A cross section of the cylinder with the cone removed is a ring. To find the area of the ring, find the area of the outer circle and of the inner circle. Then subtract the area of the inner circle from the outer circle.​

194 children, 58 students, and 97 adults attended the movie.

Let's use algebra to solve this problem.

Let's assume the number of children who attended the movie is C, the number of students is S, and the number of adults is A.

From the problem, we know that:

The seating capacity of the theater is 349:

C + S + A = 349

The theater charges $5 for children, $7 for students, and $12 for adults:

5C + 7S + 12A = $2540

There are half as many adults as there are children:

A = 1/2C

Now we can substitute A = 1/2C from the third equation into the first and second equations:

C + S + 1/2C = 349

3/2C + S = 349

5C + 7S + 12(1/2C) = $2540

5C + 7S + 6C = $2540

11C + 7S = $2540

Now we have two equations with two variables, C and S.

We can solve for S in the first equation:

3/2C + S = 349

S = 349 - 3/2C

Now we can substitute S = 349 - 3/2C into the second equation:

11C + 7S = $2540

11C + 7(349 - 3/2C) = $2540

11C + 2443 - 10.5C = $2540

0.5C = 97

C = 194

Therefore, 194 children attended the movie of total sales.

We can use A = 1/2C from the third equation to find the number of adults:

A = 1/2C

A = 1/2(194)

A = 97

Therefore, 97 adults attended the movie.

We can use C + S + A = 349 to find the number of students:

C + S + A = 349

194 + S + 97 = 349

S = 58

Therefore, 58 students attended the movie.

In summary, 194 children, 58 students, and 97 adults attended the movie.

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Answer:

24 with a remainder of 1 (or Q.24 R.1)

Explanation:
divide the amount of books by the amount of students.

If the only marks that remain are at 1 inch and 2 inches, 9 inches and one mark, the missing mark corresponds to the number 6.

This is a classic problem in recreational mathematics, also known as the "burnt ruler problem". To solve it, we need to think creatively and use rational expressions and equations.

First, we note that the distance between the two marks is 9-2=7 inches. We can imagine the ruler as a number line from 0 to 9, where the two marks correspond to the numbers 1 and 2. We want to find the other mark, which corresponds to some number x between 2 and 9.

Next, we observe that we can use the ruler to construct line segments of length 1, 2, 3, 4, 5, 6, 7, 8, and 9 by adding or subtracting these lengths using the two marks as reference points. For example, we can construct a line segment of length 3 by starting at the mark at 2, moving 1 inch to the right, and then moving 2 more inches to the right.

Now, we notice that any line segment of length n can be expressed as a difference of two line segments of smaller lengths. For example, a line segment of length 7 can be expressed as the difference between a line segment of length 2 and a line segment of length 5. More generally, we can write:

n = a - b

where a and b are integers between 1 and n-1.

Using this observation, we can try to find a way to express the length of the missing segment x as a difference of two integers between 1 and 7. We can start by listing all possible values of a and b:

a=2, b=1: 2-1=1

a=3, b=1: 3-1=2

a=4, b=1: 4-1=3

a=5, b=1: 5-1=4

a=6, b=1: 6-1=5

a=7, b=1: 7-1=6

a=3, b=2: 3-2=1

a=4, b=2: 4-2=2

a=5, b=2: 5-2=3

a=6, b=2: 6-2=4

a=4, b=3: 4-3=1

a=5, b=3: 5-3=2

a=6, b=3: 6-3=3

a=5, b=4: 5-4=1

a=6, b=4: 6-4=2

a=6, b=5: 6-5=1

We notice that the only values of a and b that work are 6 and 1, respectively, since 6-1=5, which is the length of the line segment between the two marks that was not given.

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A. Kyle swam 4 laps in the pool on Monday. He swam 6 times as many laps on Tuesday.

a. The expression 6 x 4 represents the number of laps Kyle swam on Tuesday.

b. The words "6 times as many as 4" represent the number of laps Kyle swam on Tuesday.

c. The number of laps Kyle swam on Tuesday can be found by solving the equation x = 6 x 4.

d. Kyle swam 10 laps on Tuesday.

a) True. Since Kyle swam 6 times as many laps on Tuesday as he did on Monday (4 laps), you would multiply 6 by 4 to find the number of laps he swam on Tuesday.

b) True. This phrase means that Kyle swam 6 times the number of laps he swam on Monday (4 laps), which gives you the number of laps he swam on Tuesday.

c) True. This equation represents the total number of laps Kyle swam on Tuesday. By solving the equation, you can determine that Kyle swam 24 laps on Tuesday.

d) False. Based on the information given and the calculations made, Kyle actually swam 24 laps on Tuesday, not 10.

