On the opening night of a new movie, a theater sells a total of 510 tickets worth a total of $5,015. Tickets cost $7.50 for children and $11.00 for adults. How many children attended opening night of this movie?
92
170
340
418

The 90% confidence interval of absences per tutorial over the past 5 years is approximately 11.151 to 12.049 absences.

To estimate the 90% confidence interval of absences per tutorial over the past 5 years, follow these steps:

1. Identify the given data:
  Sample size (n) = 225
  Sample mean (x) = 11.6
  Sample standard deviation (s) = 4.1
  Confidence level = 90%

2. Calculate the standard error (SE):
  SE = s / sqrt(n)
  SE = 4.1 / sqrt(225)
  SE ≈ 0.273

3. Determine the critical value (z) for a 90% confidence interval:
  For a 90% confidence interval, the critical value (z) is approximately 1.645.

4. Calculate the margin of error (ME):
  ME = z * SE
  ME = 1.645 * 0.273
  ME ≈ 0.449

5. Estimate the confidence interval:
  Lower limit = x - ME
  Lower limit = 11.6 - 0.449
  Lower limit ≈ 11.151

  Upper limit = x + ME
  Upper limit = 11.6 + 0.449
  Upper limit ≈ 12.049

The 90% confidence interval of absences per tutorial over the past 5 years is approximately 11.151 to 12.049 absences.

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Answer:

x = 9

PQ = 19

QR = 19

RP = 10

Step-by-step explanation:

if 3x - 8 = 2x+1

then,

3x -2x = 1+8

x = 9

for pq,

2x+1

2x + 1 = 2*9+1

=>18 +1 = 19

for qr,

3x-8 = 3*9-8

=>27-8 =19

for rp,

x+1=9+1

=> 10

The number of balloons on each package will be 15

From the information, Jason is a party planner. In 124 packages, he has a total of 1,860 balloons and each package has the same number.

Therefore, the number of balloons on each package will be:

= 1860 / 124

= 15

When a plane has to travel 2,800 miles at an average speed of 560 miles per hour. The number of hours used will be:

= 2800/560

= 5

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x is equal to 3 if not then I just we are asking the wrong questions

Answer:

-15.6 or -15 3/5

Step-by-step explanation:

Answer:

\(-40c^{2} d^{2} -32cd\)

Step-by-step explanation:

-20c³ is the expression which is equivalent to (-5cd⁻⁴)(2cd²)².

To simplify the given expression, (-5cd⁻⁴)(2cd²)², we can apply the power of a product rule, which states that (ab)² is equal to a²b².

Let's break down the expression step by step:

(-5cd⁻⁴)(2cd²)²

First, let's square the expression (2cd²)²:

(2cd²)² = (2)²(c)²(d²)² = 4c²d⁴

Now, we substitute this result back into the original expression:

(-5cd⁻⁴)(4c²d⁴)

To simplify further, we can multiply the coefficients and combine the variables:

(-5)(4) = -20

(c)(c²) = c³

(d⁻⁴)(d⁴) = 1

Putting it all together, the expression (-5cd⁻⁴)(2cd²)² simplifies to -20c³.

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Answer:

Step-by-step explanation:

You are given several lists from which to choose (share them, please) and in each case you must decide whether or not the numbers are in ordere from least to greatest.

Using 37/6, -5.1717, √33, -26/5 as an example (since it is only one of several llsts), we convert all the numbers into mixed decimal fractions:

37/6 = +6.17

-5.172

5.74

-5.3

This particular list has NOT been arranged in order from least to greatest.

You must now perform the same test on the other lists and then choose the list whose numbers are shown in order from least to greatest.

The list that shows these numbers in order from least to greatest is to be considered as the -5.17, 26/5, √33, 37/6.

Since

If we divide 37 by 6 so it comes 6.1666

The next value is -5.1717

The root of 33 is 5.744

And, the value of  -26/5 is 5.2

So based on this, we can say that The list that shows these numbers in order from least to greatest is to be considered as the -5.17, 26/5, √33, 37/6.

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Answer:

Berries with any blush of red are not ripe, yet may ripen further once picked if kept at room temperature. That said though, you really want to ...

Answer:

\(Cost \ total= \$ 1755\)

Step-by-step explanation:

Find the total cost of a rectangular shaped carpet, given the carpets length,  width, and the cost of carpet per square foot. Using the formula for the area of a rectangle.

