Pls helpp ..................

A Broadway theater has 400 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $ 80 comma main

Tomtit [17]

Answer:

80 orchestra seats

180 main seats

140 balcony seats

Step-by-step explanation:

Total number of seats = 400

Orchestra seats sell for $80

Main seats sell for $65

Balcony seats sell for $40

If all the seats are sold, gross revenue = $23,700

If all the main seats and balcony seats are sold but only half of the orchestra seats are sold, the gross revenue = $20,500

Let x = Orchestra seats

Let y = main seats

Let z = balcony seats

x+y+z= 400............. (1)

Orchestra seats sell for $80, Main seats sell for $65 and bslcony seats sell for $40. The gross revenue if all the seats are sold = $23,700

80x + 65y + 40z = 23,700 ........(2)

If half of the orchestra seats are sold while all main and balcony seats are sold, we have

80(0.5x) + 65y+ 40z = 20,500

40x + 65y + 40z = 20,500 .....(3)

we have the simultaneous equations

x+y+z= 400............. (1)

80x + 65y + 40z = 23,700 ........(2)

40x + 65y + 40z = 20,500 .....(3)

Using elimination method to solve equation 2 and 3, we subtract equation 3 from 2

40x = 3200

x = 3200/40

x = 80 orchestra seats

Put x= 80 into equation 1 and 2

From equation 1,

x +y+z = 400

y + z = 400 - x

y+z = 400 -80

y+z = 320 .........(4)

From equation 2,

80x + 65y + 40z = 23,700

80(80) + 65y +40z = 23,700

6400 + 65y + 40z = 23,700

65y+40z = 23,700 - 6400

65y + 40z = 17,300 .........(5)

Multiply equation (4) by 40 and equation (5) by 1

So we have

40y + 40z = 12,800

65y + 40x = 17,300

subtract both equations from each other. we have

-25y = -4500

y = -4500/-25

y = 180 main seats

Put x = 80 and y= 180 into equation (1)

80+180+z = 400

260 + z = 400

z = 400-260

z = 140 balcony seats

6 0

3 years ago

Four times the difference of a number and 7 is 32

notka56 [123]

I'm not exactly sure but I think it might be but if you were to do 4(x-7) that would be 15 because fifteen minutes seven equals eight and eight time four is thirty two Hope this helps!

6 0

3 years ago

First two two terms of the given number sequence 3n + 1 are...

PtichkaEL [24]

Answer:

the sequence begins as {4, 7, ... }

Step-by-step explanation:

a(n) = 3n + 1

The first term is a(1) = 3(1) + 1 = 4, and

the second term is a(s) = 3(2) + 1 = 7

So the sequence begins as {4, 7, ... }

5 0

2 years ago

At an ocean-side nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water t

grandymaker [24]

Answer:

(a1) The probability that temperature increase will be less than 20°C is 0.667.

(a2) The probability that temperature increase will be between 20°C and 22°C is 0.133.

(b) The probability that at any point of time the temperature increase is potentially dangerous is 0.467.

(c) The expected value of the temperature increase is 17.5°C.

Step-by-step explanation:

Let X = temperature increase.

The random variable X follows a continuous Uniform distribution, distributed over the range [10°C, 25°C].

The probability density function of X is:

$f(X)=\left \{ {{\frac{1}{25-10}=\frac{1}{15};\ x\in [10, 25]} \atop {0;\ otherwise}} \right.$

(a1)

Compute the probability that temperature increase will be less than 20°C as follows:

$P(X$

Thus, the probability that temperature increase will be less than 20°C is 0.667.

(a2)

Compute the probability that temperature increase will be between 20°C and 22°C as follows:

$P(20$

Thus, the probability that temperature increase will be between 20°C and 22°C is 0.133.

(b)

Compute the probability that at any point of time the temperature increase is potentially dangerous as follows:

$P(X>18)=\int\limits^{25}_{18}{\frac{1}{15}}\, dx\\=\frac{1}{15}\int\limits^{25}_{18}{dx}\,\\=\frac{1}{15}[x]^{25}_{18}=\frac{1}{15}[25-18]=\frac{7}{15}\\=0.467$