Question

Alexander can earn money for the cans he recycles. Which of the following statements describes the variables in this situation correctly?
A. The number of cans recycled is the independent variable because it affects the amount of money earned.

B. The number of cans recycled is the dependent variable because it affects the amount of money earned.

C. The amount of money earned is the independent variable because it affects the number of cans recycled.

D. The amount of money earned is the dependent variable because it affects the number of cans recycl

Answer 1

I believe that your answer to this question would be "A" because the number of cans recycled don't depend on anything but the amount of money does. So your answer is "A"!!!! X) :D :)

Answer 2

Answer:

A. The number of cans recycled is the independent variable because it affects the amount of money earned.

Step-by-step explanation:

First, let's start by defining a matherical function:

A mathematical function is a relation that is established between two sets, through which each element of the first set is assigned a single element of the second set or none. The initial set or starting set is also called the domain; the final set or arrival set, can be called range.

The generic element of the domain is known as an independent variable; to the generic element of the range, as a dependent variable. This means that, in the framework of the mathematical function, the elements of the range depend on the elements of the domain.

Now, let's analyze the problem. Alexander can earn money for the cans he recycles. So, we can represent this situation as follows:

$y=ax$

Where:

$y=Money\hspace{3} earned\hspace{3} for\hspace{3} each \hspace{3} can \hspace{3}recycled\\a=Constant\hspace{3} which \hspace{3}represents \hspace{3}the\hspace{3} amount \hspace{3}of \hspace{3}money\hspace{3} earned\hspace{3} for\hspace{3} each\hspace{3} can\\x=Number\hspace{3}of\hspace{3}cans\hspace{3}recycled$

As we can see, the number of cans recycled is the independent variable, and the amount of money earned is the dependent variable, this is because the amount of money earned depends directly of the the number of cans recycled. For example, let's assume that alexander earns 0.5$ for each can recycled, and also let's assume that he reclycled 81 cans. So the amount of money he earns is:

$y(x)=ax\\\\y(81)=(0.5)*(81)=40.5$