Around the third week of a college class, a professor decides she’s had enough, is tired of dealing with bureaucracies, and wants out. so one day, instead of coming to class, she flies to tahiti and sells souvenirs on the beach. if this happened, the college would simply assign a substitute to finish the course. what does this tell you about the nature of the authority wielded by a professor?

It is a "legal-rational authority".

Legal-rational authority is one that is based on plainly characterized laws. The submission of individuals do not depend on the limit of any pioneer however on the authenticity and capability that methodology and laws offer to people in authority. Contemporary society relies upon this kind of rationalization, as the complexities of its issues require the development of an administration that typifies order and systematization.

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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."