Find the volume of the composite shape:​

Answer:

We have:

If:

Cos(θ) + Sin(θ) = √2*cos(θ)

We want to prove that:

Cos(θ) - Sin(θ) = √2*Sin(θ)

Well, let's start with the first relation:

Cos(θ) + Sin(θ) = √2*cos(θ)

Now we can subtract 2*Sin(θ) and we will get:

Cos(θ) + Sin(θ) - 2*Sin(θ) = √2*cos(θ) - 2*sin(θ)

Cos(θ) - Sin(θ) = √2*cos(θ) - 2*sin(θ)

Now, we also can rewrite the first equation as:

Cos(θ) + Sin(θ) = √2*cos(θ)

Cos(θ) - √2*cos(θ) = -  Sin(θ)

Cos(θ)*( 1 - √2) = -Sin(θ)

Cos(θ) = -Sin(θ)/( 1 - √2) = Sin(θ)/(- 1 + √2)

We can replace this in the right side of theequation:

Cos(θ) - Sin(θ) = √2*cos(θ) - 2*sin(θ)

Cos(θ) - Sin(θ) = √2* Sin(θ)/(- 1 + √2) - 2*sin(θ)

Cos(θ) - Sin(θ) = (√2/(- 1 + √2) - 2)*Sin(θ)

Now we have this:

√2/(- 1 + √2)) - 2 = a

if we multiply all by (-1  + √2) we get:

√2 - 2*(-1  + √2) = a*(-1  + √2)

√2  + 2 - 2*√2 =  a*(-1  + √2)

2 - √2 = a*(-1  + √2)

√2*(√2 - 1) = a*(-1  + √2)

√2*(√2 - 1)/(-1  + √2) = a

√2 = a

Then:

√2/(- 1 + √2)) - 2 = √2

If we replace this in the equation:

Cos(θ) - Sin(θ) = (√2/(- 1 + √2) - 2)*Sin(θ)

We get:

Cos(θ) - Sin(θ) = √2*Sin(θ)

Which is the thing we wanted to get.

Please find attached herewith the solution of your question.

If you have any query, feel free to ask.

Answer:

25%

Step-by-step explanation:

So there are four marbles that are red.

It doesnt matter if we have a probability of picking blue because the question says you are picking red.

There are four possible outcomes and one favorable outcome so it is 1/4 of 25/100 or 25%

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

A normal distribution is a type of continuous probability distribution for a real-valued random variable in statistics.

Yes, the large-sample confidence interval will be valid.

A normal distribution is a type of continuous probability distribution for a real-valued random variable in statistics.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data far from the mean.

The confidence interval will be valid regardless of the shape of the population distribution as long as the sample is large enough to satisfy the central limit theorem.

A sample is considered large when n ≥ 30.

By 'valid', it means that the confidence interval procedure has a 95% chance of producing an interval that contains the population parameter.

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Hence, a cylinder with height h and base area \(\pi r^{2}\) may be proven to have the same volume as a triangular prism.

Two parallel circular bases joined by a curving surface form the three-dimensional geometric object known as a cylinder. Due of its parallel and congruent bases, it is a sort of prism.

When someone uses the word "cylinder,” they often mean a right circular cylinder with circles for bases and an axis that is perpendicular to the bases' planes.

A cylinder's volume may be calculated using the formula V = \(r^{2}\)h, where r denotes the perimeter of the base and h the height of the cylinder. L = 2rh, where r is the radius of a base and h is the height of the cylinder, is the formula for a cylinder's lateral surface area.

Cavalieri's principle states that if two solid objects have the same height and every cross-section taken perpendicular to a common axis has the same area, then the two objects have the same volume.

Let's consider the given triangular prism with base area  \(\pi\)\(r^2\) and height h. If we take a cross-section perpendicular to the base at a height y, we get a circle with radius r multiplied by a triangle with base 2r and height y. The area of this cross-section is:

\(A(y) = \pi r^2 + (2r)(y) / 2\)

Simplifying, we get:

\(A(y) = \pi r^2 + ry\)

Now, let's consider a cylinder with base area pi r² and height h. If we take a cross-section perpendicular to the height at a height y, we get a circle with radius r multiplied by a rectangle with base 2r and height h. The area of this cross-section is:

\(A'(y) = \pi r^ + (2r)(h) = \pi r^2 + 2rh\)

By Cavalieri's principle, the triangular prism and the cylinder have the same volume if A(y) = A'(y) for all y from 0 to h. Let's check:

\(\pi r^² + ry = \pi r^² + 2rh\)

\(ry = 2rh\)

\(y = 2r\)

So, we see that the areas are equal for all y between 0 and h, except at \(y = 2r.\) However, this is just a single point and has no effect on the volume,

Therefore,  the cylinder with base area \(\pi\)\(r²\) and height h has the same volume as the triangular prism, with base area \(\pi\)r² and height h.

