Answer:
If the circular track has a circumference of 0.5 mile, then its circumference in feet is:
0.5 mile x 5,280 feet/mile = 2,640 feet
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference and r is the radius of the circle. Substituting the values we have:
2,640 = 2 x 3.14 x r
Solving for r, we get:
r = 2,640 / (2 x 3.14) = 420.38 feet
Therefore, the radius of the circular track, in feet, is approximately 420.38 feet. Rounded to the nearest hundredth, the answer is 420.38 feet, which corresponds to the third option.