To predict the stopping distance when traveling at a speed of 80 miles per hour, we will use the provided quadratic regression equation:
[tex]\[ y = 0.006x^2 + 0.31x + 4 \][/tex]
where:
- \( y \) is the stopping distance,
- \( x \) is the speed in miles per hour.
Here are the steps to find the stopping distance for a speed of 80 mph:
1. Substitute \( x = 80 \) into the equation:
[tex]\[
y = 0.006 \times (80)^2 + 0.31 \times 80 + 4
\][/tex]
2. Calculate \( 80^2 \):
[tex]\[
80^2 = 6400
\][/tex]
3. Multiply 0.006 by 6400:
[tex]\[
0.006 \times 6400 = 38.4
\][/tex]
4. Multiply 0.31 by 80:
[tex]\[
0.31 \times 80 = 24.8
\][/tex]
5. Add the results together with the constant term 4:
[tex]\[
y = 38.4 + 24.8 + 4 = 67.2
\][/tex]
Thus, the stopping distance at a speed of 80 miles per hour is predicted to be 67.2 feet.
b. The correct answer is [tex]\(\boxed{67.2 \, \text{ft}}\)[/tex]. However, as the given multiple-choice answers do not include this value, there might be an error in the provided options. The exact stopping distance should be [tex]\(\boxed{67.2 \, \text{ft}}\)[/tex].
