Find the volume and surface area of the composite figure. Give four answer in terms of π.



The figure shows a compound solid that consists of a right cylinder with a hemisphere on top of it. The height of the right cylinder is equal to 12 inches. The diameters of both the right cylinder and the hemisphere are equal to 4 inches.


PLEASE ANSWER I WILL GIVE BRAINLIST

The percentage of the logo that is shaded is given as follows:

4%.

The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:

A = πr².

The radius of the larger circle is given as follows:

r = 5 + 2 + 3

r = 10 cm.

Hence the area of the larger circle is given as follows:

A = π x 10²

A = 100π cm².

The radius of the shaded circle is given as follows:

r = 2 cm.

Hence the area of the shaded circle is given as follows:

A = π x 2²

A = 4π cm².

Meaning that the shaded percentage is given as follows:

4π/100π x 100% = 0.04 x 100% = 4%.

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An angle making a full rotation measures 360 degrees or 2π radians. Both are a method of representing the measurement of a curved distance. If an angle has a measure of 5 radians, then, the measure of that angle in degrees is 286.478897 degrees.

Here is the step-by-step explanation of the solution:

Given, an angle has a measure of 5 radians. To convert radians into degrees, we use the following formula: Degree measure of angle = Radian measure of angle × (180/π)So, substituting 5 for the radian measure of the angle we get, Angle measure in degrees = 5 × (180/π)Degree measure of angle = 5 × (180/3.14159265359)Degree measure of angle = 286.478897 degrees hence, the measure of the given angle in degrees is 286.478897 degrees.

To convert from degrees to radians, use the same approach and just substitute the given value to arrive at the solution.

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The journal entry for pension expense is recorded to reflect the cost of providing defined-benefit pension benefits to employees. This entry recognizes the expense and the corresponding increase in the pension liability.

To prepare the journal entry for pension expense, we need to consider the relevant balances related to the defined-benefit pension plan. The pension expense is typically calculated based on actuarial assumptions, such as the expected return on plan assets, discount rate, and projected benefit obligations.

The journal entry for pension expense includes debits and credits to various accounts. The debit side usually includes the pension expense account, which represents the cost incurred by the company for providing pension benefits to its employees. This expense is recognized in the income statement.

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Answer:

i dunno but the slope is -4/6

Step-by-step explanation:

To compute the values of (r) and (x) for the different states of the harmonic oscillator, we need to consider the wavefunction solutions for each state.

The wavefunctions for the harmonic oscillator are given by Hermite polynomials multiplied by a Gaussian factor. The energy eigenvalues for the harmonic oscillator are given by (n + 1/2) * h * ω, where n is the quantum number and ω is the angular frequency of the oscillator. (a) Ground State: The ground state of the harmonic oscillator corresponds to n = 0. The wavefunction for the ground state is: ψ₀(x) = (mω/πħ)^(1/4) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₀) is equal to 1/2 * h * ω. Therefore, for the ground state: (r) = 0 (since n = 0). (x) = √(ħ/(2mω)). (b) First Excited State:The first excited state corresponds to n = 1. The wavefunction for the first excited state is: ψ₁(x) = (mω/πħ)^(1/4) * √2 * (mωx/ħ) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₁) is equal to 3/2 * h * ω. Therefore, for the first excited state: . (r) = 1. (x) = √(ħ/(mω)). (c) Second Excited State:The second excited state corresponds to n = 2. The wavefunction for the second excited state is: ψ₂(x) = (mω/πħ)^(1/4) * (2(mωx/ħ)^2 - 1) * exp(-mωx²/2ħ)  where m is the mass of the oscillator. In this state, the energy (E₂) is equal to 5/2 * h * ω.

Therefore, for the second excited state: (r) = 2. (x) = √(ħ/(2mω)). In summary: (a) Ground State: (r) = 0, (x) = √(ħ/(2mω)). (b) First Excited State: (r) = 1, (x) = √(ħ/(mω)). (c) Second Excited State: (r) = 2, (x) = √(ħ/(2mω)).

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Using Taylor series, the approximation P3(1.2) = 0.77083. Error R3(1.2) < 0.000235. Thus, P3(1.2) - |R3(1.2)| = 0.770599, within 0.001 of f(1.2).

In part C, we found the third-order Taylor polynomial for f about x=1 to be P3(x) = 1 - 1/2(x-1) + 1/8\((x-1)^2\)- 1/48\((x-1)^3\).

To show that this approximation is within 0.001 of the exact value of f(1.2), we need to estimate the error using the remainder term. The remainder term for the third-order Taylor polynomial is given by R3(x) = f(x) - P3(x) = (1/4!)\((x-1)^4\)f⁴(c), where c is some number between 1 and x.

Using the given formula for fⁿ(1), we can compute f⁴(c) = (-1)³(3!)/2⁴ = -3/16. Thus, we have R3(1.2) = (1/4!)\((0.2)^4\)(-3/16) = -0.000234375.

Since R3(1.2) is negative, we know that P3(1.2) > f(1.2), so our approximation is too high. Therefore, to ensure that our approximation is within 0.001 of the exact value of f(1.2), we need to subtract the error bound from our approximation. That is, we need to use P3(1.2) - |R3(1.2)| as our estimate. Substituting values, we get P3(1.2) - |R3(1.2)| = 0.770833333 - 0.000234375 = 0.770598958.

Since |f(1.2) - P3(1.2)| < |R3(1.2)|, we can conclude that our approximation is within 0.001 of the exact value of f(1.2).

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Answer:

3\(\sqrt{2}\)

Step-by-step explanation:

using the rule of radicals

\(\sqrt{a}\) × \(\sqrt{b}\) ⇔ \(\sqrt{ab}\) , then

\(\sqrt{3}\) × \(\sqrt{6}\)

= \(\sqrt{3(6)}\)

= \(\sqrt{18}\)

= \(\sqrt{9(2)}\)

= \(\sqrt{9}\) × \(\sqrt{2}\)

= 3\(\sqrt{2}\)

Answer:

C. 3(6+1) =21

Step-by-step explanation:

33/3 is done first and that is 11+10= 21

6+1=7(3)= 21

Answer: 0.43

Step-by-step explanation: 43% = 43/100 = 0.43

Answer:

It means that the denominator is equal to zero. Hope that helps.

Step-by-step explanation:

Answer:

Step-by-step explanation:

which can't be solved under given instructions e.g,finding the squareroot of a negative number in real numbers ,dividing by zero etc.

Answer:

The solution of \(x^3-2x^2+16x-32=0\) is \(\mathbf{x=2,x=4i,x=-4i}\)

So, the real solutions is: x = 2

Imaginary solutions are : x = 4i, x = -4i

Step-by-step explanation:

We need to find real and imaginary solutions to the equations \(x^3-2x^2+16x-32=0\)

First of all we will make groups

\((x^3-2x^2)(+16x-32)=0\)

Finding common terms from the groups

\(x^2(x-2)+16(x-2)=0\\(x-2)(x^2+16)=0\)

Now we know that if ab=0 then a=0 , b=0

\(x-2=0, x^2+16=0\\Simplifying:\\x=2, x^2=-16\\Taking\: square\: root\\x=2,\sqrt{x^2}=\sqrt{-16}\\x=2, x=\pm\sqrt{-16}\\x=2,x=\m\sqrt{-1}\sqrt{16} \\We\:know\:\sqrt{-1}=i \:and \sqrt{x} \:\sqrt{16}=4 \\x=2,x=\pm4i\\x=2,x=4i,x=-4i\)

The solution of \(x^3-2x^2+16x-32=0\) is \(\mathbf{x=2,x=4i,x=-4i}\)

So, the real solutions is: x = 2

Imaginary solutions are : x = 4i, x = -4i

No, the sum of the magnitudes of two vectors can never be equal to the magnitude of the sum of the same two vectors.

The magnitude of the sum of two vectors is determined by the vector addition process, which takes into account both the magnitudes and the directions of the vectors. The magnitude of the sum of two vectors is generally greater than or equal to the sum of their individual magnitudes.

