A movie theatre sells child tickets for $7.50, adult tickets for $9.75, and student tickets for
$8. The movie theatre sold twice as many child tickets as student tickets. If a total of 191
tickets for the film were sold and the total income was $1593.50, how many of each ticket
were sold?
Find the number of child, adult, and student tickets

Answer:

I believe it is A!!!!!

Step-by-step explanation:

I took the test E2020

The linear equation perpendicular to 6x-y=7 and that passes through (-6, -1) is:

y = (-1/6)*x - 2

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Two linear equations are perpendicular if the product between the slopes is equal to -1.

We want to find a line perpendicular to:

6x - y = 7

y = 6x - 7

Where the slope is 6.

Then:

a*6 = -1

a = -1/6

Then our line is something like:

y = (-1/6)*x + b

To find the value of b, we use the fact that our line passes through (-6, -1), then:

-1 = (-1/6)*-6 + b

-1 = 1 + b

-1 - 1  =b

-2  =b

The line is y = (-1/6)*x - 2

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The volume of the cylinder is option d.10 units

To solve for the volume of the cylinder, we can first cancel out the h on both sides by dividing both sides by h:

(1/3)πr² = πr²

Next, we can simplify the equation by multiplying both sides by 3:

πr² = 3(100π)

πr² = 300π

Finally, we can solve for the volume of the cylinder by plugging in the values we have:

V = πr²h = πr²(2h/2) = (πr²/3)(3h) = (100π/30)(3) = 300π/30 = 10

Therefore, the volume of the cylinder is also 10 cubic feet, which is the same as the volume of the cone.

Hence the option (d) is correct.

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Answer:

Step-by-step explanation:

Using phase line analysis, we find that in the given autonomous differential equations, the equilibrium point P = 1/2 is stable, while P = 0 and P = 1 are unstable.

In the first equation, dP/dt = 1-2P, we can set the expression inside the derivative equal to zero to find the equilibria. Solving 1-2P = 0, we get P = 1/2 as the equilibrium point. To determine the stability, we can analyze the sign of dP/dt for values around the equilibrium. For P < 1/2, dP/dt > 0, indicating population growth. For P > 1/2, dP/dt < 0, indicating population decline. Therefore, the equilibrium P = 1/2 is unstable.

In the second equation, dP/dt = P(1-2P), we can again find the equilibria by setting the expression inside the derivative equal to zero. Solving P(1-2P) = 0, we get two equilibrium points: P = 0 and P = 1/2. Analyzing the signs of dP/dt around these points, we find that for P < 0 and 1/2 < P < 1, dP/dt > 0, indicating population growth. For 0 < P < 1/2, dP/dt < 0, indicating population decline. Hence, the equilibrium points P = 0 and P = 1/2 are both unstable.

In the third equation, dP/dt = 3P(1-P)(P-1/2), we again set the expression inside the derivative equal to zero to find the equilibria. Solving 3P(1-P)(P-1/2) = 0, we get three equilibrium points: P = 0, P = 1/2, and P = 1. Analyzing the signs of dP/dt around these points, we find that for 0 < P < 1/2 and P > 1, dP/dt > 0, indicating population growth. For 1/2 < P < 1, dP/dt < 0, indicating population decline. Thus, the equilibrium points P = 0 and P = 1 are unstable, while P = 1/2 is stable.

In summary, using phase line analysis, we find that in the given autonomous differential equations, the equilibrium point P = 1/2 is stable, while P = 0 and P = 1 are unstable.

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The equation of line that passes through the point (6, -1) & is parallel to the line represented by 8x + 3y = 15, in standard form is: 8x + 3y = 45.

Equation of a line in standard form is:

Ax + By = C

where A, B & C are constants.

As the required line is parallel to the given line, that is 8x + 3y = 15, the slope of the required line will be same as that of the given line.

Slope intercept form of a line is:

y = mx + b

where, m is slope of the line, b is a constant.

Re-writing the equation of the given line in slope-intercept form:

⇒ 3y = -8x + 15

⇒ y = (-8/3)x + 5

⇒ slope = m = -8/3

Now as the required line is parallel to the given line, hence its slope-intercept form will be

y = (-8/3)x + b

As the line passes through the point (6, -1),

⇒ -1 = (-8/3)×6 + b

⇒ b = 15

Hence, the slope-intercept form of the required line is

y = (-8/3)x + 15

Re-writing it in standard form, the equation comes out to be

8x + 3y = 45

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Answer:

Answer: B

Step-by-step explanation: Function A starts at 0,2 and function B starts at 2,2

Step-by-step explanation:

It is required to find which option is correct with what is given in the question.

