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Cerrena [4.2K]
8 months ago
6

A class at Middlebury school collected date on the types of movies students prefer. Complete each statement using the table.

Mathematics
1 answer:
likoan [24]8 months ago
4 0

Based on the information of the table, you have:

1. The ratio is 105/150. By simplifying you get for the ratio 7/10.

2. The students that prefer action movies are 75+90 = 165 and the total numbe of students is 180+240 = 420. Then, the fraction of students who prefer action movies is:

165/420 = 11/28

3. The fraction of seventh graders students that prefer action movies is:

75/180 = 5/12

4. The percent of student that prefer comedy is:

105 + 150 = 255 total student that prefer comedy

420 total number of students

the fraction is:

(x/100)420 = 255

solve for x:

x = 255(100/420)

x = 60.71

the percent of students is 60.71%

5. The percent of eighth graders student who prefer action moveis is:

(x/100)240 = 90

x = 90(100/240)

x = 37.5

the percent of students is 37.5%

6. To determine which from the given grades has the greatest percent of student that prefer action movies, calculate the percent of student in seventh-grade:

(x/100)180 = 75

x = 75(100/180)

x = 41.66

the percent of student is 41.66%

then, seventh grade has the greatest percent of student that prefer action movies.

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Need pre-cal help. Will mark best answer brainliest
OlgaM077 [116]

so, let's keep in mind that

\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}

so let's make a quick table of those solutions, say A, B, C solutions with x,y,z liters of acid, with an acidity of 0.25, 0.40 and 0.60 respectively.


\bf \begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{liters of }}{amount}\\ \cline{2-4}&\\ A&x&0.25&0.25x\\ B&y&0.40&0.4y\\ C&z&0.60&0.6z\\ \cline{2-4}&\\ mixture&78&0.45&35.1 \end{array} \\\\\\ \begin{cases} x+y+z=78\\ 0.25x+0.4y+0.6z=35.1 \end{cases}


we know she's using "z" liters and those are 3 times as much as "y" liters, so z = 3y.


\bf \begin{cases} x+y+3y=78\\ x+4y=78\\[-0.5em] \hrulefill\\ 0.25x+0.4y+0.6(3y)=35.1\\ 0.25x+0.4y=1.8y=35.1\\ 0.25x+2.2y=35.1 \end{cases}\implies \begin{cases} x+4y=78\\\\ 0.25x+2.2y=35.1 \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x+4y=78\implies \boxed{x}=78-4y \\\\\\ \stackrel{\textit{using substitution on the 2nd equation}}{0.25\left( \boxed{78-4y} \right)+2.2y=35.1}\implies 19.5-y+2.2y=35.1


\bf 1.2y=15.6\implies y=\cfrac{15.6}{1.2}\implies \blacktriangleright y=13 \blacktriangleleft \\\\\\ x=78-4y\implies x=78-4(13)\implies \blacktriangleright x=26 \blacktriangleleft \\\\\\ z=3y\implies z=3(13)\implies \blacktriangleright z=39 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{25\%}{26}\qquad \stackrel{40\%}{13}\qquad \stackrel{60\%}{39}~\hfill

5 0
2 years ago
What is the slope of the line represented by the equation 10×+5y=4<br>a.2<br>b.1/2<br>c.-1/2<br>d.-2
VikaD [51]
Equation: 10x + 5y = 4
5y = -10x + 4

Divide the equation by 5, 
y = -2x + 4/5

Now Compare it with, y = mx + c
Here,m = -2

In short, Your Answer would be Option D

Hope this helps!
6 0
3 years ago
A musician spends 90 minutes practicing piano and guitar the time spent is 30 minute less than twice the same time spent on guit
11111nata11111 [884]

Answer:

The which spends on the piano is( 50 minutes )

The which spends on the guitar is( 40 minutes )

Step-by-step explanation:

The steps of the solution in the above photo

I hope that is useful for you :)

8 0
3 years ago
A family owns two businesses that made a combined profit of $$$10 million in the previous financial year, with business B making
Archy [21]

Answer:

The equation to find the profit made by business combined is x+4x = 10.

Business A made $2 million profit and Business B made $8 million profit.

Step-by-step explanation:

Given:

Profit made in previous financial year = $10 million

We need to write an equation to find the profit made by the business.

Solution:

Let the profit (in millions) made by  business A be 'x'.

Let the profit (in millions) made by  business B be 'y'.

Now given:

business B making 4 times as much profit as business A.

so we can say that;

y =4x

Now we know that;

Profit made in previous financial year is equal to sum of profit (in millions) made by  business A and profit (in millions) made by  business B.

framing in equation form we get;

x+y =10\ million

Substituting the value of y in above equation we get;

x+4x = 10

Hence The equation to find the profit made by business combined is x+4x = 10.

On Solving above equation we get;

5x =10\\\\x =\frac{10}{5} = \$2 \ million

profit (in millions) made by  business A = \$2 \ million

profit (in millions) made by  business B = 4x =4\times 2 =\$8 \ million

Hence Business A made $2 million profit and Business B made $8 million profit.

8 0
3 years ago
PLZ HELP ME!<br> Directions up above the picture<br> **MATH (Algebra)
Vikentia [17]

Answer:

The answer to your question is t = 1.3 s

Step-by-step explanation:

Data

Equation    h(t) = -4.9t² + v₀t + h₀

v₀ = 0 m/s

h₀ = 8 m

t = ?

h = 0 m

Process

1.- Substitute the values in the formula

                  0 = -4.9t² + 0t + 8

2.- Simplification

                  0 = -4.9t² + 8

3.- Solve for t

                 4.9t² = 8

                      t² = 8/4.9

                      t² = 1.63

4.- Result

                      t = 1.27 ≈ 1.3 s

6 0
3 years ago
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