Ellen must take 4 courses this semester. She has a list of 3 math courses and 4 science courses to from which to choose. (a) Initially Ellen is under the impression that she can simply take any four of the courses on the list. If this was the case, how many different ways could Ellen select the four courses?

So the number of total combinations is 35.

Step-by-step explanation:

We know that Ellen must take 4 courses this semester. She has a list of 3 math courses and 4 science courses.  

Therefore, she have total 7 courses.  

So, we calculate the number of combinations to choose 4 out of 7  courses.

We get:

So the number of total combinations is 35.

answer: a and c are correct

step-by-step explanation:

the +5 is the vertical translation

the added negative symbol in front is the reflection over the y-axis