A movie theater has a seating capacity of 349. The theater charges $5. 00 for children, $7. 00 for students, and $12. 00 for adults. There are half as many adults as there are children. If the total ticket sales was $ 2540, How many children, students, and adults attended?

Answer:

SOH CAH TOA

Step-by-step explanation:

SOH: Sin(θ) = Opposite / Hypotenuse. 

CAH: Cos(θ) = Adjacent / Hypotenuse.

 TOA: Tan(θ) = Opposite / Adjacent.

I hope this helps

The maximum area that the 60 m can enclose is 225m², the dimensions of the maximal region are 15m x 15m, and the height as an fcn of the base is 30 - b.

Let the base of the rectangular region be "b",

and the height be "h" and,

it is given that the perimeter of the rectangular region = 60m

(a) write height as an fcn of base

by using the formula of the perimeter of a rectangle,

2(h+b) = 60m

we can write, h = 30 - b

⇒Area of the rectangular region

area(A) = height × base

substituting the value of h.

= (30 - b) × b

thus, A(b)= 30b - b²

to find the maximum area that the 60 m can enclose

\(\frac{dA(b)}{db}\) should be equal to 0.

substituting the value of A(b).

30 - 2b = 0

thus, b = 15

maximum area = 30b - b²

substituting the value of b.

= (30 × 15) - 15²

thus, maximum area = 225m².

dimensions of the maximum region,

for maximum area height = base = 15m

thus, the dimensions of the maximum rectangular region are 15m x 15m.

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Answer:

c

Step-by-step explanation:

i just took a test

Step-by-step explanation:

The divisor is the length of the vertical line

As the

fraction is

\(\sf \dfrac {Horizontal\:lines}{Vertical\:lines}\)

\(\boxed{\begin{minipage}{6 cm}\bf{\dag}\:\:\underline{\textsf{Fraction Rules :}}\\\\\bigstar\:\:\sf\dfrac{A}{B} + \dfrac{B}{C} = \dfrac{A+B}{C} \\\\\bigstar\:\:\sf{\dfrac{A}{B} - \dfrac{B}{C} = \dfrac{A-B}{C}}\\\\\bigstar\:\:\sf\dfrac{A}{B} \times \dfrac{C}{D} = \dfrac{AC}{BD}\\\\\bigstar\:\:\sf\dfrac{A}{B} + \dfrac{C}{D} = \dfrac{AD}{BD} + \dfrac{BC}{BD} = \dfrac{AD+BC}{BD} \\\\\bigstar\:\:\sf\dfrac{A}{B} - \dfrac{C}{D} = \dfrac{AD}{BD} - \dfrac{BC}{BD} = \dfrac{AD-BC}{BD}\\\\\bigstar \:\:\sf \dfrac{A}{B} \div \dfrac{C}{D} = \dfrac{A}{B} \times \dfrac{D}{C} = \dfrac{AD}{BC}\end{minipage}}\)

Answer:

it maybe 4 i am not sure

Step-by-step explanation:

The slope of the line in the given graph is -1

From the question, we are to calculate the slope of the line in the given graph

To calculate the slope, we will pick two points on the line

Picking the points (-3, 0) and (0, -3).

Using the formula for the slope of a line,

Slope = (y₂ - y₁) / (x₂ - x₁)

x₁ = -3

x₂ = 0

y₁ = 0

y₂ = -3

Slope = (-3 - 0) / (0 - (-3))

Slope = (-3) / (0 + 3)

Slope = -3 / 3

Slope = -1

Hence,

The slope of the line in the graph is -1

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Answer:

Concave

Step-by-step explanation:

Concave means that there's an indent in the polygon somewhere, for example an octagon would not be a concave shape because it doesn't have an indent in it anywhere. Hope that makes sense

Answer:

Lateral surface area of cuboid = 448 ft²

Step-by-step explanation:

Given:

Height of cuboid(h) = 14 ft

Length of cuboid(l) = 9 ft

width of cuboid(b) = 7 ft

Find:

Lateral surface area of cuboid

Computation:

Lateral surface area of cuboid = 2 h(l + b)

Lateral surface area of cuboid = 2(14)(9 + 7)

Lateral surface area of cuboid = 28(16)

Lateral surface area of cuboid = 448 ft²

Answer:

y = -4/3

x = 14/3

Step-by-step explanation:

2x+y=8

x-y=6

First of all, we need the same coefficient, so we can make both of these 2x by multiplying the second one by 2.

2x+y=8

2x-2y=12

Then we need to subtract equation 1 from 2.