Mathematically, for two vectors A and B, the magnitude of the sum (|A + B|) is given by the triangle inequality:

|A + B| ≤ |A| + |B|

Equality in the triangle inequality occurs only when the vectors are collinear, meaning they have the same direction or are in opposite directions. In such cases, the vectors can be scaled such that their magnitudes add up to the magnitude of their sum. However, in general, when vectors have different directions, the sum of their magnitudes will always be greater than the magnitude of their sum.

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Answer:

Step-by-step explanation:

Answer:

the equation of yours is wrong. the equation would be y=1/3x.

Step-by-step explanation:

here's the graph. hope it helps.

Answer:

Step-by-step explanation:

Hello,

\(x^6-6x^3y+9y^2\\\\=(x^3)^2-2\cdot x^3\cdot 3y+(3y)^2\\\\=(x^3-3y)^2\)

So the correct answer is

\(x^3-3y\)

Do not hesitate if you have any question

The solution is: the length of AG = 40.

Here, we have,

Lengths AG and CF of the parallelogram are equal.

i.e AG = CF

where AG = 2x + 20

         CF = 5x- 10

so, we get,

→ 2x + 20 = 5x-10

(collecting like terms): 5x - 2x = 20 + 10

→ 3x = 30

or, x=30÷3 = 10

∴ CF = 5x -10

        = 5(10) -10

        = 50 - 10

        = 40

and, AG = 2x + 20

              = 20 + 20

              = 40

∴ AG = 40 (answer)

Hence, The solution is: the length of AG = 40.

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Answer:

equilateral acute

Step-by-step explanation:

equilateral-- all the sides have the same length

acute-- all the angles are below 90 degree

Answer:

Step-by-step explanation:

You'r answer should be an equilateral acute.

Answer:

Step-by-step explanation:

ΔAOC is an isosceles triangle as OC = OA ----> RADIUS

42 + 42 + ∠AOC = 180   {Angle sum property}

       84 + ∠AOC = 180

              ∠AOC = 180 - 84

∠AOC = 96°

y = 96/2    {Central angle theorem}

y = 48° ------------(I)

∠B + ∠D = 180    {sum of opposite angles of Cyclic  Quadrilateral}

x + y = 180

x + 48 =  180        {from (I) }

x = 180 - 48

x =  132°

Answer:

x =  132°

Step-by-step explanation:

ΔAOC is an isosceles triangle as OC = OA ----> RADIUS

42 + 42 + ∠AOC = 180   {Angle sum property}

      84 + ∠AOC = 180

             ∠AOC = 180 - 84

∠AOC = 96°

y = 96/2    {Central angle theorem}

y = 48° ------------(I)

∠B + ∠D = 180    {sum of opposite angles of Cyclic  Quadrilateral}

x + y = 180

x + 48 =  180        {from (I) }

x = 180 - 48

x =  132°

The solution to the equation 3x2 - 30x - 72 = 0 is x = -4 and x = -12.

3x2 - 30x - 72 = 0

3x2 - 30x = 72

3x2 - 24x = 90

3x2 - 24x + 18x = 90 + 18x

3x(x - 8) = 108

x(x - 8) = 36

x = 36 or x = 8

x = -12 or x = -4

The equation 3x2 - 30x - 72 = 0is a second-degree polynomial equation with two solutions. To solve this equation, first use the distributive property to factor out 3x from the first two terms. This yields 3x(x - 8) = 108. Then divide both sides of the equation by 3 to get x(x - 8) = 36. From here, use the quadratic formula to solve for x. This yields x = 36 or x = 8. Since the equation was given in terms of x2, the two solutions are x = -12 and x = -4. To confirm this, substitute these values into the original equation and check that it is true.

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Answer:

1. 30

Step-by-step explanation:

First, place the numbers from least to greatest.

11,13,23,37,45,58

Then, find the middle number (or two middle numbers).

In this case, the middle numbers are 23 and 37.

Third, we find the mean of these numbers.

23+37=60

60/2=30

So your answer is 30.

