Madelyn's math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of best fit. Based on the line of best fit, what quiz score should someone who studied 5 hours expect?
0
x
y
0
(0,55)
(1,62)
(2,69)
(3,76)
(4,83)
Quiz Score
Time Spent on Homework per Week (hours
We need more information to determine the expected quiz score for someone who studied 5 hours. Can you provide the equation of the line of best fit or the coordinates of another point on the line?
quiz scores
111
104
97
90
83
76
69
62
55
Time Spent on Homework per Week (hours)
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Using the given data, we can create a scatter plot and find the equation of the line of best fit using linear regression. Using this equation, we can then predict the quiz score for someone who studied 5 hours.
The equation of the line of best fit is:
Quiz Score = -9.31(Time Spent on Homework per Week) + 114.81
To predict the quiz score for someone who studied 5 hours, we plug in 5 for the time:
Quiz Score = -9.31(5) + 114.81
Quiz Score = 66.66
Therefore, someone who studied 5 hours can expect a quiz score of approximately 67.
A researcher studied the relationship between the number of times a certain species of cricket will chirp in one minute and the temperature outside. Her data is expressed in the scatter plot and line of best fit below. Based on the line of best fit, what temperature would it most likely be outside if this same species of cricket were measured to chirp 116 times in one minute?
0
x
y
0
(100,63)
(104,64)
Temperature (Degrees Fahrenheit)
64
63
62
61
60
59
58
57
56
55
54
53
Chirps Per Minute
60
64
68
72
76
80
84
88
92
96
100
104
We can use the line of best fit to predict the temperature outside if the cricket chirps 116 times in one minute. From the given scatter plot and line of best fit, we can estimate that the equation of the line is:
Temperature = 0.38(Chirps per minute) + 52.49
To find the temperature when the cricket chirps 116 times per minute, we plug in 116 for chirps per minute:
Temperature = 0.38(116) + 52.49
Temperature ≈ 96.68°F
Therefore, if the cricket were measured to chirp 116 times in one minute, the temperature outside would most likely be approximately 96.68°F.
To determine what quiz score someone who studied 5 hours should expect based on the line of best fit, you need to look at the coordinates given and the corresponding quiz scores.
Given the coordinates:
(0, 55)
(1, 62)
(2, 69)
(3, 76)
(4, 83)
These coordinates represent the number of hours studied and the corresponding quiz scores. To find the line of best fit, you can calculate the equation of the line using regression analysis methods.
Once you have the equation of the line, you can substitute 5 hours into the equation to estimate the expected quiz score. Without the equation, it is not possible to provide a precise answer.
To determine the quiz score someone who studied 5 hours should expect, we need to use the line of best fit on the scatter plot of quiz scores versus the number of hours studied. The line of best fit represents the trend or relationship between these two variables.
First, let's analyze the data given. The given data shows the quiz scores plotted against the number of hours studied:
(0, 55), (1, 62), (2, 69), (3, 76), (4, 83)
Now, to find the equation of the line of best fit, we can calculate the slope (m) and y-intercept (b).
Step 1: Calculate the slope (m):
m = (change in y) / (change in x) = (83 - 55) / (4 - 0) = 28 / 4 = 7
Step 2: Calculate the y-intercept (b):
Using the slope-intercept form of a line (y = mx + b), we can substitute the slope (m) and the coordinates of any point (x, y) on the line. Let's use the point (2, 69):
69 = 7 * 2 + b
69 = 14 + b
b = 69 - 14
b = 55
Therefore, the equation of the line of best fit is: y = 7x + 55.
Now, we can substitute x = 5 into the equation to determine the expected quiz score for studying 5 hours.
y = 7 * 5 + 55
y = 35 + 55
y = 90
Therefore, someone who studied 5 hours should expect a quiz score of 90.