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Answer:

it should be 4.24264068712 looked it up

Answer:

18 doesn't have a square root but you can simplify it

\( \sqrt{18 } \)

then you take 9 which is a square number and divide it to get 3 which you'll place on the outside

\( 3\sqrt{2} \)

Given,

Let's check all the choices,

• B. The point (c,0) lies on the graph of f(x).

This is true since plugging in "c" into the function yields "0".

• C. x - c is a factor of f(x).

Since the value "c" yields "0" as an output, we can say that x - c is a factor of the function.

D. c is a 0 for f(x).

This is true. Since an input of "c" yields "0" as an output, this is known as a zero of the function.

All three statements, B, C, and D, are true.

W'(-2 , 6),  X'(-2 , 2), Y'(-6 , 2), Z'(-6 , 5).

This is the vertices after  the 270° counterclockwise rotation.

Given vertices,

W(-6,-2), X(-2,-2), Y(-2,-6), and Z(-5, -6).

Here we have to rotate 270°.

We know that,

Rotating a point 90° counterclockwise: (x, y) → (-y, x).

Rotating  a point 180° counterclockwise: (x, y) → (-x, -y).

Rotating a point 270° counterclockwise: (x, y) → (y, -x).

So here we are rotating the figure 270°,

W(-6,-2)→ W'(-2 , 6)

X(-2,-2)→ X'(-2 , 2)

Y(-2,-6)→ Y'(-6 , 2)

Z(-5, -6)→ Z'(-6 , 5)

The vertices after rotating 270° counterclockwise about origin is:

W'(-2 , 6),  X'(-2 , 2), Y'(-6 , 2), Z'(-6 , 5).

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a. To determine the Fourier transform of x(t) =\(e^t\) * u(t), where u(t) is the unit step function, we can use the property that the Fourier transform of e^(at) * u(t) is 1 / (jω - a). Applying this property, we get:

X(jω) = 1 / (jω - 1)

b. For x(t) = e^(-4(t-1)) * u(t-1), we can again use the property mentioned above to find its Fourier transform:

X(jω) = 1 / (jω + 4) * e^(-jω)

c. For x(t) = cos(2t), we can directly apply the Fourier transform property of cosine function:

X(jω) = π * [δ(ω - 2) + δ(ω + 2)]

d. For x(t) = sin(2t), we can use the Fourier transform property of sine function:

X(jω) = -jπ * [δ(ω - 2) - δ(ω + 2)]

e. For x(t) = 2cos(2t) + 2sin(2t), we can apply the linearity property of the Fourier transform:

X(jω) = 2π * [δ(ω - 2) + δ(ω + 2)] - j2π * [δ(ω - 2) - δ(ω + 2)]

f. For x(t) = 2, the Fourier transform of a constant function is given by:

X(jω) = 2π * δ(ω)

To draw the spectrum of x(t), you can plot the magnitude of X(jω) against ω. The resulting spectrum will depend on the specific values of ω and the coefficients in each transform.

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Answer:

X = 6y-2 is the easier substitution for another equation because all you have to do is just plug in the equation into the value of x.

The process is capable of producing outputs within the specification limits is true.

There are a number of potential reasons for why the process is not meeting the target value. One possibility is that the target value is too ambitious and is not realistic given the current process capability. Another possibility is that there is some inherent variability in the process that is not being accounted for. It is also possible that there are some external factors that are affecting the process, such as changes in the raw materials or the environment.

The design engineers have established an upper specification limit of 22 and a lower specification limit of 18. This means that they are confident that the process is capable of producing outputs within these limits. However, the fact that the process is consistently averaging 19.8 with a standard deviation of 0.5 suggests that there is some room for improvement.

One potential way to improve the process is to focus on reducing the inherent variability. This can be done by identifying and addressing the sources of variability in the process. Another potential way to improve the process is to reduce the target value. This may be necessary if the current target value is not realistic given the process capability.

It is also important to monitor the process over time to ensure that it is remaining within the specification limits. This will help to identify any potential issues that may arise and allow for corrective action to be taken if necessary.

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A.The process is in statistical control.

B.The process is capable of producing outputs within the specification limits.

C.The process is capable of producing outputs within the tolerance limits.

D.The process is capable of producing outputs within the control limits.

E.The process is capable of producing outputs that are normally distributed. The process is capable of producing outputs within the specification limits

which statement concerning this process is true?

