The temperature on a cloudy night is likely to be those on a clear night all other factors being equal

d. i assume the underlined word is "role." reformat if it isn't.

explanation:

role is closest to part because when replacing words, "playing a vital decision," "playing a vital activity," and "playing a vital dollar" don't make logical sense. the only meaningful choice is "playing a vital part."

this fits one of merriam-webster's definitions of role: "a function or part performed especially in a particular operation or process."

it all depends on how long the hours are. i think they wouldn't approve of it. in my opinion.