Linda is conducting an experiment to determine how much pasta people would eat when given a serving bowl of a certain size. She manipulated the serving bowl size and then measured the two variables. Based on the fact that Linda is going to assign people to different serving bowl sizes, this would be considered a(n):

Linda assigning people different bowl size is the Independent Variable

Explanation:

Linda is conducting an experimental research , analysing the effect of pasta bowl size on pasta consumption.

The causal variable in a research is an independent variable. And, the variable effected by the independent (causal) variable is the dependent variable.

In this case, pasta serving bowl sizes (quantity) are changed to observe & analyse their impact on amount of pasta eaten by people. Hence :

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."