Zoe keeps track of the miles per gallon her car gets per week. She has accumulated the following data:
(1, 24), (2, 24.38), (3, 24.76), (4, 25.14)
A. The common difference is 0.38
B. The common difference is 0.76
C. The common ratio is 0.99
D. The common ratio is 1.02
The anwser is 0.38. It’s because 25.14 - 24.78 = 0.38, 24.78 -24.38 = 0.38, and 24.38 - 24 = 0.38. The common difference is 0.38
The given data represents the relationship between the week number and the miles per gallon. To determine the common difference or common ratio, we need to see if there is a consistent pattern in the values.
Looking at the data, we can see that the miles per gallon increases by 0.38 with each week:
(1, 24)
(2, 24.38) - increase of 0.38
(3, 24.76) - increase of 0.38
(4, 25.14) - increase of 0.38
Therefore, the common difference is 0.38.
So, the correct answer is:
A. The common difference is 0.38.
To determine whether there is a common difference or common ratio in the given data, we need to look for a pattern.
In this case, we are given the miles per gallon (MPG) for Zoe's car over four weeks. We can plot the data points on a graph with the x-axis representing the weeks and the y-axis representing the MPG.
Plotting the given data points, we have:
(1, 24)
(2, 24.38)
(3, 24.76)
(4, 25.14)
Connecting these points on the graph, we can see that the values are increasing gradually each week, indicating a linear relationship. This suggests that there is a common difference between consecutive terms rather than a common ratio.
To find the common difference, we can subtract consecutive y-values:
24.38 - 24 = 0.38
24.76 - 24.38 = 0.38
25.14 - 24.76 = 0.38
The differences between consecutive terms are all the same (0.38), confirming that there is a common difference.
Therefore, the correct answer is:
A. The common difference is 0.38
Subtract the mpg for each week from the following week.
25.14 - 25.76 = ?