You roll a single 6 sided die. What are the odds of rolling a 4?

A. 1/4
B. 4
C. 4/6
D. 1/6

The area of the surface obtained by rotating the curve x = y² − 2y + 1, 0 ≤ y ≤ 2 about the y-axis isπ ∫_0^2 [(y-1)^2+1] √[1+4(y-1)^2] dy.Let's work out the solution. We need to apply the formula of surface area by revolving around the y-axis.The surface area is generated by the revolving the curve about y-axis, given as,x = y² − 2y + 1, 0 ≤ y ≤ 2.

Now, we must derive the formula to calculate the area of a surface obtained by rotating a curve around the y-axis. We use the formula given below, which involves integration of the function involved.

Let's see the formula for rotating around the y-axis:Area = 2π ∫_a^b xf(x)dxWe have given x = y² − 2y + 1, 0 ≤ y ≤ 2,To apply the above formula, we need to rearrange the given curve in terms of x,Let x = y² − 2y + 1We can obtain the value of y as, y = 1 ± √(x − 1).The limits of integration of y-axis are 0 and 2.Therefore, the area of the surface obtained by rotating the curve x = y² − 2y + 1, 0 ≤ y ≤ 2 about the y-axis isπ ∫_0^2 [(y-1)^2+1] √[1+4(y-1)^2] dy.

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Answer:

yes

Step-by-step explanation:

no

The general solution to the given linear system is x = 2t - 1, y = -t + 1, and z = t, where t represents any real number.

To find the general solution to the linear system, we can use the method of Gaussian elimination or matrix operations. Let's perform Gaussian elimination to solve this system.

First, let's write the augmented matrix for the system:

[1 1 -2 | 0]

[2 2 -3 | 1]

[3 3 1 | 7]

Using row operations, we can transform this matrix into row-echelon form:

[1 1 -2 | 0]

[0 0 1 | 1]

[0 0 0 | 0]

From this row-echelon form, we can deduce that the system is consistent and has infinitely many solutions.

To find the general solution, we can express the variables in terms of a parameter, let's say t. From the row-echelon form, we can see that z = t. Substituting this into the second equation, we find that 0t = 1, which is not possible. This indicates that the system is inconsistent. However, if we ignore the last equation and continue, we can express x and y in terms of t.

From the first equation, we have x + y - 2z = 0, substituting z = t, we get x + y - 2t = 0. Rearranging, we have x = 2t - 1 - y. This implies that x depends on y and t.

Similarly, from the second equation, we have 2x + 2y - 3z = 1, substituting z = t, we get 2x + 2y - 3t = 1. Rearranging, we have y = -t + 1 - x. This implies that y depends on x and t.

Therefore, the general solution to the given linear system is x = 2t - 1, y = -t + 1, and z = t, where t represents any real number.

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The required vectors are V1 = (5/√27, -1/√27, 1/√27) and V2 = (1, 2, 3).

Given that the sum of two vectors is (5, -5, 5),

where vį is parallel to (5, -1, 1) while v2 is perpendicular to (5, -1, 1).

Now, let's find vį:

We have, vį is parallel to (5,-1, 1).

Then, a scalar k can be found such that vį = k(5,-1,1)

Using the condition that the magnitude of vį is √23,k can be found as follows:

|vį| = k|(5, -1, 1)|⟹ √(k²(5² + (-1)² + 1²)) = √23⟹ √(27k²) = √23⟹ k = 1/√27

Thus, vį = (5/√27, -1/√27, 1/√27)

Now, let's find v2:We have, v2 is perpendicular to (5,-1, 1).

Thus, the dot product of v2 and (5,-1,1) is zero.

We can write this asv2 .

(5,-1,1) = 0v2 . (5,-1,1) = 5v2₁ - v2₂ + v2₃ = 0

Thus, the vector v2 can be chosen as(1, 2, 3) as the above equation is satisfied by v2 = (1, 2, 3)

Therefore, V1 = (5/√27, -1/√27, 1/√27) and V2 = (1, 2, 3).

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The flux of the vector field F across the surface S in the indicated direction is 8π/3.

So, the flux of the given vector field F across the surface S can be calculated by the surface integral as follows:

Φ = ∫∫S F · dS = ∫∫S (xi + yj + z2k) · n(x, y, z) dS= ∫∫S (2x/z + 2y/z + z2(-1/2)) dS= ∫∫S (2x + 2y) / z dS= ∫0²∫2π 2rcosθ / z √(r² + z²)  dr dθ= 8π/3.

The flux of the vector field F across the surface S in the indicated direction is 8π/3.

Given, vector field F = xi + yj + z2k,

S is the portion of the cone z = 2√(x² + y²) between z = 2 and z = 4 and the direction is outward.