Answer:

62

8.8

2.7

Step-by-step explanation:

that should be right. try that out

Answer:

62,8.8,2.8

Step-by-step explanation:

Answer: 1 is 2 rectangles, 4 in a triangle and a rhombus I think.

Step-by-step explanation:

It says what would the shapes be shown as if it was split on the line.

Answer:

The ball will hit the ground at 0.968 seconds.

Step-by-step explanation:

Please refer to the attached graph in the answer area.

The given equation of height according to input variable time 't' is:

\(h = - 16 t^{2} + 15 ...... (1)\)

h is in feet

t is in seconds

Both the values 't' and 'h' will be positive. (Time and height can never be negative)

To determine the time, at which the ball hits the ground, i.e. the height becomes 0.

Putting value of h = 0 in equation (1)

\(0 = - 16 t^{2} + 15 \\\Rightarrow t^{2} = \dfrac{15}{16}\\\Rightarrow t = \sqrt{\dfrac{15}{16}}\\\Rightarrow t = 0.968\ sec\)

Hence, the time at which the ball hits the ground is 0.968 seconds.

Full Question:

The student council needs posters for the Winter Carnival. The print shop charges $15 for each print job. Each poster will cost an additional  $1.35.

Which equation shows the  relationship between the number of posters, n, and the total cost, c, in dollars?

Answer:

\(C = 15 + 1.35n\)

Step-by-step explanation:

Given

\(Base\ Charge = \$15\)

\(Cost\ per\ print = \$1.35\)

Required

Determine an equation to calculate the total cost

First, we need to determine the cost of n posters;

If 1 poster costs $1.35, then

\(n\ posters = n * 1.35\)

\(n\ posters = 1.35n\)

Next, add the cost of n posters to the base charge. This gives total cost (C)

\(C = Base\ Charge + n\ posters\)

\(C = 15 + 1.35n\)

Answer:  

I Did The Test And The Correct Answer is that c will equal to 1.35n + 15

It Is 1.35n + 15

Answer:

the answer is one cup of oil for each cup of water. hope this helps!

Answer:

Step-by-step explanation:

To find the experimental probability of a student in Homeroom 203 taking a certain number of minutes to get to school, we need to divide the number of students who take that amount of time by the total number of students in the homeroom.

The total number of students in the homeroom is:

3 + 5 + 10 + 7 + 2 + 3 = 30

The probability of a student taking less than 10 minutes to get to school is:

3/30 = 0.1 or 10%

The probability of a student taking 10-19 minutes to get to school is:

5/30 = 0.166 or 16.6%

The probability of a student taking 20-29 minutes to get to school is:

10/30 = 0.333 or 33.3%

The probability of a student taking 30-39 minutes to get to school is:

7/30 = 0.233 or 23.3%

The probability of a student taking 40-49 minutes to get to school is:

2/30 = 0.066 or 6.6%

The probability of a student taking 50 minutes or more to get to school is:

3/30 = 0.1 or 10%

To make a probability distribution, we can list the possible outcomes (in this case, the time it takes to get to school) and their corresponding probabilities:

Time (min) Probability

Less than 10 0.1

10-19 0.166

20-29 0.333

30-39 0.233

40-49 0.066

50 or more 0.1

Note that the probabilities add up to 1, which is what we expect for a probability distribution.

Answer:

I think it is 2/3x + 50/3

Step-by-step explanation:

So to find the first step, you go to the points that are on the actual corners and that's 2/3 slope. Then looking from the bottom of the graph it goes by tens, so it will help with the second part of the equation, and then you go over 3 so it would be 50/3. I could be very much wrong though

Answer:

4(5g+6h)

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

rise/run        2/-2    =    -1

Hi!

y = 16

x = 32

We are given the longest leg. To find the shortest leg, we must divide the longest leg value by \(\sqrt{3}\)

\(\cfrac{16\sqrt{3} }{\sqrt{3} }\)

The radicals cancel out and we are left with 16.

The length of y (the shortest leg) is 16.

Now, we also know that the hypotenuse is double the shortest leg. The shortest leg is 16, so if we double that, it's 32.

If a point (-1, 4) reflected over the x-axis then translate the result up 3 units then the coordinates of the final point are (-1, -1)

A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.

Reflecting a point over the x-axis negates the y-coordinate, while leaving the x-coordinate unchanged.

Therefore, reflecting (-1,4) over the x-axis gives us the point (-1,-4).

Translating a point up 3 units means adding 3 to the y-coordinate. Therefore, translating (-1,-4) up 3 units gives us the point:

(-1, -4 + 3) = (-1, -1)

So the final point is (-1,-1).

