In order for a gear to work in a piece of machinery, the radius of the gear, r, must be greater than 4 cm, but not exceed 4.1 cm. Which compound inequality represents the situation?r > 4 and r ≤ 4.1r > 4 or r ≤ 4.1r < 4 and r ≥ 4.1r < 4 or r ≥ 4.1

“Greater than 4 cm” means r > 4, and “not exceed 4.1 cm” means r ≤ 4.1. Both conditions must be true at the same time, so they are joined by “and.” Therefore, the correct choice is A: r > 4 and r ≤ 4.1.

AI-written and checked against the verified answer.