Mathematics, 30.01.2020 14:56 tiwaribianca475

In a fifth grade class, 3/4 of the students like to go to the movies. of the students who like to go to the movies, 2/3 of them like action movies. of the students who like to go to action movies, 4/5 of hem also like comedies. what fraction of the students in class like to go to action movies? what fraction of the students like to go to action and comedies?

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Hi, thank you for posting your question here at .

The process of solving this problem is as follows:

Students who like action movies: 3/4*2/3 = 1/2 of the fifth grade class students
Students who like comedies: 1/2*4/5 = 2/5 of the fifth grade class students

Answer from: mparra4761

1) 1/2 students like to go to action movies,

2) 2/5 students like to go to action and comedies.

Step-by-step explanation:

Let the total number of students are x,

Thus, the number of students who like to go movies = 3/4 of total students = $\frac{3x}{4}$

The number of students who like to go action movies = 2/3 of students who like to go movies = 2/3 of 3x/4 = $\frac{6x}{12}$ = x/2

Hence, the total fraction of students who like to go action movies = Number of students who like to go action movies / Total students

= $\frac{x/2}{x}$

= 1/2

Now, the number of student who like to go comedy movie = 4/5 of the students who like to go action movies

= 4/5 of x/2

= $\frac{4x}{10}$

= $\frac{2x}{5}$

Hence, the fraction of students who like to go comedy movies

= Total students who like comedies/ Total students

= $\frac{2x/5}{x}$

= 2/5

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

Answer from: Quest

The answer would be 484

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