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By observing a set of data values, Tasha used a calculator for the tire diameter at the tread and circumference data and got an equation for the least-squares line: [tex]y = 0.1 + 3.1x[/tex].

Based on this information, select the statement that is TRUE.

A. A tire with a 28-inch diameter at the tread will have a circumference of 99.3 inches.
B. A tire with a 32-inch diameter at the tread will have a circumference of 86.9 inches.
C. A tire with a 30-inch diameter at the tread will have a circumference of 93.1 inches.
D. A tire with a 35-inch diameter at the tread will have a circumference of 1241 inches.

Answer :

The correct statement is "A tire with a 32-inch diameter at the tread will have a circumference of 99.3 inches"(b).

The equation for the least-squares line given is:

y = 0.1 + 3.1x

Where:

  • y represents the circumference of the tire.
  • x represents the diameter of the tire at the tread.

To find the circumference of a tire with a given diameter at the tread, you can plug the value of x into the equation.

Let's evaluate the options:

a. A tire with a 28-inch diameter at the tread will have a circumference:

y = 0.1 + 3.1 * 28

y = 0.1 + 86.8 = 86.9 inches

b. A tire with a 32-inch diameter at the tread will have a circumference:

y = 0.1 + 3.1 * 32

y = 0.1 + 99.2 = 99.3 inches

c. A tire with a 30-inch diameter at the tread will have a circumference:

y = 0.1 + 3.1 * 30

y = 0.1 + 93 = 93.1 inches

d. A tire with a 35-inch diameter at the tread will have a circumference:

y = 0.1 + 3.1 * 35

y = 0.1 + 108.5 = 108.6 inches

Based on the given equation, the statement that is TRUE is:

b. A tire with a 32-inch diameter at the tread will have a circumference of 99.3 inches

For more questions on Tire Circumference.

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