No, function A has initial value 0 and function B has initial value of 2. So, the functions do not have the same initial value.

In a Cartesian coordinate system each point on it is defined with respect to the two axes x and y.

The initial value of the given function A in the graph is

\(x=0\)

The initial value of the given function B in the table is

\(x=2\)

So, the correct option is

No, function A has initial value 0 and function B has initial value of 2. So, the functions do not have the same initial value.

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Answer:

C should be the correct answer

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Answer:

75 * 1000 = 75000

75000 gram

Step-by-step explanation:

1 kg = 1000g, so the answer is simple (kg * 1000 = g)

The heat loss rate (Q) in units of watts per square meter (W/\(m^2\)) for the given double-pane window is approximately 35.91 * A W/\(m^2\), where A is the area of the window in square meters.

Given:

Thickness of glass layers = 3mm

Thickness of air layer = 3mm

Outside temperature = -20°F = -28.9°C

Inside temperature = +72°F = 22.2°C

To calculate the heat loss rate, we will use the formula for heat conduction:

Q = (k * A * ΔT) / d

Where:

Q is the heat loss rate

k is the thermal conductivity

A is the area of the window

ΔT is the temperature difference between the inside and outside

d is the total thickness of the window

We need to convert the thicknesses of the glass and air layers to meters:

Thickness of glass layers = 3mm = 0.003m

Thickness of air layer = 3mm = 0.003m

We can now calculate the total thickness (d) of the window:

d = 2 * thickness of glass layers + thickness of air layer

d = 2 * 0.003m + 0.003m

d = 0.009m

Assuming the dimensions of the window are provided, let's consider:

Length = L meters

Width = W meters

The area of the window (A) is given by:

A = Length * Width

The thermal conductivity values in SI units are approximately:

k_glass ≈ 0.8 W/(m·K)

k_air ≈ 0.024 W/(m·K)

Now, let's calculate the temperature difference (ΔT) in Celsius:

ΔT = 22.2°C - (-28.9°C)

ΔT = 51.1°C

Substituting the values into the heat conduction formula:

Q = (k * A * ΔT) / d

Q = (0.8 W/(m·K) * A * 51.1°C) / 0.009 m

Simplifying further, we have:

Q = 44.89 * (0.8 * A) W

Therefore, the heat loss rate (Q) in units of watts per square meter (W/\(m^2\)) for the given double-pane window is approximately 35.91 * A W/\(m^2\), where A is the area of the window in square meters.

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Answer: 42 Centimeter

Step-by-step explanation: 42 Centimeter = 1.37795 Foot How to convert Centimeters to Feet 1 centimeter is equal to 0.0328083989 feet: 1cm = (1/2.54) inch = 0.0328083989ft the distance d in feet (ft) is equal to the distance d in centimeters (cm) divided by 30.48, that conversion formula

Answer:

$5.80

Step-by-step explanation:

To answer, we must first subtract the toal cost Joe paid by the amount he paid for his drink, because ha paid for his drink separately. so:

3.20 - 1.75 = 1.45

And because there were a total of 4 friends, we mulitply the answer by 4:

1.45 * 4 = 5.8

So, the bag of donuts costed $5.80

Hope this helps :)

IfIf a free kick is given in a soccer game where the player taking the kick is 14 yards from the left post. How far is the kicker from the right post, to the nearest yard is: A. 23 yards.

Using sine theorem

Let Left triangle=3/sinx=14/sin∝

Let Right triangle=5/sinx=y/sin(180°-∝°)

Let Sin∝°=sin(180°-∝°)  sinx=sinx

Let y represent how far is the kicker

Hence:

3/5=14/y

y=5×14/3

y=70/3

y=23.3333

y=23 yards (Approximately)

Therefore If a free kick is given in a soccer game where the player taking the kick is 14 yards from the left post. How far is the kicker from the right post, to the nearest yard is: A. 23 yards.

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Answer:

8s

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

10s + -2s

Step 2: Simplify

Answer:

\(\huge\boxed{8s}\)

Step-by-step explanation:

Expression can be broken down into a couple of parts.