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The solution to the differential equation with the given initial condition is:

[tex]u = -1/2 * ln(-2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9)[/tex]

To solve equation, we can separate the variables and write:

[tex]1/e^{(2u)} du = e^{(9t)} dt[/tex]

Integrating both sides, we get:

[tex]\int 1/e^{(2u)} du = \int e^{(9t)} dt[/tex]

Integrating the left side requires the substitution v = 2u, dv/du = 2, and du = dv/2, which gives:

[tex]\int 1/e^{(2u)} du = \int 1/2 * 1/e^v dv = -1/2 * e^{(-2u)}[/tex]

Integrating the right side gives:

[tex]\int e^{(9t)} dt = 1/9 * e^{(9t)}[/tex]

Substituting these integrals back into the original equation, we get:

[tex]-1/2 * e^{(-2u)} = 1/9 * e^{(9t)} + C[/tex]

where C is the constant of integration.

We can solve for the constant of integration using the initial condition u(0) = 4:

[tex]-1/2 * e^{(-24)} = 1/9 * e^{(90)} + C[/tex]

[tex]-1/2 * e^{(-8)} = 1/9 + C[/tex]

[tex]C = -1/2 * e^{(-8)} - 1/9[/tex]

Therefore, the solution to the differential equation [tex]du/dt = e^{(2u+9t)}[/tex] with initial condition u(0) = 4 is:

[tex]-1/2 * e^{(-2u)} = 1/9 * e^{(9t)} - 1/2 * e^{(-8)} - 1/9[/tex]

Solving for u, we get:

[tex]e^{(-2u)} = -2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9[/tex]

Taking the natural logarithm of both sides, we get:

[tex]-2u = ln(-2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9)[/tex]

Dividing by -2, we get:

[tex]u = -1/2 * ln(-2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9)[/tex]

Therefore, the solution to the differential equation with the given initial condition is:

[tex]u = -1/2 * ln(-2/9 * e^{(9t)} + 4/9 * e^{(-8)} + 2/9)[/tex]

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The volume of the part of the ball p < 5 that lies between the cones φ = π/4 and φ = π/3 is 0.

To express the volume of the part of the ball p < 5 that lies between the cones φ = π/4 and φ = π/3, we first need to determine the limits of integration in spherical coordinates.
Since the ball has radius 5, we know that the limits on ρ are 0 and 5.

For the limits on φ, we know that the region of interest lies between the cones φ = π/4 and φ = π/3, which correspond to angles of 45 degrees and 60 degrees, respectively.

Therefore, the limits on φ are π/4 and π/3.
For the limits on θ, we know that the region of interest extends all the way around the ball, so the limits on θ are 0 and 2π.
Using these limits, we can express the volume of the region of interest as:
V = ∫∫∫E ρ sin φ dρ dθ dφ
where,

E is the region of interest defined by the limits on ρ, θ, and φ that we just determined.
Substituting the limits and the volume element in spherical coordinates,
Integrating with respect to θ, we have:
V = 0
Therefore, the volume of the part of the ball p < 5 that lies between the cones φ = π/4 and φ = π/3 is 0.

This result suggests that there may be an error in the problem statement or that the region of interest is not well-defined.

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Juanita will keep $187.50 as profit from her ice cream shop's sales this month.

Juanita will keep 25% of the monthly sales as profit, which is equivalent to $750 x 0.25 = $187.50. This means that out of the total monthly sales of $750, Juanita will keep $187.50 as her profit, while the remaining $562.50 will go towards the expenses of running the ice cream shop.

Profit is the amount of money that a business earns after deducting all its expenses. It is the excess revenue that remains after all the costs of doing business have been taken into account. Profit is essential for businesses as it helps them to sustain their operations, invest in growth opportunities, and generate returns for their owners or shareholders.

In Juanita's case, her profit is 25% of the monthly sales, which is a significant amount that can help her to keep her ice cream shop running smoothly. By keeping a portion of the sales as profit, Juanita can use the money to pay for her expenses, such as rent, utilities, and supplies, while still having enough left over to reinvest in her business or save for her personal use.

