Hi~ ^-^ please help me with this problem

In high-school 135 freshmen were interviewed: thirty-five of them took PE, 42 took BIO, 60 took ENG, 10 took PE and BIO, 15 took PE and ENG, 7 took BIO and ENG, 5 took all three subjects.
a) How many students took none of the three subjects?
b) How many students took PE but not BIO?

a) 25 students took none of the three

b) 25 students took PE but not BIO

Step-by-step explanation:

a)

To find how many students took none, we can use the following formula (union of three events) to find the number of students that took PE or BIO or ENG:

P(PE or BIO or ENG) = P(PE) + P(BIO) + P(ENG) - P(PE and BIO) - P(PE and ENG) - P(BIO and ENG) + P(PE and BIO and ENG)

P(PE or BIO or ENG) = 35 + 42 + 60 - 10 - 15 - 7 + 5 = 110

110 students took any of the three, and the total students is 135, so we have 135 - 110 = 25 students that took none of the three.

b)

To find the students that took PE but not BIO, we can just subtract the students that took PE and BIO from the students that took PE:

P(PE and not BIO) = P(PE) - P(PE and BIO) = 35 - 10 = 25 students

4444444444444 i think

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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step-by-step explanation: