In a survey conducted by helena, a financial consultant, it was revealed of her 426 clients
288 own stocks.
200 own bonds.
184 own mutual funds.
123 own both stocks and bonds.
106 own both stocks and mutual funds.
102 own both bonds and mutual funds.
how many of helena's clients own stocks, bonds, and mutual funds? (assume each client invested in at least one of the three types of funds.)

There are 85 Helena's client own stocks, bonds and mutual funds.

Step-by-step explanation:

Since we have given that

Let A: who own stocks

B : who own bonds

C : who own mutual fund

So, According to question,

n(A) = 288

n(B) = 200

n(C) = 184

n(A∩B) = 123

n(B∩C) = 106

n( A∩C) = 102

n(A∪B∪C) = 426

As we know the formula :

Hence, there are 85 Helena's client own stocks, bonds and mutual funds.

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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