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Lunna [17]
2 years ago
12

Based on past musical productions, a theater predicts selling 400−8p number of tickets when each ticket is sold at p dollars. Us

ing the table from the last question answer the following questions:
1. For which ticket prices will the theater earn no revenue? Explain how you know.


2. At what ticket prices should the theater sell the tickets if it must earn at least $3,200 in revenue to break even (to not lose money) on the musical production? Explain how you know.
Mathematics
1 answer:
Dvinal [7]2 years ago
7 0

To earn at least $3,200 in revenue, the ticket prices should be $10 or $40.

<h3>What is an Equation</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

Revenue = number of tickets sold * price per ticket = (400 - 8p)p

Revenue = 400p - 8p²

For no revenue:

400p - 64p² =  0

p = $0 or p = $50

For revenue of atleast 3200:

400p - 8p² =  3200

p = $10 or p = $40

To earn at least $3,200 in revenue, the ticket prices should be $10 or $40.

Find out more on Equation at: brainly.com/question/1214333

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andreyandreev [35.5K]

The series converges to  1/(1-9x) for -1/9<x<1/9                  

Given the series is  ∑ 9x^{n} x^{n}

We have to find the values of x for which the series converges.

We know,                

∑ ar^{n-1}    converges to  (a) / (1-r) if r < 1

Otherwise the series will diverge.

Here, ∑ (9x)^{n} is a geometric series with |r| = | 9x |

And it converges for |9x| < 1

Hence, the given series gets converge for -1/9<x<1/9

And geometric series converges to a/(1-r)

Here, a = 1 and r = 9x

Therefore, a/(1-r) = 1/(1-9x)

Hence, the given series converges to   1/1-9x  for  -1/9<x<1/9

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8 0
1 year ago
In the picture below, ABCD is a rectangle. If the area of triangle ABE is 40, what is the area of the triangle?
MariettaO [177]

Area of the rectangle: 112

Step-by-step explanation:

Picture is missing: find it in attachment.

The area of a triangle is given by

A=\frac{1}{2}bh

where

b is the length of the base

h is the height

For triangle ABE, we know that

A = 40 (area)

h = 8 (height)

So we can find the length of the base AE:

AE=b=\frac{2A}{h}=\frac{2(40)}{8}=10

Now we observe that the base of the rectangle, AD, is the sum of AE and DE, therefore:

AD=AE+DE=10+4=14

We also know the height of the rectangle AB is 8, and that the area of a rectangle is

A=bh

where b is the base and h the height. Therefore, the area of this rectangle is

A=bh=(AD)(AB)=(14)(8)=112

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7 0
3 years ago
A poll agency reports that 75% of teenagers aged 12-17 own smartphones. A random sample of 234 teenagers is drawn. Round your an
GalinKa [24]

Answer:

If our random variable of interest for this case is X="the number of teenagers between 12-17 with smartphone" we can model the variable with this distribution:

X \sim Binom(n=234, p=0.75)

And the mean for this case would be:

E(X) =np = 234*0.75= 175.5

And the standard deviation would be given by:

\sigma =\sqrt{np(1-p)}= \sqrt{234*0.75*(1-0.75)}= 6.624

Step-by-step explanation:

If our random variable of interest for this case is X="the number of teenagers between 12-17 with smartphone" we can model the variable with this distribution:

X \sim Binom(n=234, p=0.75)

And the mean for this case would be:

E(X) =np = 234*0.75= 175.5

And the standard deviation would be given by:

\sigma =\sqrt{np(1-p)}= \sqrt{234*0.75*(1-0.75)}= 6.624

3 0
3 years ago
Which graph represents a function?
Sliva [168]

Answer:

D

Step-by-step explanation:

A function is where each input (here, the input is x) corresponds to exactly one output (here, the output is y). In other words, if a function is graphed, we should be able to draw a vertical line through every single part of it that will intersect it at only one place.

Let's examine each choice.

(A) Well, if we draw a vertical line through the graph, it will obviously intersect the entire line - which is an infinite number of intersections, so this is not a function.

(B) If we draw a vertical line through the portion of the graph that lies near the positive x-axis, we note that it will intersect twice, so this is not a function.

(C) If we strategically draw a vertical line through the y-axis, we see it will intersect two times, so this is not a function.

(D) We can draw a vertical line through any portion of this graph and know that it will only intersect once.

Therefore, the answer is D.

5 0
3 years ago
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