3y=-4

Solve normally

y = -1.33333 / -4/3

Substitute

x - (-4/3) = 6

x = 14/3

\(\large\huge\green{\sf{Answer:-}}\)

\( \red {\mathbb{ \underline { \tt by \: elimination \: method \: s}}}\)

from equation (i):-

\(2x - y = 8 \\ x = \frac{8 - y}{2} \)

\(x - y = 6 \\ \frac{8 - y}{2} - y = 6 \\ \frac{8 - y - 2y}{2} = 6 \\ 8 - y - 2y = 12 \\ 8 - 3y = 12 \\ - 3y = 12 - 8 \\ - 3y = 4 \\ y = \frac{ - 4}{3} \)

\(2x + y = 8 \\ 2x + ( \frac{ - 4}{3} ) = 8 \\ 2x - \frac { 4}{3} = 8 \\ \frac{6x - 4}{3} = 8 \\ 6x - 4 = 8 \times 3 \\ 6x - 4 = 24 \\ 6x = 24 + 4 \\ 6x = 28 \\ x = \frac{14}{3} \)

now,

\(2x + y = 8 \\ x - y = 6 \\ - - - - - - - \\ multiply \: eq \: (i) \: by \: 1 \\ and \: eq(ii) \: by \: 2 \\ \\ (2x + y = 8) \times 1\\ (x - y = 6) \times 2 \\ - - - - - - - \\2x + y = 8 \\ 2x - 2y = 12 \\ subtract \: these \\ 3y = - 4 \\ y = \frac{ - 4}{3} \\ \)

put value of y in equation (i)

\(2x + y = 8 \\ 2x + ( \frac{ - 4}{3} ) = 8 \\ 2x - \frac { 4}{3} = 8 \\ \frac{6x - 4}{3} = 8 \\ 6x - 4 = 8 \times 3 \\ 6x - 4 = 24 \\ 6x = 24 + 4 \\ 6x = 28 \\ x = \frac{14}{3} \)

Answer:

A. 125

Step-by-step explanation:

the sum of the remote angles is equal to the exterior angle

90+35=125

Answer:

125°

Step-by-step explanation:

First find the interior angle. Sum of all the angles in a triangle is 180°.

180 - (90 + 35) = 55

A straight angle is also 180°

180 - 55 = 125

The dimensions of the kennel and the size of the cylinder indicates;

4.1.1. The two 3D objects which the figure consists of are a triangular prism that lays on top of a rectangular prism at the bottom.

4.1.2. The area of the wood needed to build the dog kennel is approximately 2.85 m²

4.1.3. The number of containers of sealant needed to paint one coat on the dog kennel is approximately 2 containers

4.2. The new height of the water in the container will be approximately 18 cm.

The surface area of a solid is found by adding together the area of the surfaces that enclose the solid.

4.1.1. The two 3D objects in the figure are;

4.1.2. The amount of wood needed is found by finding the surface area, A, of the dog kennel as follows;

A = 2×80×60+2×50×60+50×80+2×0.5×80×40+2×√(40²+40²)×50

A = 22800 + 80·√2×50 = 22800 + 4000·√2

The amount of wood needed = (22800 + 4000·√2) cm²

1 m² = 10,000 cm²

(22800 + 4000·√2) cm² = ((22800 + 4000·√2))/10,000 m²

((22800 + 4000·√2)) cm² = (2.28 + 0.4·√2) m² ≈ 2.85 m²

4.1.3. 500 milliliters of paint is enough to for 1.5 m² area

The number of containers of paint containers required, n, is therefore;

\(n = \dfrac{(2.28 + 0.4\cdot \sqrt{2}) \, m^2 }{1.5 \, m^2/container} = (1.52+0.\overline 6\cdot\sqrt{2} ) \, containers \approx 2 \, containers\)

4.2 Diameter of the base of the water container = 20 cm

Radius of the base = (20 ÷ 2) cm = 10 cm

Height of water in the container = 15 cm

Volume of water added = 1,000 cm³

The new height will be 15 + (1,000/(π×10²)) = (15 + 10/π) cm ≈ 18 cm

The height of the water in the container will rise to approximately 18 centimeters

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Answer: B. (15)

Y= -\(\frac{3}{1}\)x + 15

Step-by-step explanation:

In the Table we see a f(x) decreasing by 3 for every 1 (x)

So we Have a Slope of -3(y) over 1(x)

Answer:

16 1/50

Step-by-step explanation:

First, turn the fractions into improper fractions.

8 9/10 can be 89/10 and 1 4/5 can be 9/5.