The flux of the vector field F is given by the surface integral:Φ = ∫∫S F · dS .

Here, dS is the outward pointing unit normal vector of the surface S. Hence the flux Φ will be positive if F points outward, otherwise negative. The surface S can be parameterized as r(x, y, z) = xi + yj + zk, where z varies from 2 to 4 and (x² + y²) = (z²/4).

Then, the unit normal vector to the surface is given by n(x, y, z) = (2x/z)i + (2y/z)j - k/2.

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True. et a be square real matrix if v is an eigenvector for eigenvalue λ then v is an eigenvector for eigenvalue λ

In linear algebra, if a is a square real matrix and v is an eigenvector of a corresponding to eigenvalue λ, then v is also an eigenvector of a corresponding to the same eigenvalue λ. The definition of an eigenvector states that it remains unchanged (up to scaling) when multiplied by the matrix, and this property holds regardless of whether the eigenvalue is repeated or not. Therefore, if v satisfies the equation a * v = λ * v, it will still satisfy the same equation when considering the eigenvalue λ.

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Answer:

2

Step-by-step explanation:

You set up and equation:

5+6x = 17

You solve it and get 2.

Step-by-step explanation:

17-5 = 12

Answer:

Yes, that is correct.

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

The bottom left and top right are each a quarter of the circle and are thus 25% each. The slivers in the middle have to add up to 50% and are all evenly sized. That means that each sliver is 50/4 or 12.5%

Since there are two green slivers, we multiply 12.5% * 2 to get 25%.

Answer:

Step-by-step explanation:

2(4x - 3) = 9 + 2x + 6               Combine the like terms on the right

2(4x - 3)  = 2x + 15                   The distributive property gets rid of the brackets

8x - 6 = 2x + 14                        Add 6 to both sides

     6              6

8x = 2x + 20                            Subtract 2x from both sides

-2x   -2x        

6x = 20

Step 2 is the error. It is a very common error. You multiply 2 and - 3 together. as well as 2 and 4 together. If you are going to forget something that will be it.

Answer:

I can help you but first I need the rest of the answers to find out what's it equivalent to.

Answer:

1 kg here you go this is the answer

Answer:

X=12

Step-by-step explanation:

X²=X×X, so 12×12=144

Answer:  [tex]x=12[/tex]

Step-by-step explanation:

[tex]x^{2} =144[/tex]

[tex]x=\sqrt{144}[/tex]

[tex]x=12[/tex]

Answer:

36

Step-by-step explanation:

sara had 27 peaches when she left the stand. when she returns the total number of peaches is 63. So to find the answer you take 63 and subtract it by 27 to get your answer.

Answer:

40 biscuits

Step-by-step explanation:

Here are the ingredients needed to make 16 biscuits.

From the above question

Ingredients to make 16 biscuits

175 g of butter

75 g of sugar

250 g of flour

Anna has

500 g of butter

300 g of sugar

625 g of flour

To find the greatest number of biscuits she can make:

For flour

250g of butter = 16 biscuits

625g of butter = x

Cross Multiply

250x = 625 × 16

x = 625 × 16/250

x = 40 biscuits

Answer:

c(maybe?)

Step-by-step explanation:

dont give me a brainliest.

Answer:

Following are the solution to these question:

Step-by-step explanation:

Please find the complete question in the attachment file.

Formula:

[tex]\to \tan \theta= \frac{Perpendicular}{Base}[/tex]

[tex]\to \tan R = \frac{45}{28} \\\\ \to \tan S = \frac{28}{45}[/tex]

Answer:

The graph in the bottom right corner

The equilibrium vector for the given transition matrix is approximately (0.359, 0.359, 0.284).

To find the equilibrium vector, we need to solve the equation [tex]T * v = v[/tex], where T is the transition matrix and v is the equilibrium vector.

Let's denote the equilibrium vector as (x, y, z). Setting up the equation, we have:

[tex]0.47x + 0.19y + 0.34z = x\\0.45x + 0.55y + 0z = y\\0x + 0y + 1z = z[/tex]

Simplifying the equations, we get:

[tex]0.46x - 0.19y - 0.34z = 0\\-0.45x + 0.45y = 0\\0x + 0y + 1z = z[/tex]

From the second equation, we can see that x = y. Substituting x = y in the first equation, we have:

[tex]0.46x - 0.19x - 0.34z = 0\\0.27x - 0.34z = 0[/tex]

Simplifying further, we get:

[tex]0.27x = 0.34z\\x = (0.34/0.27)z\\x = 1.259z[/tex]

Since the equilibrium vector must sum to 1, we have:

[tex]x + y + z = 1\\1.259z + 1.259z + z = 1\\3.518z = 1\\z - 0.284[/tex]

Substituting the value of z back into x, we get:

[tex]x = 1.259 * 0.284=0.359[/tex]

Therefore, the equilibrium vector is approximately (0.359, 0.359, 0.284).

