a. To determine which person is doing more jumping jacks per second, we can calculate the jumping jacks per second for each person.
For Kimberly:
- between 3-8 seconds: (37-17) / (8-3) = 4 jumping jacks per second
- between 8-12 seconds: (53-37) / (12-8) = 4 jumping jacks per second
- between 12-16 seconds: (69-53) / (16-12) = 4 jumping jacks per second
For Katrina:
- between 2-5 seconds: (25-10) / (5-2) = 5 jumping jacks per second
- between 5-12 seconds: (60-25) / (12-5) = 7.86 jumping jacks per second
- between 12-20 seconds: (100-60) / (20-12) = 8.33 jumping jacks per second
Therefore, Katrina is doing more jumping jacks per second.
b. To determine who had done more jumping jacks initially before the timer started, we look at the data at 0 seconds for each person. However, the information at 0 seconds is not provided in the tables. Therefore, we cannot determine who did more jumping jacks initially before the timer started based on the given information.
c. A proportional relationship exists when the ratio of jumping jacks to time remains constant. Looking at the data, we can determine that Kimberly's jumping jacks per second remain constant at 4 jumping jacks per second regardless of the time intervals. Therefore, Kimberly shows a proportional relationship between the number of jumping jacks and time. On the other hand, Katrina's jumping jacks per second vary depending on the time intervals, so she does not show a proportional relationship.
The tables below show the number of jumping jacks completed after a given period of time in seconds.
Kimberly:
Time (seconds)
• 3
• 8
• 12
• 16
Jumping Jacks
• 17
• 37
• 53
• 69
katrina:
Time (seconds)
• 2
• 5
• 12
• 20
Jumping Jacks
• 10
• 25
• 60
• 100
(3 points)
a. Which person is doing more jumping jacks per second? _
b. Which person had done more jumping jacks initially before the timer started? _
c. Which person shows a proportional relationship? _
1 answer