Does the governor appoint the leaders of all state departments

state managers, governors are responsible for implementing state laws and overseeing the operation of the state executive branch. As state leaders, governors advance and pursue new and revised policies and programs using a variety of tools, among them executive orders, executive budgets, and legislative proposals and vetoes.

Governors carry out their management and leadership responsibilities and objectives with the support and assistance of department and agency heads, many of whom they are empowered to appoint. A majority of governors have the authority to appoint state court judges as well, in most cases from a list of names submitted by a nominations committee.

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."