\(\boxed{\left\begin{array}{ccc}\text{\underline{Area of a Rectangle:}}\\\\A=l \times w\end{array}\right}\)

Where...

Given:

\(l=15 \ ft\\w=9 \ ft\\ 1 \ ft^2= \$ 13\)

Find:

\(Cost \ total = \ ?? \\)

(1) - Calculating the total area of the carpet, which is a rectangle

\(A=l \times w\\\\\Longrightarrow A=15 \ ft \times 9 \ ft\\\\\therefore \boxed{A=135 \ ft^2}\)

(2) Calculate the total cost of the carpet by multiplying the total area of the carpet by the cost of one square foot of carpet

\(Cost \ total=135 \ ft^2 \times \$ 13\\\\\therefore \boxed{\boxed{Cost \ total= \$ 1755}}\)

Thus, the total cost of the carpet is found.

Answer:

-7-11=-18

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

10(49-49)

---------------

2(7)(7^2-16)(7+3)

  0

---------

4620

answer is 0

Answer:

E) 998

Step-by-step explanation:

Members in the first year (p) is 350.

Each year members increased by (r) 14%.

We need to find the number of members after (t) 8 years.

Total members = P (1 + r)^t

= 350 ( 1 + 0.14)^8 = 998 members

So, the answer is E) 998

Dawn sold $600, Bob sold $480, and Susan sold $400 in total for the day.

To find out how much each person sold in total for the day, we need to solve the given equations. Let's assign variables to the unknowns:
- Let's say Dawn's sales are represented by D
- Bob's sales are represented by B
- Susan's sales are represented by S

According to the information provided, we have three equations:

1. Dawn's sales were $120 more than Bob's sales:
  D = B + $120

2. Bob and Susan combined to sell $280 more than Dawn:
  B + S = D + $280

3. The combined sales of Dawn, Bob, and Susan were $1480:
  D + B + S = $1480

We can now solve these equations simultaneously to find the values of D, B, and S.

First, let's substitute the value of D from equation 1 into equation 2:
B + S = (B + $120) + $280
B + S = B + $400

Next, let's simplify equation 2:
S = $400

Now, let's substitute the values of D and S into equation 3:
(B + $120) + B + $400 = $1480
2B + $520 = $1480
2B = $1480 - $520
2B = $960
B = $960 / 2
B = $480

Finally, let's substitute the value of B into equation 1 to find the value of D:
D = B + $120
D = $480 + $120
D = $600

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Answer: yes I do believe

Answer: 25% i believe

Step-by-step explanation:

The probability that it lands inside the triangle is,

P = 25%

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Since, the probability is equal to,

P = size of the event space/size of the sample space

Here, In this problem

size of the sample size = area of the rectangular dartboard = 648 square centimeters

And, size of the event space = area of the triangular part = 162 square centimeters.

Hence, the probability that it lands inside the triangle is,

P = 162 / 648

P = 0.25

P = 25%

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Answer:

C

Step-by-step explanation:

\( \sqrt{3x} + 8 = x - 2\)

Answer:

Yi- -3/4

slope- 0

Step-by-step explanation:

We will use the formula:

A = p( 1+ r/n)^nt

where

A= amount

P = principal

n=number of time interest is compounded per unit time

T= time(years)

r i= interest rate (decimal)

From the question:

A=$ 1000000

P = ?

t = 4

r = 0.04

n= 4

we will go ahead and substitute into the formula and then solve for p

852, 821.26 = P

The initial amount deposited initially is $852 821.26

Answer:

Step-by-step explanation:Idon't say you have to mark my ans as brainliest but my friend if it has helped you don't forget to thank me...

The volume of the cylindrical water tank with the given value of radius and height to the nearest whole number is 1459ft³.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )

Given the data in the question;

We substitute our values into the expression above.

V = π × r² × h

V = 3.14 × (6.5ft)² × 11ft

V = 3.14 × 42.25ft² × 11ft

V = 1459ft³

The volume of the cylindrical water tank with the given value of radius and height to the nearest whole number is 1459ft³.

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m=n and C=D, as CD is an nxn matrix and In and Im have dimensions nxn and mxm, respectively.

To prove that m=n, let us consider the dimensions of the matrices involved. The matrix product CD has dimensions nxm times mxn, which gives an nxn matrix. On the other hand, the identity matrices In and Im have dimensions nxn and mxm, respectively. Therefore, for the products CA and AD to be well-defined, we must have m=n.