Overall, understanding the concept of profit is crucial for entrepreneurs and business owners to ensure that they can generate enough revenue to cover their expenses and make a profit that will help them to grow and succeed in the long run.

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Carla's right rectangular prism could have either a 3x4 or a 2x6 rectangle as the bottom layer, with a height of 2 units, to achieve the given volume of 24 cubic units.

Carla built a right rectangular prism using unit cubes, with a volume of 24 cubic units and a height of 2 units. To determine the possible figure for the bottom layer of the prism, we need to understand the relationship between the volume, height, and the base area.

The volume of a rectangular prism can be calculated using the formula: Volume = Base Area × Height. In Carla's case, the volume is 24 cubic units, and the height is 2 units. By rearranging the formula, we can find the base area: Base Area = Volume ÷ Height. Substituting the given values, Base Area = 24 ÷ 2, which equals 12 square units.

Now, we need to find a possible figure for the bottom layer with an area of 12 square units. Since the bottom layer is made of unit cubes, it must have whole-number dimensions. There are two possible rectangular figures that meet this requirement: 1) a 3x4 rectangle, and 2) a 2x6 rectangle. Both of these figures have an area of 12 square units (3x4 = 12 and 2x6 = 12) and can be formed using unit cubes.

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The equation of the attached graph is

The equation is written by the general formula

y = A cos (Bx + C) + D

where:

A = amplitude.

B = 2π/T

where T = period

C = phase shift.

D = vertical shift.

A = amplitude

A = (maximum - minimum) / 2

Using the graph,

maximum = 1

minimum = -1

A = [1 - (-1)] / 2 = 2/2 = 1

B = 2π/T

where T = 2π

B = 2π/(2π) = 1

C = phase shift = 0

D = vertical shift

D = 1 - 1 = 0

substituting results to

y = 1 cos (1x + 0) + 0

this is written as

y = 1 cos (1x) + 0

y = cos (x)

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The type of sequence is a geometric sequence with a common ratio of 1/3

To determine whether the given sequence is a geometric sequence, we need to check if there is a common ratio between any two consecutive terms.

The common ratio, denoted by "r", is calculated by dividing any term of the sequence by its preceding term.

Let's check if there is a common ratio between any two consecutive terms of the given sequence:

15/45 = 1/3

5/15 = 1/3

5/3 / 5 = 1/3

Since the ratio between any two consecutive terms is the same (1/3), the sequence is a geometric sequence.

To find the explicit formula for a geometric sequence, we use the formula:

an = a1 * r^(n-1)

So, we have

an = 45* (1/3)^(n-1)

For the recursice sequence, we have

an = a(n - 1) * 1/3

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Answer: 5 like either, 5 like neither.

Step-by-step explanation: If we add up those who like science, math and both, we get 90. That leaves 10 students, and because all the other numbers end in 5’s or 0’s, I’d say we split this evenly. So 5 like either, and 5 like neither.

Answer:

Like either science or math but not both: 60

Like neither: 30

Step-by-step explanation:

Total: 100

Like science: 35

Like math: 45

Like both: 10

Subtract 10 from "like science" and 10 from "like math"

Like only science: 25

Like only math: 35

Like both science and math: 10

Total who like math, science, or both: 70

Like either science or math but not both: 25 + 35 = 60

Like neither: 100 - 70 = 30

The value of x is 48 km/hr.

How to solve for X

Total distance = 68 km

Total time = 50 minutes

First part:

Duration = 20 minutes

Speed = x km/hr

Second part:

Duration = 25 minutes

Speed = 2x km/hr

Third part:

Duration = 50 - (20 + 25) = 5 minutes

Speed = 3x km/hr

We can calculate the distance traveled in each part using the formula:

distance = speed × time

For the first part:

distance1 = x × (20/60) = (1/3)x (because 20 minutes = 1/3 hour)

For the second part:

distance2 = 2x × (25/60) = (5/6)x (because 25 minutes = 5/12 hour)

For the third part:

distance3 = 3x × (5/60) = (1/4)x (because 5 minutes = 1/12 hour)

Now, we know that the total distance is 68 km, so:

distance1 + distance2 + distance3 = 68

(1/3)x + (5/6)x + (1/4)x = 68

To solve for x, we'll first find a common denominator for the fractions, which is 12:

(4/12)x + (10/12)x + (3/12)x = 68

Now, add the fractions:

(4+10+3)/12 * x = 68

17/12 * x = 68

To isolate x, we'll multiply both sides by the reciprocal of the fraction (12/17):

x = 68 * (12/17)

x = 4 * 12

x = 48

So, the value of x is 48 km/hr.

