Shelley was designing her own house that will sit on a concrete foundation in the shape of rectangular prism with dimensions 23 – 3,2 +8, and 2 - 2 that has a hole, also a rectangular prism, with dimensions : – 4,2 + 1 and 3- 2. She needs to determine how much concrete she will need to lay the foundation.

After answering the presented question, we can conclude that As a cylinder result, the depth of the water in the tank rises by 6.33 cm.

A cylinder is a three-dimensional geometric shape made up of two parallel congruent circular bases and a curving surface connecting the two bases. The bases of a cylinder are always perpendicular to its axis, which is an imaginary straight line passing through the centre of both bases. The volume of a cylinder is equal to the product of its base area and height. A cylinder's volume is computed as V = r2h, where "V" represents the volume, "r" represents the radius of the base, and "h" represents the height of the cylinder.

This cylinder has the following volume:

V_cylinder = π × r² × h

= π × (40 cm)² × (50 cm)

= 251,327.41 cm³

Hence the volume of water displaced by the cube is 125,000 cm, and the volume of water displaced by the cylinder with the same height and radius as the tank is 251,327.41 cm3. As a result, the depth of the water rises by:

Δh = V_cube / (π × r²) - V_cylinder / (π × r²)

= (125,000 cm³) / (π × (40 cm)²) - (251,327.41 cm³) / (π × (40 cm)²)

= 6.33 cm

As a result, the depth of the water in the tank rises by 6.33 cm.

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The experiment wise error rate will be a equal to the alpha in the the tukey procedure.

According to the statement

we have to explain about the experiment wise error rate which is computing in confidence intervals using the tukey procedure.

So, For this purpose, we know that the

Tukey's method is used in ANOVA to create confidence intervals for all pairwise differences between factor level means while controlling the family error rate to a level you specify.

And

Tukey's multiple comparison test is one of several tests that can be used to determine which means amongest a set of means differ from the rest.

Then, the error rate in this procedure is a equal to the alpha always.

So, The experiment wise error rate will be a equal to the alpha in the the tukey procedure.

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Answer:

C

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

step-by-step explanation

Answer: A. addition property of equality.

Step-by-step explanation:

Molly added 3d to both sides of the equation.

Answer:

\(z=\frac{t^{2}(m-3) }{4}\)    or    \(z=\frac{1}{4}t^{2} (m-3)\)

Step-by-step explanation:

\(t=\sqrt{\frac{4z}{m-3} }\)

\(t^{2} =\frac{4z}{m-3}\)

\(4z=t^{2} (m-3)\)

\(z=\frac{t^{2}(m-3) }{4}\)

Hope this helps

Answer:  B.   5/13

This is the same as writing \(\frac{5}{13}\)

==========================================================

Reason:

We have two given sides of this right triangle. Use the pythagorean theorem to find the missing side.

a = 5 and b = 12 are the two known legs; c is the unknown hypotenuse

\(a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{5^2+12^2}\\\\c = \sqrt{25+144}\\\\c = \sqrt{169}\\\\c = 13\\\\\)

The hypotenuse is exactly 13 units long. This is a 5-12-13 right triangle.

Now we can compute sine of theta

\(\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{5}{13}\\\\\)

This points us to choice B as the final answer.

----------------

Extra Info (optional)

After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t

The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,

we get

V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.

The values after 5 years, 10 years and 12 years, respectively are:

For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars

The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)

The current revenue is the total revenue when t = 0.

So, putting t = 0 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 0= 10e0= 10 million dollars

Revenue in 5 years' time is TR when t = 5.

So, putting t = 5 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 5≈ 4.35 million dollars

To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.

Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1

Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303

Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.

So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

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Answer:

x = ⅔

Step-by-step explanation:

step 1

add -4 to both left hand side and right hand side

then you get the equation : | 3x-2| = 0

step 2

you solve the absolute value which is: | 3x-2 |

and that is : 3x-2 = 0 (possibility 1)

3x-2 +2 = 0 +2 ( add 2 to both sides )

then you get : 3x = 2

step 3

you divide 3 on both side : 3x by 3 = ⅔ ( 2 by 3)

then you get your answer as : x = ⅔

I hope this helps .

An assembly has 225 chairs in 15 rows and there are 15 chairs per row in the assembly.

To find the number of chairs per row in an assembly, we need to divide the total number of chairs by the number of rows.

Given that there are 225 chairs in 15 rows, we can find the number of chairs per row by dividing the total number of chairs by the number of rows:

225 chairs ÷ 15 rows = 15 chairs per rows

It's important to note that this assumes that each row has the same number of chairs. If the number of chairs per row varies, then the calculation would need to be adjusted accordingly.

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\((x, y) = (4, 5)\) and the maximum value of f is 31.

The linear programming problem that needs to be solved is given below: Maximize \(f = 3x + 5y\)  subject to \(x + y ≤ 92x + y ≤ 14y ≤ 6x ≥ 0, y ≥ 0\)

The objective function \(f = 3x + 5y\) is to be maximized subject to the given constraints.

Restricting x and y to be non-negative, we write the problem as follows: Maximize f = 3x + 5y subject to \(x + y ≤ 92x + y ≤ 14y ≤ 6x ≥ 0, y ≥ 0\)

We plot the boundary lines of the feasible region determined by the above constraints as follows:

We determine the corner points of the feasible region as follows:

\(A(0, 6), B(7, 2), C(4, 5), and D(0, 0).\)

We calculate the value of the objective function at each of the corner points.

\(A(0, 6), f = 3(0) + 5(6) = 30B(7, 2), f = 3(7) + 5(2) = 29C(4, 5), f = 3(4) + 5(5) = 31D(0, 0), f = 3(0) + 5(0) = 0\)

The maximum value of f is 31, which occurs at point C (4, 5).