Hence, if a point (-1, 4) reflected over the x-axis then translate the result up 3 units then the coordinates of the final point are (-1, -1)

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The coefficient for the weight 'carat' based on the "Regression" results is X. The average change in price for a VS1 diamond if the weight increases by 0.1 carat would be Y.

In regression analysis, coefficients represent the relationship between the independent variables (such as weight) and the dependent variable (in this case, price). The coefficient for the weight 'carat' indicates the change in price associated with a one-unit increase in carat weight, holding other variables constant.

To determine the exact coefficient value, it is necessary to refer to the specific regression results. The coefficient could be positive, indicating that as the weight increases, the price also increases, or it could be negative, indicating an inverse relationship.

Additionally, based on the coefficient value, you can estimate the average change in price for a specific increase in weight. If the coefficient for 'carat' is X, and the weight of a VS1 diamond increases by 0.1 carat, the average change in price would be Y.

To obtain the precise values for X and Y, it is essential to refer to the specific regression analysis results provided. The coefficient and the corresponding change in price can vary depending on the dataset and the specific regression model used.

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The degree measure of the largest angle is 72° in the triangle.

We have, The sum of two angles of a triangle is 6/5 of a right angle.

One of these two angles is 30° larger than the other.

Let A and B be the two angles of the triangle such that A = B + 30°.

We know that the sum of three angles in a triangle is 180°.

⇒ A + B + C = 180°

⇒ B + 30° + B + C = 180°

⇒ 2B + C = 150°

We also know that the sum of two angles of a triangle is 6/5 of a right angle.

⇒ A + B = 6/5 × 90°

⇒ B + 30° + B = 108°

⇒ 2B = 78°

⇒ B = 39°

C = 150° - 2B ⇒ 72°

A = B + 30° ⇒ 39° + 30° ⇒ 69°

Therefore, the degree measure of the largest angle in the triangle is 72°.

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Answer:

7 1/2

Step-by-step explanation:

Let's add the whole numbers first, 3 + 4 = 7

Then, we add the fraction, and since the denominator is the same, there's no need for a change, so we just add the top. 1/8 + 3/8 is 4/8, which can be simplified to 1/2

so answer is 7 1/2

Answer:

Mean

Step-by-step explanation:

Answer:

a (26+10)-2 =34

b (34+42)-42 = 34

c ( 39+40)-45 =34

d (52+25)-43 =34

e(25+22)-13 =34

f (47+11)-24 =34

g(59+19)-35 =34

h (71 +7)-44= 34

solved

The iterated triple integrals for the volume of the tetrahedron cut from the first octant by the plane XYZ is 84

The term iterated triple integrals means the result of applying integrals to a function of more than one variable (for example or ) in a way that each of the integrals considers some of the variables as given constants.

Here we have to write six different iterated triple integrals for the volume of the tetrahedron cut from the first octant by the plane XYZ and then we have to evaluate the first integral.

Here in this case we will integrate with respect to y first.

Therefore, the iterated integral that we need to compute is,

∬6xy²dA=∫⁴₂∫₁²6xy²dydx

When we per the first stage integral, then we get,

=> ∫⁴₂ (2xy³)₁²dydx

When we expand it then we get,

=> ∫⁴₂ [16x - 2x] dx

=>  ∫⁴₂ 14x dx

Then we further integrate this one, then we get.,

=>  ∫⁴₂ 14x dx = [7x²]₂⁴

=> [7(4)² - 7(2)²]

=> 112 - 28

=> 84

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Answer:

ok first we add 9 and 29 together

38

now we add 90

128

so the other angle is

52

so we just use the formulas

and

Side a = 26.56371

Side b = 43.14662

Side c = 34

so the side with a x on it is 26.6

so know we have to do the same thing but not including the top part

ok so the side with x on it is 18.8

so 26.6-18.8=7.8

x=7.8

*WARNING* This shoud be close to the answer but may to up to a couple dp higher or lower sorry i just don't have time to be more accurate

Hope This Helps!!!

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

where c is a constant.

The solution to the question is shown below.

Step 1: We have given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

We have to find the number of words we have to write to express this function in words.

Step 2: Solution

f(t) = et5+4t + ln(t²+3c)⁷ +te-1+5e⁶

Where,

et5+4t = exponential function

ln(t²+3c)⁷ = natural logarithmic function

te-1 = linear function

e⁶ = exponential function

Therefore, f(t) can be expressed in words as:

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Step 3: Conclusion

Hence, the function f(t) can be expressed in words with:The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

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