A film class had 33 students who liked Hitchcock movies, 21 students who liked Spielberg movies, and 17 students who liked both kinds of films. How many students were in the class if every students is represented in the survey

37 students were in the class.

Step-by-step explanation:

We solve this problem building the Venn's diagram of these values.

I am going to say that:

A is the number of students who liked Hitchcock movies.

B is the number of students who liked Spielberg movies.

C is the probability that a mean is neither of those.

We have that:

In which a is the number of students who liked Hitchcock movies but not Spielberg's and is the number of students who like both Hitchcock and Spielberg movies.

By the same logic, we have that:

How many students were in the class if every students is represented in the survey

This is

17 students who liked both kinds of films.

This means that

21 students who liked Spielberg movies

This means that . So:

33 students who liked Hitchcock movies

This means that . So:

Finally

37 students were in the class.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1