When we have multiple terms with the same variable, we can perform operations on them assuming they have the same variable - for example, 5x + 6x = 11x, as 5+6=11.

We can apply the same logic here, however, note that adding a negative is the same as subtracting a positive. For example, 5 + -2 is the same as 5-2.

\(10 - 2 = 8\)

Therefore, our final expression is \(8s\).

Hope this helped!

The probability that a randomly selected purchaser with an extended warranty has a basic model camera is approximately 0.0354

Denote S= Event that a purchase bought a basic camera, then P(S)=0.32

Denote D= Event that a purchase bought a deluxe camera, then

S and D are mutually exclusive.

P(D)=1-P(S)=0.68

P(W/S)=0.4

P(W/D)=4.9

We need to calculate the probability that a randomly selected purchaser who bought an extended warranty has a basic model. By notations, this is equivalent to finding P(S/W).

P(S/W)=P(W/S)*P(S)/P(W)

Since S and D are disjoint and P(S)+P(D)=1,

P(W)=P(W∩S)+P(W∩D)

P(W)=[0.4*0.32]+[4.9*0.68]

=3.61

Hence, our required probability is: P(S/W)=P(W/S)*P(S)/P(W)

\(=\frac{0.4*0.32}{3.61}\\=0.0354\)

Hence, the probability that a randomly selected purchaser with an extended warranty has a basic model camera is approximately 0.0354

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After 8.5 seconds down the hill, they will be moving at a velocity of 17.19 m/s.

The speed of an object after a certain time can be calculated using the following equation:

v = u + at

Where:v is the final velocity, u is the initial velocity, a is the acceleration of the object, t is the time taken by the object

So, the person is on skis at the top of a 12-degree ski run and starts from rest, which means the initial velocity u is 0 m/s.

The downhill slope creates an acceleration for the person. The acceleration due to gravity is acting down the slope.

The component of gravity along the slope is given by:g = 9.81 × sin (12°) = 2.022 m/s²

Putting all values in the equation:

v = u + atv = 0 + 2.022 × 8.5v = 17.19 m/sTherefore, the person's final velocity after 8.5 seconds down the hill is 17.19 m/s.

After 8.5 seconds down the hill, they will be moving at a velocity of 17.19 m/s.

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Answer:

16.) c. 2x²+7x-15

17.) c. \(y=\frac{4}{9}x+\frac{17}{9}\)

18.) D

Step-by-step explanation:

have a wonderful day! :D

Answer: 10/250

Don't overcomplicate it! It says fraction or decimal.

1 ticket = 1/250 chance

10 tickets = 10/250 chance

hope this helps

Answer:

elena

Step-by-step explanation:

Answer:

Step-by-step explanation:

it is given

a II b and b II c

and c perpendicular to d

as a is parallel to b and b is parallel to c ,

so a would-be parallel to c also, but c is perpendicular to d

so, a also will be perpendicular to d.

so the answer is

a is perpendicular to d

Answer:

See below.

Step-by-step explanation:

20.

\( \sqrt{43} - \pi = 6.5574 - 3.1416 = 3.4158 \)

Plot the number between 3.4 and 3.5, but much closer to 3.4 than to 3.5 since it is approximately 3.42.

21.

(7.3 * 10^6) / (3.2 * 10^4) = 7.3/3.2 * 10^6/10^4 = 2.3 * 10^2

Answer:

Step-by-step explanation:

It could be apple because there is more apple that blackberry fruit drops

Step-by-step explanation:

apple flavoured and 8 are blackberry

flavoured. She chooses a sweet at random and eats it. Then she chooses another sweet at

random. Calculate the probability

Hence option (B) is a correct choice and rest all other options are incorrect

1/b^2 ∑ (-1)^k(t^2/b^2)^k                                        
                             

Step-by-step explanation:

 Remember that the sum of infinite GP is given by the formula blow:
First term=a
Common ratio=r

S=a/1 - r                                          

Wherever the common ratio r falls within the interval (-1,1)

When the given series is compared to the infinite sum:

First term=a
Common ratio=r
S=  a/1-r = 1/b^2+t^2
Now given: |t| < |b|=0<t^2/b^2<1
S=1/B^2.1/1-(-T^2/B^2)
=A=1
R=-T^2/B^2
Writing the general form:

Hence option (B) is a correct choice.

