In a controlled experiment, a scientist is studying how long it takes feathers of different sizes to fall to the ground. What is the manipulated/independent variable

independent variable: Size of the feather.

Explanation:

In an experiment, the manipulated/independent variable is, as the name implies, the variable that the scientist can control.

In this case, the scientist has only one variable that he can control at will, and this is the size of the feather (he can choose which feather he uses for the experiment)

So the manipulated variable will be the size of the feather.

And the dependent variable is the one that "answers" to the changes in the manipulated variable.

In this case, will be the time that it takes to the feather to fall to the ground.

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c) both a and b.