Final answer:
The unit rate is calculated by multiplying 10 2/3 rotations by the reciprocal of 1/4 minute. The calculation yields 42 rotations per minute, making the answer D. 42 rotations per minute.
Step-by-step explanation:
The unit rate of 10 2/3 rotations in 1/4 minutes can be found by calculating how many rotations would occur in one full minute. To do this, we convert 10 2/3 rotations to an improper fraction, which is 32/3 rotations. We then divide this number by 1/4 minute to find the rate per minute:
(32/3 rotations) / (1/4 minutes) = (32/3) × (4/1) rotations per minute = 128/3 rotations per minute.
By converting the fraction 128/3 into a whole number, we get approximately 42.67, which rounds down to 42 rotations per minute.
Therefore, the correct answer is D. 42 rotations per minute.