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vredina [299]

3 years ago

align="absmiddle" class="latex-formula">

Mathematics

1 answer:

otez555 [7]3 years ago

6 0

If you put in n the calculator you should get the answer very easily. What i got is 3.734111864 im not sure if its correct tho

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A Broadway theater has 800 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $ 40 comma main

KatRina [158]

Answer:

orchestra seats: main seats: balcony seats: 160: 400: 240

Step-by-step explanation:

Let number of orchestra seats = x

Let number of main seats = y

Let number of balcony seats = z

As per given statement, total seats are 800

$x +y+z=800 ..... (1)$

Sales price of each orchestra seat = $40

Sales price of each main seat = $30

Sales price of each balcony seat = $20

If all the seats are sold, total revenue is $23200.

$\Rightarrow 40x + 30y+20z=23200 ...... (2)$

If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $ 20 comma 000.

$\Rightarrow 40\times \dfrac{x}{2} + 30y+20z=20000\\\Rightarrow 20x + 30y+20z=20000 ...... (3)$

Here, we have 3 variables and 3 equations. Let us solve them.

Subtracting Equation (3) from equation (2):

$\Rightarrow 20x = 3200\\\Rightarrow x = 160$

Putting value of x in equations (1) and (2):

Equation (1)

$\Rightarrow 160 +y+z=800\\\Rightarrow y+z=640 ...... (4)$

Equation (2)

$\Rightarrow 40\times 160 +30y+20z=23200\\\Rightarrow 30y+20z=16800\\\Rightarrow 3y +2z=1680 ...... (5)$

Equation (5) - 2 $\times$ Equation(4):

$\Rightarrow y =400$

Putting value of y in equation (4):

$400 +z = 640\\\Rightarrow z =240$

Hence, answer is:

orchestra seats: main seats: balcony seats: 160: 400: 240

4 0

3 years ago

Find the volume of this cube in cm³

Degger [83]

Answer:

It is c: 15.625 cm³

Step-by-step explanation:

Formular for cube volumes:

${ \tt{volume = (side \times side \times side)}} \\ { \tt{v = (s_{1} \times s_{2} \times s_{3}) }}$

since sides of a cube are identical:

${ \sf{s_{1} = {s_{2} = {s_{3}}}}}$

Therefore:

${ \sf{volume = (250 \times 250 \times 250) \: mm {}^{3} }} \\ { \sf{v =15,625,000 \: {mm}^{3} }}$

but 1 mm³ = 0.000001 cm³

${ \sf{v = (15,625,000 \times \{1 \times {10}^{ - 6} \} ) \: cm}} \\ { \sf{v = 15.625 \: {cm}^{3} }}$

8 0

3 years ago

Is the answer to this question 30?

uranmaximum [27]

Answer:

30 feet

Step-by-step explanation:

You got it.

3/30=30/300

8 0

3 years ago

Read 2 more answers

A researcher surveyed 150 high school students and found that 68% played a musical insturment. What would be a reasonable range

maria [59]

Answer:

The reasonable range for the population mean is (61%, 75%).

Step-by-step explanation:

The interval estimate of a population parameter is an interval of values that consist of the values within which the true value of the parameter lies with a certain probability.

The mean of the sampling distribution of sample proportion is, $\hat p$ .

One of the best interval estimate of population proportion is the 95% confidence interval for proportion,

$CI=\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

Given:

n = 150

$\hat p$ = 0.68

The critical value of z for 95% confidence level is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

Compute the 95% confidence interval for proportion as follows:

$CI=\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

$=0.68\pm1.96\sqrt{\frac{0.68(1-0.68)}{150}}\\\\=0.68\pm 0.0747\\\\=(0.6053, 0.7547)\\\\\approx (0.61, 0.75)$

Thus, the reasonable range for the population mean is (61%, 75%).

5 0

4 years ago

Last year, a property manager bought five identical snow shovels and six identical bags of salt. the total of the snow shovels w

ikadub [295]

Just compare the change in unit cost to the original unit cost.

Shovels: (70.38 ÷ 2 - (172.50/5) ÷ (172.50/5) = 0.02
Salt: (26.04 ÷ 4 - (6.20) ÷ 6.20 = 0.05

So, the shovels went up 2% and the salt went up 5%

3 0

4 years ago

Read 2 more answers