A researcher compared the heights and shoe sizes for 50 men, selected at random. The equation shown describes a line of the best fit for the data where x is the shoe size and y is the height, in inches. y = 1.6x + 48
A. 7 1/2
B. 10 1/2
C. 12
D. 14
Based on the given equation y = 1.6x + 48, we can determine the slope of the line, which is 1.6. Since the slope represents the change in y for every 1 unit change in x, we can say that for every 1 unit increase in shoe size (x), the height (y) will increase by 1.6 inches.
Now, let's look at the answer choices:
A. 7 1/2
B. 10 1/2
C. 12
D. 14
If the shoe size is 7 1/2, we can plug it into the equation:
y = 1.6(7.5) + 48
y = 12 + 48
y = 60
So, if the shoe size is 7 1/2, the predicted height is 60 inches.
If the shoe size is 10 1/2, we can plug it into the equation:
y = 1.6(10.5) + 48
y = 16.8 + 48
y = 64.8
So, if the shoe size is 10 1/2, the predicted height is 64.8 inches.
If the shoe size is 12, we can plug it into the equation:
y = 1.6(12) + 48
y = 19.2 + 48
y = 67.2
So, if the shoe size is 12, the predicted height is 67.2 inches.
If the shoe size is 14, we can plug it into the equation:
y = 1.6(14) + 48
y = 22.4 + 48
y = 70.4
So, if the shoe size is 14, the predicted height is 70.4 inches.
Therefore, the correct answer is:
D. 14
To determine the height of a man with a shoe size of 10 1/2, we can substitute the shoe size value (10 1/2) into the equation y = 1.6x + 48 and solve for y.
Given: x = 10 1/2
Substituting x = 10 1/2 into the equation, we have:
y = 1.6(10 1/2) + 48
First, we need to convert the shoe size 10 1/2 into decimal form. To do this, we can convert the fraction 1/2 into decimal form:
1/2 = 0.5
Now, we can substitute the decimal value of the shoe size into the equation:
y = 1.6(10.5) + 48
Next, we can calculate the multiplication:
y = 16.8 + 48
y = 64.8
Therefore, a man with a shoe size of 10 1/2 would have a height of approximately 64.8 inches.
The answer is not available in the given options, so it would be either not provided or there may be a mistake in the given options.
To determine the shoe size that corresponds to a certain height according to the given equation (y = 1.6x + 48), we need to rearrange the equation to solve for x (shoe size).
The equation is: y = 1.6x + 48
Let's plug in the height value (y) for the options provided to find the corresponding shoe size (x):
A. For 7 1/2, y = 7.5
7.5 = 1.6x + 48
B. For 10 1/2, y = 10.5
10.5 = 1.6x + 48
C. For 12, y = 12
12 = 1.6x + 48
D. For 14, y = 14
14 = 1.6x + 48
Now we can solve for x (shoe size) in each case.
A. 7.5 = 1.6x + 48
Subtract 48 from both sides:
-40.5 = 1.6x
Divide by 1.6:
x ≈ -25.31
B. 10.5 = 1.6x + 48
Subtract 48 from both sides:
-37.5 = 1.6x
Divide by 1.6:
x ≈ -23.44
C. 12 = 1.6x + 48
Subtract 48 from both sides:
-36 = 1.6x
Divide by 1.6:
x ≈ -22.50
D. 14 = 1.6x + 48
Subtract 48 from both sides:
-34 = 1.6x
Divide by 1.6:
x ≈ -21.25
Therefore, none of the given shoe sizes match any of the provided heights.