Answers: 585, 587, and 593
Basically everything except 599
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Why?
Those answers in bold are closer to 590 than they are to 580 or 600. When rounding to the nearest ten (not tenth) we look at the units digit. If it is 5 or larger, then we bump the tens digit up by 1 and replace the units digit with a 0.
This explains why 585 and 587 round to 590
The number 599 rounds to 600 for similar reasoning, but we cross it off the list since we want 590.
The number 593 rounds to 590 because the 3 in the units digit isn't 5 or larger. So we just replace the 3 with 0 and keep everything else as is.