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
#Katrina
Kimberly
Neither
#Both
7. 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
06
20 20
100
The person doing the most jumping jacks per minute is Kimberly, as she completes more jumping jacks in each given period of time compared to Katrina.
The person showing a proportional relationship between time and jumping jacks is Katrina, as the number of jumping jacks she completes increases proportionally as the time increases.
The person that did the most jumping jacks initially before the time started cannot be determined based on the given information.
Therefore, the answer is neither Kimberly nor Katrina.
12. Suppose that the water level of a river is 34 feet after 3 days of rain and 62 feet after 10 days of rain.
Given the two points we know: (3, 34) and (10, 62) what would the point-slope equation look like?
(1 point)
(y - 10) = 4(x + 62)
(y - 3) = 4(x - 34)
(y - 34) = 4(x - 3)
(y - 34) = 4(x - 10)
To find the point-slope equation using the given points (3, 34) and (10, 62), we need to find the slope (m) first. Slope is determined by the change in y divided by the change in x.
m = (y2 - y1) / (x2 - x1)
m = (62 - 34) / (10 - 3)
m = 28 / 7
m = 4
Now we can use the slope (4) and one of the points (3, 34) to form the point-slope equation.
(y - y1) = m(x - x1)
(y - 34) = 4(x - 3)
Therefore, the correct point-slope equation is (y - 34) = 4(x - 3).
1. The person doing the most jumping jacks per minute: Both Katrina and Kimberly can complete different numbers of jumping jacks per minute, as there is no information provided in the given tables to determine who does the most.
2. The person showing a proportional relationship between time and number of jumping jacks: Both Katrina and Kimberly can show a proportional relationship between time and number of jumping jacks, as indicated by the increasing number of jumping jacks as time increases in both of their tables.
3. The person that did the most jumping jacks initially before the time started: Neither Katrina nor Kimberly did any jumping jacks initially before the time started, as indicated by their tables starting with zero minutes and zero jumping jacks.
To determine the person doing the most jumping jacks per minute, you would compare the number of jumping jacks completed by each person in a given minute.
First, examine the tables provided:
Kimberly:
Time (min): 3, 8, 12, 16
Jumping Jacks: 28, 58, 82, 106
Katrina:
Time (min): 2, 5, 10, 20
Jumping Jacks: 16, 40, 60, 100
To find the number of jumping jacks done per minute for each person, divide the number of jumping jacks by the corresponding time:
For Kimberly:
Jumping Jacks per minute:
- Between 3 and 8 minutes: (58-28) / (8-3) = 30 / 5 = 6 jumping jacks per minute
- Between 8 and 12 minutes: (82-58) / (12-8) = 24 / 4 = 6 jumping jacks per minute
- Between 12 and 16 minutes: (106-82) / (16-12) = 24 / 4 = 6 jumping jacks per minute
For Katrina:
Jumping Jacks per minute:
- Between 2 and 5 minutes: (40-16) / (5-2) = 24 / 3 = 8 jumping jacks per minute
- Between 5 and 10 minutes: (60-40) / (10-5) = 20 / 5 = 4 jumping jacks per minute
- Between 10 and 20 minutes: (100-60) / (20-10) = 40 / 10 = 4 jumping jacks per minute
Based on this calculation, Katrina did the most jumping jacks per minute with a rate of 8 jumping jacks. Therefore, the answer to the first question is Katrina.
For the second question, to identify the person showing a proportional relationship between time and the number of jumping jacks, you need to check if the jumping jacks increase continuously in a predictable way as the time increases. If the ratio between jumping jacks and time remains constant, it represents a proportional relationship.
For Katrina:
- Between 2 and 5 minutes: The ratio of jumping jacks to time is 24 / 3 = 8 jumping jacks per minute.
- Between 5 and 10 minutes: The ratio of jumping jacks to time is 20 / 5 = 4 jumping jacks per minute.
- Between 10 and 20 minutes: The ratio of jumping jacks to time is 40 / 10 = 4 jumping jacks per minute.
We see that for Katrina, the ratio of jumping jacks to time remains the same (8:3, 4:1, 4:1), indicating a proportional relationship between time and the number of jumping jacks.
For Kimberly:
- Between 3 and 8 minutes: The ratio of jumping jacks to time is 30 / 5 = 6 jumping jacks per minute.
- Between 8 and 12 minutes: The ratio of jumping jacks to time is 24 / 4 = 6 jumping jacks per minute.
- Between 12 and 16 minutes: The ratio of jumping jacks to time is 24 / 4 = 6 jumping jacks per minute.
Similarly for Kimberly, the ratio of jumping jacks to time remains the same (6:1, 6:1, 6:1), indicating a proportional relationship between time and the number of jumping jacks.
Therefore, the answer to the second question is BOTH Katrina and Kimberly show a proportional relationship between time and the number of jumping jacks.
For the last question, to determine the person who did the most jumping jacks initially before the time started, you need to look at the starting values for each person.
Katrina started at 16 jumping jacks while Kimberly started at 28 jumping jacks.
Comparing these values, we see that Kimberly did the most jumping jacks initially before the time started.
Therefore, the answer to the last question is Kimberly did the most jumping jacks initially before the time started.