Repeat this method for the other problems.

Answer:

Parallel slope: 2

Perpendicular slope: -1/2

Step-by-step explanation:

For a parallel line, the slope are the same.  The slope is the number before the x.

For perpendicular slopes, you turn the slope upside down and take the opposite sign.

Your monthly payment for the 60-month, 5.54% APR motorcycle loan to purchase your dream Harley-Davidson will be $136.88.

To calculate the monthly payment for a motorcycle loan, we can use the formula for the present value of an annuity. The formula is:

PMT = PV * r / (1 - (1 + r)^(-n))

Where:
PMT = Monthly payment
PV = Present value of the loan
r = Monthly interest rate
n = Number of months

In this case, the present value of the loan (PV) is $7,200, the monthly interest rate (r) is 5.54% divided by 12 (0.0554 / 12), and the number of months (n) is 60.

Plugging in these values into the formula, we get:

PMT = 7200 * (0.0554 / 12) / (1 - (1 + (0.0554 / 12))^(-60))

Evaluating this expression, the monthly payment comes out to be approximately $136.88.

Therefore, your monthly payment for the 60-month, 5.54% APR motorcycle loan to purchase your dream Harley-Davidson will be $136.88.

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The mean of the distribution is 0.55, and the standard error is 0.0363.

To find the mean and standard error of the sampling distribution for the proportion of supporters with sample size n=169, we use the given true proportion (p) and the sample size (n).

1. Calculate the mean: The mean of the sampling distribution is equal to the true proportion, which is p=0.55.

2. Calculate the standard error: Use the formula SE=sqrt[p(1-p)/n]. Plug in the values: SE=sqrt[0.55(1-0.55)/169] ≈ 0.0363.

So, the mean is 0.55, and the standard error is 0.0363.

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The formula for a circle's area is \(A=\pi r^2\). We are given an area of 38.465 square inches for a quarter of it.

Multiply this value by 4 to compensate for the quarter circle.

\(4 \times 38.465=\pi r^2\)

\(153.86=\pi r^2\)

Divide both sides by pi (Note: I'm using the conventional value of 3.14)

\(49=r^2\)

Take the positive square root of both sides

\(7=r\)

The radius is 7 inches. Let me know if you have any questions, thanks!

The area of a rhombus can be found by multiplying the length of one of its sides by the height of a perpendicular line from the center to a side.

The height of the rhombus is the distance from the center of the rhombus to one of its sides, perpendicular to that side.

The formula for the area of a rhombus can be written as A = s*h, where A is the area, s is the length of one of the sides of the rhombus, and h is the height of the rhombus.

It's important to note that this method of finding the area of a rhombus without diagonals can only be used when the rhombus is a regular polygon, a polygon with all sides and angles congruent. When the rhombus is not a regular polygon, then you can find the area by using the diagonals.

Additionally, it's important to mention that a rhombus can be defined as a parallelogram with all sides congruent or a square with its angles not 90 degrees.

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The probability that a student with a brother also has a sister is 15/21.

From the data, it is clear that the total number of students in the class is

15+6+2+2=25

Therefore there are 25 total students in the class.

According to conditional probability the probability of having a sister given that the person has a brother can be given by

\(\frac{Probability of having a brother and sister}{Total Probability of having a brother}\)

Therefore it can also be stated as

P(s|b)= P(s∩b)/P(b)

Thus from the data given

P(s|b)= (15/25)/(21/25)

Therefore,

P(s|b)= 15/21

Thus the probability of having a sister for a student with a brother is 15/21.

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Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.

2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.

3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.

4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.

5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.

6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.

Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

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answer:

b. $91.43/qt

step-by-step explanation:

it's a lot of work

Answer:

2(2x - 3)(x^2 -4)

Step-by-step explanation:

the second one

Answer:

29) 10

Step-by-step explanation:

the other I can't do...

Answer:

29) x = 10

30) 1.275 × 10⁻⁵

Step-by-step explanation:

29) 2x / 5 = 4 ⇒ 2x = 20 ⇒ x = 10