What are real numbers simple definition?

Real numbers can be defined as the union of both rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”. All the natural numbers, decimals and fractions come under this category.

INCOMPLETE QUESTION: if b and t are real numbers such that 0<|t|<|b|, which of the following infinite series has sum 1b2 t2
A) 1/b^2 ∑(t^2/b^2)^k.
B) 1/b^2 ∑(-1)^K(t^2/b^2)^k.
C)B^2∑(T^2/B^2)^K
D)b^2∑(-1)(t^2/b^2)^k

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Answer: y = 4x + 1

Step-by-step explanation:

First, we will create a point-slope equation.

Given:

     y - y1 = m(x - x1)

Distribute:

     y - - 3 = 4(x - - 1)

Combine two negatives into a positive:

     y + 3 = 4(x + 1)

Distribute the 4:

     y + 3 = 4x + 4

Subtract 3 from both sides of the equation:

     y = 4x + 1

The answer is:

Work/explanation:

I will begin by writing the equation in point slope form, which is:

\(\sf{y-y_1=m(x-x_1)}\)

where m = slope, and (x₁,y₁) is a point

Plug in the data from the problem

\(\begin{gathered}\bf{y-(-3)=4(x-(-1)}\\\bf{y+3=4(x+1)}\\\bf{y+3=4x+4}\\\bf{y=4x+4-3}\\\bf{y=4x+1}\end{gathered}\)

Answer:

x=-7

Step-by-step explanation:

7x2-x=7

7x2=14.

14-x=7

When you finished the last step, you will subtract 14 to both sides.

14-x=7

14-14-x=7-14

this will cancel out the 14 on the left.

And will leave you with:

-x=7-14

7-14 is -7.

and this will get you to

-x=-7

To finish this off, you have to turn the negative x/variable, into a positive x/variable.

So, you will divide both sides of the equation by the same term.

-x = -7

into

\(\frac{-x}{1} =\frac{-7}{1}\)

and it will be -7.

I hope this helps      :)

The algebraic expression 6x(3y + 4z) can be simplified as 18xy + 24xz

the algebraic expression given in the question is a linear equation in three variables that are x , y and z and the simplification of this algebraic expression would also contain all the three variables

To solve this question we have to use the algebraic of  distributive property of addition over multiplication

so, using the above property and substituting the values given in the question we get

6x(3y +4z) = 6x(3y) + 6x(4z)

                  = 18 xy + 24 xz

Hence, The algebraic expression 6x(3y + 4z) can be simplified as 18xy + 24xz

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The probability that exactly 2 have curly hair is (c) 0.3105

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

Sample size, n = 4

p = 0.35

The probability is then calculated as

\(P(x) = ^nC_x * p^x * (1 - p)^{n-x\)

substitute the known values in the above equation, so, we have the following representation

\(P(2) = ^4C_2 * 0.35^2 * (1 - 0.35)^2\)

Evaluate

P(2) = 0.3105

Hence, the probability that exactly 2 have curly hair is (c) 0.3105

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The simplified value of the expression\(\sqrt{ ((2^3 * 64^(1/2) + 1176 + (3^2)^3 + (11 * 3)^1) - 153) }\) is 43.

Given expression: \(\sqrt{(2^3 * 64^(1/2) + 1176 + (3^2)^3 + (11 * 3)^1) - 153)}\)

Step 1: Evaluate the exponentiations.

\(2^3 = 8\) and \(3^2 = 9.\)

The expression becomes: \(\sqrt{((8 * 64^(1/2) + 1176 + 9^3 + (11 * 3)^1) - 153)\\}\)

Step 2: Simplify the square root.

\(64^{(1/2)\) is the square root of 64, which is 8.

The expression becomes: \(\sqrt{((8 * 8 + 1176 + 9^3 + (11 * 3)^1) - 153)}\)

Step 3: Evaluate the multiplications and additions.

8 * 8 = 64, \(9^3\) = 729, and 11 * 3 = 33.

The expression becomes: \(\sqrt{(64 + 1176 + 729 + 33 - 153)\\}\)

Step 4: Perform addition and subtraction.

64 + 1176 + 729 + 33 - 153 = 1849

Step 5: Take the square root of the result.

\(\sqrt{1849\\}\) = 43

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