Find the area and circumference of the circle.
(x - 1)^2 + (y-2)^2 = 100
The area of the circle is ______
(Simplify your answer. Type an exact answer, using as needed.)

The circumference of the circle is _____ (Simplify your answer. Type an exact answer, using as needed.)

Answer:

19x − y = 0

__

Answer:

y = 0.5

Step-by-step explanation:

The equation provided is: ρ²(sin²(φ)sin²(θ) + cos²(φ)) = 16, This equation is in spherical coordinates,

where ρ represents the radial distance from the origin, φ is the polar angle (or the angle between the positive z-axis and the vector), and θ is the azimuthal angle (or the angle between the positive x-axis and the projection of the vector onto the xy-plane).

Now, let's analyze the equation further: 1. Divide both sides of the equation by 16 to isolate ρ²: ρ² = 16 / (sin²(φ)sin²(θ) + cos²(φ)) 2. Take the square root of both sides to find ρ: ρ = √(16 / (sin²(φ)sin²(θ) + cos²(φ))).

From this, we can see that the surface is defined by the radial distance ρ, which depends on the angles φ and θ. This indicates that the given equation represents a 3-dimensional surface in spherical coordinates.

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To compute the 99% confidence interval for the population mean, you need to determine the appropriate sample size to ensure that the sample mean does not deviate from the population mean by more than 1.3. The key terms involved in this process are the confidence interval, sample size, population mean, and sample mean.

The confidence interval represents the range within which the population parameter (in this case, the population mean) is likely to fall, given a certain level of confidence. A 99% confidence interval means that you are 99% confident that the true population mean falls within the specified range.

To calculate the required sample size, you will need to use the formula for the margin of error (E), which is E = (Zα/2 * σ) / √n, where Zα/2 is the critical value associated with the desired level of confidence (99%), σ is the population standard deviation, and n is the sample size.

Since you want the sample mean to not deviate from the population mean by more than 1.3, you will need to set E = 1.3 and solve for n. After finding the critical value for a 99% confidence interval (which is approximately 2.576) and assuming you know the population standard deviation, you can plug these values into the formula and solve for n.

By doing this, you will be able to determine the appropriate sample size to ensure that the 99% confidence interval for the population mean is within 1.3 units of the sample mean.

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Answer:  where is the picture

Step-by-step explanation:

Answer:

A because they create parallel lines but only have different intercepts.

Answer:

1. 3.33

2. 8.75

3. 4.8

4. 2.5

Step-by-step explanation:

Answer:

The sequence is -5 so the next 2 values are -12, and -17

Step-by-step explanation:

Answer:

Step-by-step explanation:

line 1.

y=3

line 2.

x=-1.2

line 3.

x=3

line 4.

y=-2.6

length=3-(-1.2)=3+1.2=4.2

width=3-(-3)=3+3=6

area=4.2×6=25.2

The algebraic expression for "The product of 9 and two more than a number" is 9(x + 2).

In the given word phrase, "a number" is represented by the variable x. The phrase "two more than a number" can be translated as x + 2 since we add 2 to the number x. The phrase "the product of 9 and two more than a number" indicates that we need to multiply 9 by the value obtained from x + 2. Therefore, the algebraic expression for this word phrase is 9(x + 2).

"A number": This is represented by the variable x, which can take any value.

"Two more than a number": This means adding 2 to the number represented by x. So, we have x + 2.

"The product of 9 and two more than a number": This indicates that we need to multiply 9 by the value obtained from step 2, which is x + 2. Therefore, the algebraic expression becomes 9(x + 2).

In summary, the phrase "The product of 9 and two more than a number" can be algebraically expressed as 9(x + 2), where x represents the number.

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If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

For this question we need to subtract and multiply the numbers. We know that 2 = 25% of 8 so:

\(\boxed{8-2=6}\\\boxed{6/2=3}\)

We are going to take that 25% and multiply it with 3 to get are final answer.

\(\boxed{25*3=75}\\\boxed{So,2=75}\)

Therefore, If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

Answer:

Angle P: 110°

Angle S: 110°

Step-by-step explanation:

Since angle P and angle S are congruent, that means they are equal to each other.

Setup an equation so that they are equal to each other and solve for x.

2x + 10 = 3x - 40

2x - 2x +10 = 3x -2x - 40

10 = x - 40

10 + 40 = x - 40 + 40

x = 50

For each angle, plugin for x and solve. You should get the same answer since they are congruent.

Angle P:

2x + 10

2(50) + 10

100 + 10

110°

Angle S:

3x - 40

3(50) - 40

150 - 40

110°

All of the translations describes the same inclination for a straight line because the they all have a pitch (slope) of 2/5.

Mathematically, the pitch (slope) of a geometric figure or straight line can be calculated by using this formula:

Pitch (slope) = V/H

Where:

Based on the information provided, the pitch (slope) of this line is given by:

Pitch (slope) = Up 2/Right 5 = 2/5

Pitch (slope) = Up 4/Right 10 = 2/5

Pitch (slope) = Down 42/Left 5 = 2/5

Pitch (slope) = Up 1/Right 5/2 = 2/5

Pitch (slope) = Down 2/5/Left 1 = 2/5

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The antiderivative of sin is -cos(x) + C.

The antiderivative of a function is the inverse operation of differentiation which is is also known as its indefinite integral.

So, the integral of sin

                 ∫sin(x) = -cos(x) + C

where C = constant of integration.

This can be verified by differentiating -cos(x) + C with respect to x, which gives sin(x).

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Answer:

B. (1, -2)

Step-by-step explanation:

In order to for it to be a function, the inputs need to have only one output.

The table shows:

(-1, 2), (0, -4), (1, -2), (1, 5), (2, 0), (3, 2), (4, 9)

If a x-value is repeating it is not a function.

The area of a cross section of the shape formed by the intersection of the solid and a plane parallel and 2 inches above the base is 20.93 cm².

Calculate the area of the cylinder.

A cylinder's surface area is determined by multiplying its base circumference by its height.

2r, where r is the cylinder's radius (5 cm), equals the circumference of the cylinder.

Therefore, the area of the cylinder is 2πr x 5 cm = 2π x 5 cm2 = 31.4 cm².

Calculate the area of the cone.

A cone's area is determined by multiplying its height by a factor of three times the base's radius.

2r, where r is the cone's radius (5 cm), equals the circumference of the cone.

Therefore, the area of the cone is 1/3 x 2πr x 5 cm = 2π x 5 cm2 / 3 = 10.47 cm².

Determine the cross section area.

The area of the cylinder less the area of the cone equals the area of the cross section.

Therefore, the area of the cross section is 31.4 cm2 - 10.47 cm2 = 20.93 cm².

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Answer:

It number 1 trust me pls se

Step-by-step explanation:

In 13.567% of the 30 cities, the mean prevalence of childhood asthma will be higher than 2.5%.

Given that:

X: childhood asthma prevalence

With mean u = 2.22%

and standard deviation σ= 1.39%

To find : Determine the probability that the average prevalence of childhood asthma in a sample of n cities is higher than 2.5%.

Although we are unsure about the distribution of the variable, keep in mind that from n ≥ 30, the sampling distribution can be roughly compared to the normal distribution according to the central limit theorem:

X≈N(μ;σ²/n)

Additionally, compute the requested probability using the standard normal distribution:

P(X>2.5)= 1 - P(X≤2.5)

Determine the Z value given the X value:

Z = (X - u)/ (σ/√n)

Z = (2.5-2.2)/(1.39/√30)

Z = 1.10

Using the Z-tables you have to look for the value of

P(Z≤1.10)= 0.86433

1 - 0.86433= 0.13567

Then P(X>2.5)= 1 - P(X≤2.5)= 1 - P(Z≤1.10)= 1 - 0.86433= 0.13567

So, 13.567% of the 30 cities will have a mean childhood asthma prevalence greater than 2.5%

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Answer:

177x

Step-by-step explanation:

{(5, 2), (4, 2), (3, 2), (2, 2), (1, 2)}, {(−8, −3), (−6, −5), (−4, −2), (−2, −7), (−1, −4)} and {(−6, 4), (−3, −1), (0, 5), (1, −1), (2, 3)} are the sets of ordered pairs considered as a function.

{(−4, −2), (−1, −1), (3, 2), (3, 5), (7, 10)} is not a function.

In mathematics, ordered pair is a pair of numbers that are written in a specific order. They are generally written in (x, y) form. For example (3, 5) is an ordered pair.

The function can also be represented by a set of ordered pairs. A function Is a set of ordered pairs in which no two different ordered pairs have the same value of x coordinate.

Option (a) : {(5, 2),(4, 2),(3, 2),(2, 2),(1, 2)}

No two ordered pairs have the same value of the x coordinate.

So it is a function.

Option (b) : {(-4, -2),(-1, -1),(3, 2),(3, 5),(7, 10)}

Two ordered pairs have the same value of x coordinate (3, 2) and (3, 5).

So, it can not be considered a function.

Option (c) : {(-8, -3),(-6, -5),(-4, -2),(-2, -7),(-1, -4)}

No two ordered pairs have the same value of the x coordinate.

So it is a function.

Option (d) : {(-6, 4),(-3, -1),(0, 5),(1, -1),(2, 3)}

No two ordered pairs have the same value of the x coordinate.