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Answer:

y = -3x + 20.

Step-by-step explanation:

The correct point-slope equation of a line with slope -3 that contains the point (8,-4) is:

y - (-4) = -3(x - 8)

Expanding the right-hand side:

y + 4 = -3x + 24

Subtracting 4 from both sides:

y = -3x + 20

Therefore, the answer is not given in any of the options provided. The correct equation is y = -3x + 20.

Step-by-step explanation:

g(x)  is just f(x) shifted UP three units ...so

  g(x) = f(x) +3

The confidence level represents the degree of certainty that the interval contains the true population parameter.

The statement "determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520" means that if the farmer were to repeat the sampling process many times and calculate the confidence interval each time, 95% of those intervals would contain the true mean number of suitable apples per tree.

Therefore, we can be 95% confident that the true mean number of suitable apples produced per tree is within the interval of 375 to 520 for this particular sample of 40 trees.

The confidence level represents the degree of certainty that the interval contains the true population parameter.

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The function d(n) = 3^n-1 for n>2 generates the given geometric sequence.

The common ratio of the given geometric sequence is 3, which means that each term is obtained by multiplying the previous term by 3.

a(n)= 3^n for n>0 generates the sequence 3^1, 3^2, 3^3, 3^4, ... = 3, 9, 27, 81, ..., which is not the same as the given sequence.

b(n) = 3(3)^n for n>0 generates the sequence 3(3)^1, 3(3)^2, 3(3)^3, 3(3)^4, ... = 9, 27, 81, 243, ..., which is not the same as the given sequence.

c(n)= 3^n for n>2 generates the sequence 3^3, 3^4, 3^5, 3^6, ... = 27, 81, 243, 729, ..., which is not the same as the given sequence.

d(n) = 3^n-1 for n>2 generates the sequence 3^2, 3^3, 3^4, 3^5, ... = 9, 27, 81, 243, ..., which is the same as the given sequence starting from the third term.

Therefore, the function d(n) = 3^n-1 for n>2 generates the given geometric sequence.

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Answer: A

a(n) = 3^n for n > 0

Step-by-step explanation: Khan

The volume of the figure, which is made up of 2 rectangular prisms, would be 276 cm ³.

The figure shown is made up of two rectangular prisms which means that we can find the volume of the entire figure by finding the volumes of the rectangular prisms and then adding up these volumes to find the total volume.

Volume of the first rectangular prism:

= Length x Width x Height

= 10 x 6 x 3

= 180 cm ³

Volume of the second rectangular prism:

= Length x Width x Height

= 4 x 6 x 4

= 96 cm ³

The total volume of the figure:

= 180 + 96

= 276 cm ³

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Answer:

1 orange

Step-by-step explanation:

you just color 1 circle.

Using regression analysis, we get the following quadratic function:

y = 557[tex]x^{2}[/tex] + 1,690x + 60,000

We can use the data given and fit a quadratic equation in the form of y = a[tex]x^{2}[/tex] + bx + c, where y represents the number of flu cases and x is the number of years since 2012.

x (years since 2012) y (number of flu cases)

0 60,000

1 62,000

2 63,000

3 64,000

4 65,000

5 66,000

6 67,000

7 68,000

8 69,000

9 70,000

10 71,000

11 72,000

12 73,000

13 74,000

14 75,000

15 76,000

Next, we can use this table to find the coefficients a, b, and c that give us the best-fit quadratic function.

Using a regression analysis, we get the following quadratic function:

y = 557[tex]x^{2}[/tex] + 1,690x + 60,000

Here, the coefficient of x is 1,690, which represents the linear term in the quadratic equation. It tells us how much the number of flu cases changes with each year since 2012, assuming a quadratic relationship.

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Year Number of Flu Cases

2000 20,000

2001 22,000

2002 25,000

2003 28,000

2004 32,000

2005 35,000

2006 38,000

2007 42,000

2008 45,000

2009 50,000

2010 55,000

2011 58,000

2012 60,000

2013 62,000

2014 63,000

2015 64,000

Find a quadratic function that models the number of cases of flu each year, where y is years since 2012. What is the coefficient of x?

Answer: I do not have enough information to solve this equation

Step-by-step explanation:

I do not have enough information to solve this equation

The perimeter of the shape is 53.7 units

Perimeter is a math concept that measures the total length around the outside of a shape.

