Answer:
Step-by-step explanation:
Given that among 500 freshmen pursuing a business degree at a university, 315 are enrolled in an economics course, 213 are enrolled in a mathematics course, and 123 are enrolled in both an economics and a mathematics course.
From the above we find that
a) either economics of Math course is

Out of 500 students 405 have taken either Math or Economics
Hence
c) student who have taken neither = 
Exactly one course is either math or economics - both
= 
Given:
Point S is translated 5 units to the left and 12 units up to create point S'.
To find:
The distance between the points S and S'.
Solution:
Point S is translated 5 units to the left and 12 units up to create point S'.
The diagram for the given problem is shown below.
From the below figure it is clear that the distance between the point S and S' is the height of a right triangle whose legs are 5 units and 12 units.
By Pythagoras theorem,




Taking square root on both sides.


Therefore, the distance between S and S' is 13 units.