Then you multiply them together:

89/10 * 9/5= 801/50

Now, since 801/50 is 16.02 turn that into a mixed fraction. It becomes 16 1/50.

That's your answer.

After integrating the double integral of ∫∫D 8xy dA, the value is obtained as 27.

What is Integration?

The summing of discrete data is indicated by the integration. To determine the functions that will characterise the area, displacement, and volume that result from a combination of small data that cannot be measured separately, integrals are calculated.

To evaluate the double integral ∫∫D 8xy dA over the triangular region D with vertices (0,0), (1,2), and (0,3), we need to set up the integral with respect to x and y and determine the limits of integration.

Since the region is a triangle, we can use the limits of integration as follows -

0 ≤ x ≤ 1- (2/3)y and 0 ≤ y ≤ 3

The integral can be set up as follows -

\(\iint D\ 8xy\ dA= \int\limits_{0}^{3}\int\limits_{0}^{1-\frac{2}{3}y} 8xy\ dx\ dy\)

We integrate with respect to x first and obtain -

\(\int\limits_{0}^{3}\int\limits_{0}^{1-\frac{2}{3}y} 8xy\ dx\ dy = \int\limits_{0}^{3} [4x^2y]_0^{(1-\frac{2}{3}y)} dy\)

= ∫₀³ (4(1-(2/3)y)²y) dy

Simplifying this expression, we obtain -

∫∫D 8xy dA = ∫₀³ [8/9 y³ - 8/3 y² + 4y] dy

Evaluating this integral, we obtain -

\(\iint D\ 8xy\ dA = [\frac{8}{36}y^4 - \frac{8}{9}y^3 + 2y^2]\) from 0 to 3

∫∫D 8xy dA = 27

Therefore, the double integral of 8xy over the triangular region D is equal to 27.

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Answer:

Yes its very sad (the words)

Step-by-step explanation:

Not going to lie but it does kind of sound like camila cabeo sang it.

I really like the tune and the singing too

Answer:

Step-by-step explanation:

To solve, we first need to know how to find the average of a group of numbers. To find the average of a group of numbers, you add all the numbers together and divide that answer by the number of numbers you have. For instance, to find the average of 1, 2, 3, 4 and 5, we would add all the numbers together, which would equal 15. We would then divide that number by 5, because there are 5 numbers total: 15/5 = 3. So the average is 3.

Now, to find the average in your problem, we need to look at what we know:

He received an 85 and 60 on two of the test scores

He needs an overall average of 70

Let's set this up in equation form:

%2885+%2B+60+%2B+x%29%2F3+%3E=+70

Now, let's get rid of our fraction on the left. We can do this by multiplying the entire equation by 3, giving us:

85 + 60 + x >= 210

Next, combine the numbers on the left, which will give us:

145 + x >= 210

Finally, subtract 145 from both sides, which will give us our answer:

145 + x - 145 >= 210 - 145 =

x >= 65

So, in order to average at least 70, he must score a 65 or higher on his third test.

A Type II error occurs when we fail to reject a null hypothesis that is actually false. In this case, the null hypothesis is that the proportion of students who were quarantined at some point during the Fall Semester of 2020 is equal to or less than 0.65.

The alternative hypothesis is that the proportion is greater than 0.65. If we make a Type II error, we fail to reject the null hypothesis when it is actually false, meaning we do not conclude that the proportion is higher than 0.65 even though it actually is higher.

Therefore, the correct explanation for a Type II error, in this case, we would be: "Did not conclude the percent was higher than 65%, but it was higher."

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The correct option is B. The statement "The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A." is true. The statement is the definition of the algebraic multiplicity of an eigenvalue of A.

A matrix is diagonalizable if and only if each eigenvalue of the matrix has an algebraic multiplicity that is equal to its geometric multiplicity. To get the characteristic equation of a matrix, the determinant of the matrix A   I is set to zero. The characteristic equation of an nn matrix A is given by AI = 0. The characteristic equation's roots are the matrix's eigenvalues.

The algebraic multiplicity of an eigenvalue is the number of times it appears as the root of the characteristic equation. The geometric multiplicity of an eigenvalue is the number of linearly independent eigenvectors corresponding to that eigenvalue. So, the correct option is B.

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A) The volume of each dog compartment is 168,836 cm³.

To find the volume of each dog compartment, we multiply the length, width, and height of the compartment. Given that the length (l) is 38 cm, the width (w) is 97 cm, and the height (h) is 46 cm, the volume (V) can be calculated as follows:

V = l * w * h = 38 cm * 97 cm * 46 cm = 168,836 cm³

Therefore, the volume of each dog compartment is 168,836 cm³.

