In a group of 20 people who like rock, country, and classical music, 14 like rock, 17 like classical, 11 like both rock and country, 9 like both rock and classical, 12 like both country and classical, and 8 like rock, country, and classical.
how many like country

There are 13 people who like country music.

Step-by-step explanation:

Since we have given that

Number of people who like rock n(A) = 14

Number of people who like classical n(B) = 17

Let the number of people who like country n(C) be 'x'.

Number of people who like both rock and country = 11

Number of people who like both rock and classical = 9

Number of people who like both country and classical = 12

Number of people who like rock, country and classical = 8

As we know the formula:

n(A∪B∪C)=n(A)+n(B)+n(C)-n(A∩B)-n(B∩C)-n(C∩A)+n(A∩B∩C)

Hence, there are 13 people who like country music.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

answer: y = -12x + 108

step-by-step explanation: do (y = m x+b) formula.