Now, let us show that C=D. We have:

CA = In (given)

AD = Im (given)

Multiplying both sides of the first equation by D on the right and both sides of the second equation by C on the left, we get:

CAD = D (from CA=In)

CAD = C (from AD=Im)

Since CAD is equal to both D and C, we have D=C. Therefore, the matrices C and D are equal, and we have proved that m=n and C=D.

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The exact value of the cotangent of theta in simplest radical form is -21/20.

What is the simplest radical form?

The simplest radical form is the expression of a radical without any factors inside the radical that can be further simplified.

To find the exact value of cotangent of theta, we need to find the values of cosine and sine of theta first.

Given that the terminal side of the angle passes through the point (21,-20), we can use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the angle and the x and y-axes:

\(h = \sqrt{(21^2 + (-20)^2)} = \sqrt{(841 + 400)} = \sqrt{(1241)}\)

Then, we can find the values of cosine and sine of theta using the x and y-coordinates of the point:

cos(theta) = adjacent/hypotenuse = 21/sqrt(1241)

sin(theta) = opposite/hypotenuse = -20/sqrt(1241)

Now we can find the value of cotangent of theta:

cot(theta) = cos(theta) / sin(theta) = (21/sqrt(1241)) / (-20/sqrt(1241))

= -21/20

Therefore, the exact value of the cotangent of theta in simplest radical form is -21/20.

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a) The unit rate of change of d with respect to t is equal to 1.6

b) the graph of the line in the attached figure.

Given: A proportionate relationship between d and t with the characteristic that a rise in t of 5 units causes a rise in d of 8 units.

To locate: A rise of 5 units in t causes a rise of 8 units in d, according to the line's unit rate of change with respect to t.

=> Slope  =   Δd/Δt   = 8/5 = 1.6

the proportional relationship between d  and t

=> d ∝ t

=> d = 1.6t

t           d=1.6t

0          0

1           1.6

2           3.2

3           4.8

Plot the points and draw a line passing through points.

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The instantaneous acceleration at any time t is given by 10t. The limit definition of a derivative is true because it allows us to find the instantaneous rate of change of a function at a specific point.

To use the limit definition of a derivative to calculate instantaneous acceleration, we need to find the derivative of the velocity function with respect to time. The derivative of velocity gives us acceleration.

The limit definition of a derivative is given by:

f'(x) = lim (h→0) [f(x+h) - f(x)] / h

To calculate instantaneous acceleration, we substitute the velocity function, v(t), into the limit definition. Let's say v(t) = 5t^2.

Using the limit definition, we have:

a(t) = lim (h→0) [v(t+h) - v(t)] / h

Substituting v(t) = 5t^2, we get:

a(t) = lim (h→0) [5(t+h)^2 - 5t^2] / h

Expanding and simplifying:

a(t) = lim (h→0) [10th + 5h^2] / h

Now, we can cancel out the h term:

a(t) = lim (h→0) 10t + 5h

Taking the limit as h approaches 0, we get:

a(t) = 10t

Therefore, the instantaneous acceleration at any time t is given by 10t.

The limit definition of a derivative is true because it allows us to find the instantaneous rate of change of a function at a specific point. By taking the limit as the change in input approaches zero, we are able to approximate the exact rate of change at that point. This concept is fundamental to calculus and is used in various applications such as physics, engineering, and economics.

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Answer:

um i really dont know but if i dont know the the answer to sum i put c but i recommend not doing that

Step-by-step explanation:

Answer:

The second option, 2 is a prime number, but not odd

Step-by-step explanation:

A prime number is a result of two other whole numbers multiplied by themselves. There is no whole number that you can multipy by itself to get 2 because 1 × 1 = 1 and 2 × 2 = 4. Therefore, it is a prime number. But, that does not mean it is an odd number because odd numbers are 1, 3, 5, 7, etc. and even numbers are 2, 4, 6, 8, etc.

Answer:

Centre = (2, -3)

radius = 5units

Step-by-step explanation:

The standard form of a circle is expressed as;

x²+y²+2gx+2fy+c = 0

Centre = (-g, -f)

radius r = √g²+f²-c

Given the equation;

x²+y²-4x+6y-12 = 0

Compare

2gx = -4x

2g = -4

g = -2

Similarly;

2fy = 6y

2f = 6

f = 3

Centre = (-(-2), -3)

Centre = (2, -3)

Radius = r = √(-2)²+3²+12

r = √4+9+12

r = √25

r = 5 units

As a result, the radian measure of the relevant center angle is around 3.07 radians.

