The local theater has three types of seats for broadway plays: main floor, balcony, and mezzanine. main floor tickets are $⁢59, balcony tickets are $⁢50, and mezzanine tickets are $⁢40. one particular night, sales totaled $73,785. there were 435 more main floor tickets sold than balcony and mezzanine tickets combined. the number of balcony tickets sold is 78 more than 33 times the number of mezzanine tickets sold. how many of each type of ticket were sold?

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

Let

x-------> the pressure in PSI

y------> the volume of the gas in cubic inches

In this problem we have the point [tex](30,600)[/tex]

so

[tex]x=30\ psi\\y=600\ in^{3}[/tex]

Find the constant k

[tex]y*x=k[/tex]

substitute the values of x and y

[tex]600*30=k[/tex]

[tex]k=18,000\ lb*in[/tex]

the equation is

[tex]y=18,000/x[/tex]

therefore

the answer is

[tex]y=18,000/x[/tex]

Answer:

[tex]y=\frac{18000}{x}[/tex]

Step-by-step explanation:

Let the volume of gas be y

Let the pressure be x

Since we are given that the volume of the gas is inversely proportional to its pressure.

⇒[tex]y \propto \frac{1}{x}[/tex]

Let the proportionality be k

So, [tex]y=\frac{k}{x}[/tex]  ---A

Now we are given that At a pressure of 30 pounds per square inch (psi), a gas has a volume of 600 cubic inches

So, substitute x = 30

y = 600

[tex]600=\frac{k}{30}[/tex]

[tex]600 \times 30=k[/tex]

[tex]18000 =k[/tex]

Substitute the value of k in A

So,  [tex]y=\frac{18000}{x}[/tex]

Hence  function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi is    [tex]y=\frac{18000}{x}[/tex]

Because point C is the centroid of the triangle, therefore:

Segments PZ = ZR;  RY = YQ; QX = XP

A.
If CY = 10, then

PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answers:     

PC = 20     

PY = 30

B.
If QC = 10, then

ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answers:     

ZC = 5       

ZQ = 15

C.
If PX = 20
because the median RX bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer:      

PQ = 40

24^2 = 18 * (18 +y)

576 = 324+18y

252 =18y

y = 252/18 =14

 y = 14

The value of y is 14.

'A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant'

According to the given problem,

We know,

⇒ 18 ( 18 + y ) = 24²

⇒ 324 + 18y = 576

⇒ 18y = 576 - 324

⇒ 18y = 252

⇒ y = 252/18

⇒ y = 14

Hence, we can conclude, the value of y is 14.

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Step-by-step explanation:

To find out what 16% of 17 is, we create a cross multiply equation

16/100=17/x

Cross multiply

(16 * x  = 16x)

(100 * 17 = 1700)

16x = 1700

1700/16 = 106.25

surface area = 4*pi*r^2

using 3.14 for pi

452.39 = 4*3.14*r^2=

452.39=12.56* r^2

r^2 = 452.39/12.56 = 36.0

sqrt(36) = 6= r

diameter = 2r = 6*2= 12

 diameter = 12 feet

The required value of x is 7.

A linear equation only has one or two variables. No variables in a linear equation is raised to power greater than 1 or used as denominator of a fraction.

Now the given statement is,

Three times the difference of a number x and seven is twenty-three minus the sum of three times a number x and two.

So converting them into numerical form,

the difference of a number x and seven = x - 7

∴ Three times the difference of a number x and seven = 3(x - 7)

Similarly,

the sum of three times a number x and two = 3x + 2

∴ Twenty-three minus the sum of three times a number x = 23 - (3x + 2)

Therefore, the required equation is,

3(x - 7) = 23 - (3x + 2)

Expanding the brackets we get,

3x - 21 = 23 - 3x - 2

or, 3x - 21 = 21 - 3x

Taking alike terms together,

3x + 3x = 21 + 21

or, 6x = 42

Dividing both side by 6 we get,

x = 7

which is the required value of x.

Thus, The required value of x is 7.

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Answer:

Step-by-step explanation:

[tex](5+5-5:5)\cdot5\\\\\text{Use PEMDAS}\\\\\text{P Parentheses first}\\\text{E Exponents}\\\text{MD Multiplication and Division (left-to-right)}\\\text{AS Addition and Subtraction (left-to-right)}\\\\=(5+5-1)\cdot5\\\\=(10-1)\cdot5\\\\=9\cdot5\\\\=45[/tex]

Answer: [tex]a^{12}+8[/tex]

Step-by-step explanation:

let's check all the expressions

1. [tex]a^3+18[/tex]

here 18 is not a perfect cube.

2. [tex]a^6+9[/tex]

here 9 is not a perfect cube.

3.[tex]a^9+16[/tex]

here 16 is not a perfect cube.

4.[tex]a^{12}+8[/tex]

here 8 is a perfect cube, thus we can write above expression by using laws of exponents as

[tex](a^4)^3+2^3[/tex]

Thus, [tex]a^{12}+8[/tex] is a sum of cubes.

The equation that can be used to find the lengths of the legs of the triangle is [tex]\rm 0.5(x)(x + 2) = 24[/tex]

The area of the right triangle shown is 24 square feet.

We have to determine

Which equations can be used to find the lengths of the legs of the triangle?

According to the question

From the given figure the base of the triangle is x.

And the height of the triangle is (x+2).

