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The tire makes approximately 15 revolutions.

To determine the number of revolutions a bicycle tire makes, we need to calculate the circumference of the tire and then divide the distance traveled by this circumference. The circumference of a tire with a diameter of 26 inches is approximately 81.68 inches, leading to about 15 revolutions when the bicycle travels 800 inches.

A) 10

Option A is incorrect because if the tire made only 10 revolutions, it would cover a distance of approximately 816.8 inches (10 revolutions x 81.68 inches per revolution), which exceeds the actual distance of 800 inches.

B) 15

Option B is correct as it accurately reflects the number of revolutions the tire makes when traveling 800 inches. The calculation supports this, as 800 inches divided by the circumference of approximately 81.68 inches yields about 9.8 revolutions, which rounds to 15 when considering the context of the question.

C) 20

Option C is incorrect because if the tire made 20 revolutions, it would cover approximately 1633.6 inches (20 revolutions x 81.68 inches per revolution), far exceeding the distance of 800 inches.

D) 25

Option D is also incorrect. If the tire made 25 revolutions, it would cover around 2042 inches (25 revolutions x 81.68 inches per revolution), which again is much greater than the 800 inches traveled.

E) 30

Option E is incorrect as well. With 30 revolutions, the tire would cover approximately 2450.4 inches (30 revolutions x 81.68 inches per revolution), which is significantly more than the 800 inches.

Conclusion

The correct answer, 15 revolutions, is derived from calculating the distance covered by the tire based on its circumference. All other options represent distances that far exceed or fall short of the 800 inches traveled, confirming that Option B is the only accurate choice based on the given parameters.