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Answer:

with atleast two right angles in rectangle and it do not describe unique because it is simple

The side lengths of the given triangle are 3 m, 10 m, and 10 m.

Let's assume the length of the third side of the triangle is x.

According to the given information, the two equal sides of the triangle are each 8 m less than six times the third side. Therefore, the lengths of the two equal sides can be expressed as:

6x - 8

6x - 8

The perimeter of a triangle is the sum of all three sides. In this case, the perimeter is given as 23 m:

x + (6x - 8) + (6x - 8) = 23

Simplifying the equation:

x + 6x - 8 + 6x - 8 = 23

13x - 16 = 23

13x = 23 + 16

13x = 39

x = 39 / 13

x = 3

Now that we have the value of x, we can find the lengths of the two equal sides:

Equal side 1 = 6x - 8 = 6 * 3 - 8 = 10 m

Equal side 2 = 6x - 8 = 6 * 3 - 8 = 10 m

Therefore, the side lengths of the triangle are 3 m, 10 m, and 10 m.

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Answer:

[911,∞)

Step-by-step explanation:

Given: S be the number of cans collected by Shane.

Since,  Abha collected 178 more cans than Shane did.

Then, the number of cans collected by Abha = S+178

Also, Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling.

So,  

Hence, the solution set of the inequality will be [911,∞)

a. Critical value, t∗, for a 99% Confidence Interval, n=16 is given by t∗=2.921. 

b. The margin of error is 0.97.

a) Critical Value, t∗ for a 99% Confidence Interval: Critical value, t∗, for a 99% Confidence Interval, n=16 is given by t∗=2.921. 
Note: t-table, with 15 degrees of freedom is used to determine the critical value for the given confidence interval. 

b) Margin of Error for a 99% Confidence Interval:Margin of error for a 99% confidence interval, n=16 is given by E = t∗× s/√n, where s is the standard deviation. 
E = 2.921 × 1.4/√16 = 0.97 (rounded off to two decimal places). 
Hence, the margin of error is 0.97.

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Find the critical value, t∗, for a 99% Confidence interval.

The sample size is 16.The degree of freedom (df) = n - 1 = 16 - 1 = 15.

From t-table for 15 degrees of freedom (df) and 99% level of confidence (α = 0.01) (two-tail) t* = 2.947.a) t* = 2.947.

b) Find the margin of error for a 99% Confidence interval.

The margin of error (E) for a 99% confidence interval is given by:

E = t* × s / √n

Where s is the sample standard deviation.

s = 1.4 (given)E = 2.947 × 1.4 / √16E = 0.7285 or ≈ 0.73

Therefore, the margin of error for a 99% confidence interval is approximately 0.73.

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Answer:

3(7b+6)

Step-by-step explanation:

Simply find the greatest common factor between 21b and 18, which is 3. Then that's your simplest factorized expression.

Let X = R and A = {0, R, {1}, R\{2}}. Then a is option (b) A is not a σ-algebra over R.

To be a σ-algebra over a set X, a collection of subsets A must satisfy three properties:

1. X must be in A.

2. If A is in A, then the complement of A (X\A) must also be in A.

3. If A₁, A₂, A₃, ... are subsets in A, then their union (A₁ ∪ A₂ ∪ A₃ ∪ ...) must also be in A.

Let's examine the given collection of subsets A = {0, R, {1}, R\{2}} over the set X = R.

1. X = R is not in A. (Property 1 is violated.)

2. The complement of {1}, which is R\{1}, is not in A. (Property 2 is violated.)

3. Taking A₁ = {1} and A₂ = R\{2}, their union A₁ ∪ A₂ = {1} ∪ (R\{2}) = {1,2} is not in A. (Property 3 is violated.)

Since A does not satisfy the three properties of a σ-algebra over R, the correct answer is (b) A is not a σ-algebra over R.

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Answer:

3/9 or 1/3

Step-by-step explanation:

Answer:

She needs 70ft of lights

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

I took the test

The box plot that represents the number of bus drivers with the given five-number summary is: option B (see image attached below).

A box plot is graphed to indicate the five-number summary as:

Given the five-number summary of the number of bus riders as: minimum = 18, lower quartile = 22, median = 26, upper quartile = 29, and maximum = 37, the box plot that represents the data is: Option B (see image attached below.

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Answer:

C

Step-by-step explanation:

Answer:

Multiply  34  by 3  

102x