum number of jumping jacks completed by Kimberly and Katrina. You can find this information by looking at the "Number of Jumping Jacks" column in each table.
For Kimberly:
- After 3 minutes: 28 jumping jacks
- After 8 minutes: 58 jumping jacks
- After 12 minutes: 82 jumping jacks
- After 16 minutes: 106 jumping jacks
For Katrina:
- After 2 minutes: 16 jumping jacks
- After 5 minutes: 40 jumping jacks
- After 12 minutes: 96 jumping jacks
- After 20 minutes: 160 jumping jacks
By comparing the maximum numbers, you can see that Kimberly did the most jumping jacks with 106, as Katrina's highest is 160. Therefore, Kimberly is the person who did the most jumping jacks.
To find the person who did the most jumping jacks initially before the time started, you need to look at the number of jumping jacks when the time was 0 minutes. However, since the given tables do not provide that information, we cannot determine who did the most jumping jacks initially.
To identify the person showing a proportional relationship between time and the number of jumping jacks, we need to examine if the ratio of the number of jumping jacks to time remains constant for both Kimberly and Katrina.
Let's calculate the ratios for both individuals:
For Kimberly:
- 28/3 = 9.33 (approximately)
- 58/8 = 7.25
- 82/12 = 6.83 (approximately)
- 106/16 = 6.63 (approximately)
For Katrina:
- 16/2 = 8
- 40/5 = 8
- 96/12 = 8
- 160/20 = 8
By comparing the ratios, we can see that both Kimberly and Katrina show a proportional relationship between time and the number of jumping jacks, with a ratio of approximately 8 for both. Therefore, both Kimberly and Katrina exhibit a proportional relationship between time and the number of jumping jacks.
To determine the answers to these questions, let's analyze the given tables:
1. The person doing the most jumping jacks: We can compare the maximum number of jumping jacks for each person.
Kimberly: The maximum number of jumping jacks for Kimberly is 106.
Katrina: The maximum number of jumping jacks for Katrina is 160.
Based on the comparison, Katrina did the most jumping jacks.
2. The person that did the most jumping jacks initially before the time started: By looking at the first entry in each table, we can determine the initial number of jumping jacks.
Kimberly: The initial number of jumping jacks for Kimberly is 28.
Katrina: The initial number of jumping jacks for Katrina is 16.
Based on the comparison, Kimberly did the most jumping jacks initially before the time started.
3. The person showing a proportional relationship between time and the number of jumping jacks: To determine this, we need to check whether the ratio of jumping jacks to time remains constant for each person.
Kimberly: To check the ratio for Kimberly, we can divide the number of jumping jacks by the corresponding time:
28/3 ≈ 9.33
58/8 = 7.25
82/12 ≈ 6.83
106/16 = 6.63
Katrina: To check the ratio for Katrina, we can divide the number of jumping jacks by the corresponding time:
16/2 = 8
40/5 = 8
96/12 = 8
160/20 = 8
For both Kimberly and Katrina, the ratios remain constant at approximately 6.6 and 8, respectively. Therefore, both Kimberly and Katrina show a proportional relationship between time and the number of jumping jacks.
In summary:
- Katrina did the most jumping jacks.
- Kimberly did the most jumping jacks initially before the time started.
- Both Kimberly and Katrina show a proportional relationship between time and the number of jumping jacks.
wasnt the person showing a proportional relationship between time and # of jumping jacks katrina
Apologies for the confusion.
You are correct. Upon re-analyzing the ratios, it appears that only Katrina shows a proportional relationship between time and the number of jumping jacks. The ratios for Katrina remain constant at 8, indicating a proportional relationship. On the other hand, the ratios for Kimberly vary, indicating a non-proportional relationship. Therefore, only Katrina shows a proportional relationship between time and the number of jumping jacks.