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3 years ago

A movie theater charges $15 for standard viewing, $20 for 3D viewing, and $35 for Dinner and a

Mathematics

1 answer:

Ludmilka [50]3 years ago

5 0

The quantity of each type of seats sold are as follows:

Standard viewing = 2000

3D seats = 800

Movie and a dinner seat = 200

According to the question,there are four times as many 3D, x seats as Dinner and a Movie, y seats.

That is, x = 4y

Also, total seats

= (x) + (y) + (z) = 3000...….............eqn(1)

Also, If the theater brings in $53,000 when tickets to all 3000 seats are sold.

20x + 35y + 15z = 53000...........eqn(2)

By substituting 4y for x in equations 1 and 2; we have;

5y + z = 3000..…........eqn(3) and

115y + 15z = 53000.........eqn(4)

By solving equations 3 and 4 simultaneously; we have;

y = 200 and z = 2000

and since x = 4y

x = 800

The quantity of each type of seats sold is as follows:

Standard viewing = 2000

3D seats = 800

Movie and a dinner seat = 200

Read more:

brainly.com/question/12413726

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Solve for y. 9x+5y=7

Yuliya22 [10]

Answer: y=7/5-9x/5

Step-by-step explanation:

im sorry if this dont help

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2 years ago

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If 1/2 cup of soup equals 120 milliliters, then how many milliliters are in 3 1/2 cups of soup?

pav-90 [236]

Ok. So since they give you that 1/2 cup of soup equals 120 milliliters it makes this very easy. So since we know 120milliliters=1/2 and that 3 1/2= 7 1/2s (please note that the 7 1/2s doesnt mean seven and 1/2 it means seven 1/2s) you just add 120 to itself 7 times getting an answer of 840. (please vote brainliest ^^)

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3 years ago

The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to rep

Alchen [17]

Ooh, fun

geometric sequences can be represented as
$a_n=a(r)^{n-1}$
so the first 3 terms are
$a_1=a$
$a_2=a(r)$
$a_2=a(r)^2$

the sum is -7/10
$\frac{-7}{10}=a+ar+ar^2$
and their product is -1/125
$\frac{-1}{125}=(a)(ar)(ar^2)=a^3r^3=(ar)^3$

from the 2nd equation we can take the cube root of both sides to get
$\frac{-1}{5}=ar$
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
$\frac{-7}{10}=\frac{ar}{r}+ar+(ar)r$
subsituting -1/5 for ar
$\frac{-7}{10}=\frac{\frac{-1}{5}}{r}+\frac{-1}{5}+(\frac{-1}{5})r$
which simplifies to
$\frac{-7}{10}=\frac{-1}{5r}+\frac{-1}{5}+\frac{-r}{5}$
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for $ax^2+bx+c=0$
$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$
so
for 2r²-5r+2=0
a=2
b=-5
c=2

$r=\frac{-(-5) \pm \sqrt{(-5)^2-4(2)(2)}}{2(2)}$
$r=\frac{5 \pm \sqrt{25-16}}{4}$
$r=\frac{5 \pm \sqrt{9}}{4}$
$r=\frac{5 \pm 3}{4}$
so
$r=\frac{5+3}{4}=\frac{8}{4}=2$ or $r=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}$

use them to solve for the value of a
$\frac{-1}{5}=ar$
$\frac{-1}{5r}=a$
try for r=2 and 1/2
$a=\frac{-1}{10}$ or $a=\frac{-2}{5}$

test each
for a=-1/10 and r=2
a+ar+ar²= $\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}$
it works

for a=-2/5 and r=1/2
a+ar+ar²= $\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}$
it works

both have the same terms but one is simplified

the 3 numbers are $\frac{-2}{5}$ , $\frac{-1}{5}$ , and $\frac{-1}{10}$

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3 years ago

Need help factoring X squared +11x+24

Andrei [34K]

Answer:

(X+3)(X+8)

Step-by-step explanation:

In the attached file

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3 years ago

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The owners of an industrial plant want to determine which of two types of fuel (gas or electricity) will produce more useful ene

madreJ [45]

Answer:

d. H0: $(\mu_e - \mu_g) = 0$ vs. $Ha: (\mu_e - \mu_g) \neq 0$

Step-by-step explanation:

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

On this case the Management try to determine if there is a difference in the average investment/quad between using electricity and using gas. So this needs to be on the alternative hypothesis. And the complement of the alternative hypothesis would be on the null hypothesis.

Null hypothesis : $\mu_e = \mu_g$

Alternative hypothesis: $\mu_e \neq \mu_g$

Or equivalently:

Null hypothesis : $\mu_e - \mu_g = 0$

Alternative hypothesis: $\mu_e - \mu_g \neq 0$

Other important thing is that on the alternative hypothesis we never can have the symbol equal.

So on this case the best options is:

d. H0: $(\mu_e - \mu_g) = 0$ vs. $Ha: (\mu_e - \mu_g) \neq 0$

7 0

3 years ago