Final answer:
The acceptable diameters for golf balls according to the USGA standards must not be less than 1.680 inches (42.672 mm). Therefore, the acceptable diameters among the options given are 42.675 mm and 42.673 mm.
Step-by-step explanation:
The acceptable diameters for golf balls, as stipulated by the United States Golf Association (USGA) standards, falls within a specific range. All golf balls used in play must have a diameter not less than 1.680 inches (42.672 mm), so any golf ball with a diameter greater than this minimum can be used in professional play. With that said, the golf ball sizes provided in the question – 42.675 mm, 42.6668 mm, 42.664 mm, 42.673 mm, and erroneously 72.676 mm – need to be compared against this standard. Out of these, 42.664 mm is not acceptable as it does not meet the minimum diameter requirement. Also, 72.676 mm is practically irrelevant as it exceeds not just the size of a standard golf ball but is likely a typographical error. The acceptable diameters for golf balls are thus 42.675 mm and 42.673 mm since they are greater than the minimum required diameter.