An arc is any smooth curve that connects two locations. The length of an arc is referred to as its arc length. A graph arc is an ordered pair of neighboring vertices in a graph. An arc is defined as any segment (other than the complete curve) of a circle's circumference.

Here,

The formula for the length of an arc in a circle is given by:

Arc Length = (Central Angle / 2π) * Circumference

We know the Arc Length and the Radius of the circle, so we can find the Central Angle as follows:

Arc Length = (Central Angle / 2π) * 2π * Radius

66/5 * π = (Central Angle / 2π) * 2π * 22

66/5 * π = Central Angle * 22

Central Angle = (66/5 * π) / 22

The radian measure of an angle is equal to the ratio of the length of the arc that it intercepts to the radius of the circle. Hence, the radian measure of the central angle is given by:

Central Angle (in radians) = Arc Length / Radius

= (66/5 * π) / 22

So, the radian measure of the corresponding central angle is approximately 3.07 radians.

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A. The equation of motion is d²θ/dt² + (9.8/0.5)θ = 0.

B. The time at which the pendulum first reaches its maximum angle from the vertical can be found by solving the equation of motion.

C. The maximum angle from the vertical can be determined by substituting the time obtained in part (B) into the equation of motion.

D. The time it takes for the pendulum to reach maximum deflection in the other direction can be found by solving the equation of motion for θ = 0.

E. The period of the pendulum is given by T = 2π√(0.5/9.8).

We have,

A.

For a pendulum with length L = 0.5 meters, initial angle θ₀ = 0.2 radians, and initial angular velocity (dθ/dt)₀ = 0.4 radians/sec, the equation of motion can be determined by substituting these values into the given differential equation.

The equation of motion is: d²θ/dt² + (g/L)θ = 0.

B.

To find the time at which the pendulum first reaches its maximum angle from the vertical, we can solve for the critical points of the equation of motion.

The maximum angle occurs when θ = ±π/2.

By solving the equation (d²θ/dt² + (g/L)θ = 0) for θ = ±π/2, we can find the corresponding time.

C.

The maximum angle (in radians) from the vertical can be determined by substituting the time obtained in part (B) into the equation of motion and solving for θ.

D.

To find the time it takes for the pendulum to reach maximum deflection in the other direction after reaching its maximum angle, we need to find the next critical point.

This occurs when θ = 0.

By solving the equation of motion (d²θ/dt² + (g/L)θ = 0) for θ = 0, we can find the corresponding time.

E.

The period of the pendulum, which is the time for one swing back and forth, can be calculated using the formula T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.

Thus,

A. The equation of motion is d²θ/dt² + (9.8/0.5)θ = 0.

B. The time at which the pendulum first reaches its maximum angle from the vertical can be found by solving the equation of motion.

C. The maximum angle from the vertical can be determined by substituting the time obtained in part (B) into the equation of motion.

D. The time it takes for the pendulum to reach maximum deflection in the other direction can be found by solving the equation of motion for θ = 0.

E. The period of the pendulum is given by T = 2π√(0.5/9.8).

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The complete question:

Consider a pendulum with a length of L meters and an angle θ (in radians) from the vertical. The motion of the pendulum can be described by the following differential equation:

d²θ/dt² + (g/L)sin(θ) = 0

where g represents the acceleration due to gravity (9.8 m/sec²).

(a) Determine the equation of motion for a pendulum with a length of L meters, an initial angle of θ₀ radians, and an initial angular velocity (dθ/dt)₀ radians/sec.

(b) Find the time at which the pendulum first reaches its maximum angle from the vertical. Provide your answer in seconds.

(c) Calculate the maximum angle (in radians) reached by the pendulum from the vertical.

(d) Determine the time it takes for the pendulum to reach maximum deflection in the opposite direction after reaching its maximum angle. Identify the next critical point. Provide your answer in seconds.

(e) Calculate the period of the pendulum, which is the time it takes for one complete swing back and forth.

Answer:

C = (5F - 160)/9

Step-by-step explanation:

Given:

F = 9/5C + 32

Solve the formula for C in terms of F

F = 9/5C + 32

F - 32 = 9/5C

C = (F - 32) ÷ 9/5

C = (F - 32) × 5/9

= (5F - 160)/9

C = (5F - 160)/9