So it is a function.

Therefore, Options (a), (c), and (d) are the functions.

Option (b) is not a function.

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Answer:

20%

Step-by-step explanation:

You can get this answer algebraically by following these steps:

2 ÷ 100 ( x ÷ 100 ) = 2/5

2 x/100 = 2/5

2x = 200/5

2x = 40

40 ÷ 2 = 20

∴ x= 20%

Answer:

20%

Step-by-step explanation:

A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

To solve this, we can use this equation:

Well, if percentages are fractions of 100, we can convert 20% into \(\frac{20}{100}\), or 0.2.

Therefore, 2/5 is 20% of 2.

Answer:

1.27 radians

Step-by-step explanation:

Part a: The equation of the tangent line is: y - 5 = -15(x - 0)

Part b:The second derivative is a constant value, -15. Since the second derivative is negative, it means the function is concave down at (0, 5).

Part c:The particular solution is y = -10cos(x² + 3x + π) + 15(x² + 3x + π) - 5 - 15π

Part A: To find the equation of the line tangent to the solution curve at the point (0, 5), to follow these steps:

Step 1: Find the derivative of the given differential equation.

Given differential equation: dy/dx = 5(2x + 3)sin(x² + 3x + π)

Differentiate both sides with respect to x:

dy/dx = d/dx (5(2x + 3)sin(x²+ 3x + π))

dy/dx = 5 × (2(sin(x² + 3x + π)) + (2x + 3)cos(x² + 3x + π))

Step 2: Evaluate the derivative at the point (0, 5).

To find the slope of the tangent line at (0, 5), substitute x = 0 into the derivative:

dy/dx = 5 × (2(sin(π)) + (2×0 + 3)cos(π))

dy/dx = 5 × (2(0) + 3(-1)) = -15

Step 3: Use the point-slope form of the equation to write the equation of the tangent line.

The point-slope form of the equation is: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point (0, 5).

Simplifying, we get: y = -15x + 5

Part B: To find the second derivative at (0, 5) and determine the concavity of the solution curve at that point, follow these steps:

Step 1: Find the second derivative of the given differential equation.

Given differential equation: dy/dx = 5(2x + 3)sin(x² + 3x + π)

Differentiate the previous result for dy/dx with respect to x to get the second derivative:

d²y/dx² = d/dx (-15x + 5)

d²y/dx² = -15

Step 2: Determine the concavity.

Part C: To find the particular solution y = f(x) with the initial condition f(0) = 5,  to integrate the given differential equation:

dy/dx = 5(2x + 3)sin(x² + 3x + π)

Step 1: Integrate the equation with respect to x:

∫dy = ∫5(2x + 3)sin(x² + 3x + π) dx

y = ∫(10x + 15)sin(x² + 3x + π) dx

Step 2: Use u-substitution:

Let u = x² + 3x + π, then du = (2x + 3) dx

Now the integral becomes:

y = ∫(10x + 15)sin(u) du

Step 3: Integrate with respect to u:

y = -10cos(u) + 15u + C

Step 4: Substitute back for u:

y = -10cos(x² + 3x + π) + 15(x² + 3x + π) + C

Step 5: Apply the initial condition f(0) = 5:

Substitute x = 0 and y = 5 into the equation:

5 = -10cos(π) + 15(0² + 3(0) + π) + C

5 = 10 + 15π + C

Simplifying,

C = 5 - 10 - 15π

C = -5 - 15π

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So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The probability of getting at least 2 fours is the sum of the probabilities of getting exactly 2, 3, 4, or 5 fours:

P(X ≥ 2) = P(X=2) + P(X=3) + P(X=4) + P(X=5)

Using the binomial formula, we can calculate each of these probabilities:

P(X=k) = (n choose k) p^k (1-p)^(n-k)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from n distinct items.

P(X=2) = (5 choose 2) (1/6)² (5/6)³ = 0.1608

P(X=3) = (5 choose 3) (1/6)³ (5/6)² = 0.0322

P(X=4) = (5 choose 4) (1/6)⁴ (5/6)¹ = 0.0013

P(X=5) = (5 choose 5) (1/6)⁵ (5/6)⁰ = 0.00003

Therefore,

P(X ≥ 2) = 0.1608 + 0.0322 + 0.0013 + 0.00003 = 0.1943

So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.

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Answer:

12g+40=88

Step-by-step explanation:

40 represent the unlimited part and the 12g is the 12 dollars per gig.

hope this helped

Answer:

16

Step-by-step explanation:

9-9:9 +9 - 9 :9 =

9 - 1 +9 - 1 =

8 +9 - 1 =

17 - 1 =

16