B)The volume of the dog box that is not used to hold dogs is 200,589 cm³.

To find the volume of the dog box that is not used to hold dogs, we need to subtract the volume of the dog compartments from the total volume of the dog box. The total volume of the dog box can be calculated by multiplying its length, width, and height. Given that the length (L) is 117 cm, the width (W) is 97 cm, and the height (H) is 61 cm, the total volume (V_total) can be calculated as follows:

V_total = L * W * H = 117 cm * 97 cm * 61 cm = 707,097 cm³

Since each dog compartment has a volume of 168,836 cm³, and there are three compartments, the total volume occupied by the dog compartments is:

V_dog_compartments = 168,836 cm³ * 3 = 506,508 cm³

To find the volume of the remaining space, we subtract the volume of the dog compartments from the total volume of the dog box:

V_remaining_space = V_total - V_dog_compartments = 707,097 cm³ - 506,508 cm³ = 200,589 cm³

Therefore, the volume of the dog box that is not used to hold dogs is 200,589 cm³.

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The solution to the given differential equation is y = C₁ * (x + 8)⁻² + C₂ * (x + 8)⁻⁷ where C₁ and C₂ are constants determined by the initial or boundary conditions.

To solve the given differential equation, (x + 8)²y" - B(x + 8)y' + 14y = 0, using Y = (X - X₀)m, follow these steps:

1. Substitute Y = (X - X₀)m into the differential equation: (X - X₀ + 8)^2m" - B(X - X₀ + 8)m' + 14m = 0.
2. Solve for m: m" - (B/((X - X₀) + 8))m' + (14/((X - X₀) + 8)²)m = 0.
3. Find the general solution for m: m = C₁\(e^(r1X)\) + C₂\(e^(r2X)\), where r₁ and r₂ are the roots of the characteristic equation, and C₁ and C₂ are constants.
4. Determine the roots of the characteristic equation: r₁ and r₂.
5. Substitute the roots into the general solution for m.
6. Finally, substitute m back into the original substitution, Y = (X - X₀)m.

y(x), will be a function involving the roots, r₁ and r₂, and constants C₁ and C₂. The explanation involves substituting Y = (X - X₀)m into the differential equation, solving for m, finding the general solution for m, determining the roots of the characteristic equation, and substituting the roots back into the original substitution to find y(x).

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Answer:

$843.36

Step-by-step explanation:

:))

The sine function with a phase shift of π/2 units to the right is given as follows:

B. y = 2sin(x + π/2).

The standard definition of a sine function is given as follows:

y = Asin(Bx + C) + D.

The parameters are given as follows:

For a phase shift of π/2 units to the right, the parameter C is given as follows:

C = π/2.

Hence option B is the correct option.

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The graph of the inequality y ≤ (x + 2)² is the graph (a)

From the question, we have the following parameters that can be used in our computation:

(y\le(x+2)^2\)

Express properly

So, we have

y ≤ (x + 2)²

The above expression is a quadratic inequality with a less or equal to sign

This means that

The graph opens upward and the bottom part is shaded

Using the above as a guide, we have the following:

The graph of the inequality is the first graph

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Answer: -0.5

Step-by-step explanation: screenshot

Answer:

-0.2

Step-by-step explanation:

So the Equation is -1.4=0.6y-1.1, so to get the variable by itself, you would need to add 1.1 to both sides. Leaving you with -0.3=0.6y. so divide each side by -0.3. Leaving you with -0.2 hope this helps :)

Answer: B) 6.5

Step-by-step explanation:

   We will use the Pythagorean theorem to solve. The "c" variable is the hypotenuse and the other variables are the legs.

a² + b² = c²

3.6² + b² = 7.4²

12.96 + b² = 54.76

b² = 41.8

b = \(\sqrt{41.8}\)

b ≈ 6.5

     The length of the missing side is about B) 6.5.

Answer:

B)6.5

Step-by-step explanation:

H²=P²+B²

7.4²=3.6²+B²

B=√41.8

B=6.465≈ 6.5

Answer:

Step-by-step explanation:

So start by reading it then when you read it you see that theres some numbers what I would do is read the whole thing then wright the numbers then figger whether its multiplication division or what ever else it can be so you start of by moultiplieing the 10 ans 230 and the answer to that is 2300 then i wuld do 5 times 390 which is 1950 then I would add them and if you read that you should be able to get the answer you add the 1950 and the 2300 and get 4250 thats what you right by the last blank and you wright the numbers that we got when we multiplied the numbers for the first blank

Hope this helped