A theorem of circle geometry states that the tangent from a point on a circle are equal.

Therefore the base sides is calculated as

9.9 + 3.2

= 13.1

since the perimeter is the addition of all the sides then;

P = 13.1 + 21.9 + 18.7

P = 53.7

therefore the perimeter of the triangle is 53.7

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The area of the semicircle is approximately 57 square feet.

The arc length of the semicircle can be found using the formula:

arc length = (θ/360) × 2πr

where θ is the angle in degrees, r is the radius, and π is approximately 3.14.

In this case, the diameter of the semicircle is 12 feet, so the radius is half of that, or 6 feet. The angle of the semicircle is 180 degrees, since it is a semicircle. Plugging these values into the formula, we get:

arc length = (180/360) × 2π(6) ≈ 18.85 feet

Therefore, the arc length of the semicircle is approximately 19 feet.

To find the area of the semicircle, we can use the formula:

area = (πr^2)/2

Plugging in the value of the radius from before, we get:

area = (π(6^2))/2 ≈ 56.55 square feet

Therefore, the area of the semicircle is approximately 57 square feet.

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The solution to this system of equations are x =5 and y =10

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

5x - 2y = 5 2x + 2y = 30

Express properly

So, we have

5x - 2y = 5

2x + 2y = 30

Add the equations to eliminate y

7x = 35

Divide both sides by 7

x = 5

Next, we have

2(5) + 2y = 30

So, we have

2y = 20

y = 10

Hence, the value of y is 10

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The sample mean difference from these 24 pairs of siblings is 1.79 inches.

To find the sample mean difference from these 24 pairs of siblings, you can use the given 95% confidence interval for the mean difference in heights, which is (-0.76, 4.34).

The sample mean difference is the midpoint of the confidence interval. To calculate this, add the lower bound (-0.76) and the upper bound (4.34) of the confidence interval, and then divide by 2:

(-0.76 + 4.34) / 2 = 3.58 / 2 = 1.79 inches

So, the sample mean difference from these 24 pairs of siblings is 1.79 inches.

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Answer:

2x and 9x are the coefficients.

Step-by-step explanation:

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression (including variables such as a, b and c ).

Based on the above,  Frank will need to have about 533 water stations per kilometer for the 30-kilometer trail run.

If each runner is said to have about 250 milliliters (0.25 liters) of water per station and there are said to be 4000 liters of water available in total, we have to calculate the total number of water stations  by:

4000 liters of water ÷ 0.25 liters of water per station

= 16000 stations

we have 30-kilometer run, we have to divide the total number of stations by the distance and it will be:

16000 stations ÷ 30 kilometers

= 533.33 stations per kilometer

Therefore, about 533 water stations per kilometer for the 30-kilometer trail run is needed by Frank.

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see full question below

frank is designing a 30-kilometers trail run water that will be given to runners. if 4000 liters of water is available,  each runner was given about 250 milliliters (0.25 liters) of water per station.  how many water stations will there be 30-kilometer run.

The sale price of the sofa can be represented by the equation p - 0.3p. This equation correctly represents the sale price after a 30% discount has been applied to the regular price.

The question is about the regular price of a sofa represented by p, and its sale price which is 30% off the regular price. You'd like to know if the statement "the sale price of the sofa can be represented by p-0.3p" is true.

Step 1: Understand the problem
The regular price of the sofa is represented by p. The sale price is 30% off the regular price.

Step 2: Represent the sale price
To find the sale price, we need to subtract the discount (30% of p) from the regular price (p).

Step 3: Calculate the discount
The discount can be calculated as 30% of p, which is 0.3 * p (or 0.3p).

Step 4: Determine the sale price
Now, subtract the discount from the regular price: p - 0.3p.

Step 5: Confirm the statement
The statement "the sale price of the sofa can be represented by p-0.3p" is indeed true.

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The number sequence that follows the rule of subtracting 15 starting from 105 is 105, 90, 75, 60, 45.

To obtain this sequence, we start with 105 and subtract 15 from it to get 90. Then we subtract 15 from 90 to get 75, and so on until we reach 45. Each term in the sequence is obtained by subtracting 15 from the previous term.

It is important to note that this is an arithmetic sequence with a common difference of -15. The formula for finding the nth term of an arithmetic sequence is: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, and d is the common difference. Using this formula, we can find any term in the sequence by plugging in the appropriate values.

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