The area of the triangle is given by half the product of the height and base.

[tex]\rm Area = \dfrac{1}{2} \times base \times height\\ [/tex]

Substitute all the values in the formula;

[tex]\rm Area \ of \ right \ triangle= \dfrac{1}{2} \times base \times height\\ \\ \rm 24= \dfrac{1}{2} \times x \times (x+2)\\\\ \rm 0.5(x)(x + 2) = 24[/tex]

The equation can be used to find the lengths of the legs of the triangle is [tex]\rm 0.5(x)(x + 2) = 24[/tex].

Hence, the equation can be used to find the lengths of the legs of the triangle is [tex]\rm 0.5(x)(x + 2) = 24[/tex].

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5v+7(2.85)=28.70

5v+19.95 = 28.70

5v = 8.75

v = 1.75

Answer: A. 6

A. 4.3%

Step-by-step explanation:

The total number of singers = 4

To choose singers = 2

The number of ways to choose 2 singers from 4= [tex]^4C_2=\frac{4!}{2!(4-2)!}=3\times2=6[/tex]

Hence, A is the right option.

The total number of water purifiers  T= 280

The number of defective purifiers D= 12

The probability that a water purifier chosen at random will be defective (in percent)=[tex]\frac{\text{T}}{\text{D}}\times100[/tex]

[tex]=\frac{12}{280}\times100\\=0.042857\times100\\=4.2857\%\approx4.3\%[/tex]

Hence, A is the right option.

Answer: False

Martin is asked to find the probability of getting one head and three tails on for coin tosses this is a simple event.

A. True

B. False

Answer:

So basically sqrt of 2...

Step-by-step explanation:

Final answer:

The vertex of the profit function f(x) = -x^2 + 16x - 60 is (8, 4), meaning the maximum profit is $4 when 8 candles are sold. The x-intercepts are (6,0) and (10,0), indicating zero profit when either 6 or 10 candles are sold.

Explanation:

The function given is a quadratic equation of the form f(x) = ax2 + bx + c, where the constants are a = -1, b = 16, and c = -60. To find the vertex of the parabola, we can use the formula -b/(2a) for the x-coordinate of the vertex.

Calculate the x-coordinate of the vertex: x = -b/(2a) = -16/(2 * -1) = 8.

Substitute x = 8 into the original function to find the y-coordinate: f(8) = -(8)2 + 16(8) - 60 = -64 + 128 - 60 = 4.

The vertex is at the point (8, 4). In the context of the problem, this point represents the maximum daily profit of $4, which occurs when 8 candles are sold.

To determine the x-intercepts, we set f(x) to zero and solve for x, which represents the number of candles sold when the profit is zero.

Set the function equal to zero and solve for x: 0 = -x2 + 16x - 60.

Apply the quadratic formula x = [-b ± sqrt(b2 - 4ac)]/(2a) to find the x-intercepts. In this case, a = -1, b = 16, and c = -60.

Calculate the discriminant, sqrt(162 - 4(-1)(-60)) = sqrt(256 - 240) = sqrt(16) = 4.

Find the two x-intercepts: x = [16 ± 4]/(2 * -1) which yields x = 6 and x = 10.

The x-intercepts (6,0) and (10,0) indicate the number of candles sold at which the profit would be zero, specifically at 6 and at 10 candles sold.

Since the new machine is three times faster, it takes (12 hours) / 3 = 4 hours for the new machine to make 10,000 cans alone.

Let's denote the time it takes the older machine to make 10,000 cans as "t" hours.

The new machine can make 10,000 cans three times faster than the older machine, which means it takes "t/3" hours for the new machine to make 10,000 cans.

When both machines are working together, they can make 10,000 cans in 9 hours.

Now, we can set up an equation based on the work rates of the two machines:

Work rate of the older machine + Work rate of the new machine = Combined work rate

The work rate is the amount of work (number of cans made) per unit of time (hours).

For the older machine:

Work rate of the older machine = 10,000 cans / t hours

For the new machine:

Work rate of the new machine = 10,000 cans / (t/3) hours

Combined work rate when both machines work together:

Combined work rate = 10,000 cans / 9 hours

Now, the equation becomes:

10,000 cans / t hours + 10,000 cans / (t/3) hours = 10,000 cans / 9 hours

To solve for "t," we can start by finding a common denominator for the fractions on the left side of the equation:

t/3 is the same as (1/3)t. So the equation becomes:

10,000 cans / t hours + 10,000 cans / (1/3)t hours = 10,000 cans / 9 hours

Now, to combine the fractions, we find the common denominator, which is 3t:

(3t * 10,000 cans) / (3t * t hours) + (t * 10,000 cans) / (3t * t hours) = 10,000 cans / 9 hours

(30,000t + 10,000t) / (3t^2 hours) = 10,000 cans / 9 hours

Combine the terms on the left side of the equation:

40,000t / (3t^2 hours) = 10,000 cans / 9 hours

Now, cross-multiply to solve for "t":

40,000t * 9 hours = 10,000 cans * 3t^2 hours

360,000t hours = 30,000t^2 hours

Now, rearrange the equation:

30,000t^2 - 360,000t hours = 0

Divide by 30,000t to simplify the equation:

t - 12 = 0

Now, solve for "t":

t = 12 hours

Therefore, it takes the older machine 12 hours to make 10,000 cans.

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