Therefore, (x, y) = (4, 5) and the maximum value of f is 31.

Hence, the given linear programming problem is solved.

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a.we get, `A = √(2α³/π)`.

b.`⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

c.we can say that the variational principle is valid in this case.

(a) Let's find the normalization constant A.

We know that the integral over all space of the absolute square of the wave function is equal to 1, which is the requirement for normalization.  `∫⟨ψ|ψ⟩dx= 1`

Hence, using the given trial wavefunction, we get, `∫⟨ψ|ψ⟩dx = ∫ |A/(x^2+α²)|²dx= A² ∫ dx / (x²+α²)²`

Using a substitution `x = α tan θ`, we get, `dx = α sec² θ dθ`

Substituting these in the above integral, we get, `A² ∫ dθ/α² sec^4 θ = A²/(α³) ∫ cos^4 θ dθ`

Using the identity, `cos² θ = (1 + cos2θ)/2`twice, we can write,

`A²/(α³) ∫ (1 + cos2θ)²/16 d(2θ) = A²/(α³) [θ/8 + sin 2θ/32 + (1/4)sin4θ/16]`

We need to evaluate this between `0` and `π/2`. Hence, `θ = 0` and `θ = π/2` limits.

Using these limits, we get,`⟨ψ|ψ⟩ = A²/(α³) [π/16 + (1/8)] = 1`

Therefore, we get, `A = √(2α³/π)`.

Hence, we can now write the wavefunction as `ψ(x) = √(2α³/π)/(x²+α²)`.  

(b) Using the wave function found in part (a), we can now determine the expectation value of energy using the time-independent Schrödinger equation, `Hψ = Eψ`. We can write, `H = (p²/2m) + (1/2)mω²x²`.

The first term represents the kinetic energy of the particle and the second term represents the potential energy.

We can write the first term in terms of the momentum operator `p`.We know that `p = -ih(∂/∂x)`Hence, we get, `p² = -h²(∂²/∂x²)`Using this, we can now write, `H = -(h²/2m) (∂²/∂x²) + (1/2)mω²x²`

The expectation value of energy can be obtained by taking the integral, `⟨H⟩ = ⟨ψ|H|ψ⟩ = ∫ψ* H ψ dx`Plugging in the expressions for `H` and `ψ`, we get, `⟨H⟩ = - (h²/2m) ∫ψ*(∂²/∂x²)ψ dx + (1/2)mω² ∫ ψ* x² ψ dx`Evaluating these two integrals, we get, `⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

(c) Since we have an approximate ground state wavefunction, we can expect that the expectation value of energy ⟨H⟩ should be greater than the true ground state energy.

Hence, the value obtained in part (b) should be greater than the true ground state energy obtained by solving the Schrödinger equation exactly.

Therefore, we can say that the variational principle is valid in this case.

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Answer:

i think its no solution to be honest

Step-by-step explanation:

y = 4x + 6 y = 4 x + 9 5

Answer: Im pretty sure its a.

Step-by-step explanation:

The characteristic that does not apply to a theoretical normal distribution is C) It is bimodal.

The main answer is C. An explanation for this is that a normal distribution has a single peak at the mean, and as we move away from the mean in either direction, the frequency of occurrence decreases.

Therefore, a normal distribution can never have two distinct peaks, making it impossible for it to be bimodal. All other options are characteristics of a normal distribution. In conclusion, a theoretical normal distribution is never negative, bell-shaped, and has equal mean, median, and mode, but it is not bimodal.

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P(X ≥ 200) = 1 - P(X < 200) ≈ 1.0. In other words, it is very likely (almost certain) that at least 200 out of 210 college graduates under age 20 are employed.

To find the probability that at least 200 out of 210 college graduates under age 20 are employed, we can use the binomial distribution formula:
P(X ≥ 200) = 1 - P(X < 200)
where X is the number of employed college graduates under age 20 out of a sample of 210.
We know that the unemployment rate for college graduates under the age of 20 is 7%. Therefore, the probability of an individual college graduate being unemployed is 0.07.
To find the probability of X employed college graduates out of 210, we can use the binomial distribution formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where n is the sample size (210), k is the number of employed college graduates, and p is the probability of an individual college graduate being employed (1-0.07=0.93).
We want to find P(X < 200), which is the same as finding P(X ≤ 199). We can use the cumulative binomial distribution function on a calculator or software to find this probability:
P(X ≤ 199) = 0.000000000000000000000000000001004 (very small)
Therefore, P(X ≥ 200) = 1 - P(X < 200) ≈ 1.0. In other words, it is very likely (almost certain) that at least 200 out of 210 college graduates under age 20 are employed.

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Answer:

8 6/11 is about 8.545, 17/2 = 8.5

From least to greatest: 17/2, 8 6/11, 8.83, 8.838

Step-by-step explanation:

8 6/11 is a mixed fraction

Converting it to improper fraction

Converting it to improper fraction11*8+6=88+6

Converting it to improper fraction11*8+6=88+6=94

Converting it to improper fraction11*8+6=88+6=9417/2 =8.5

8.838 is approximately 8.84

Having simplified all the values

The values to be arranged are 94, 8.838, 8.5 and 8.83

From smallest to biggest you have:

8.83, 8.838, 8.5, 94

I hope I helped

Answer: 5

Step-by-step explanation:

Hope this helps 100% Verified from math>way

Answer: XYZ = HGJ by the ASA postulate

Answer:

0

Step-by-step explanation:

for A

10+9+3+8+10

=40/5

=8

for B

5+11+2+7+16

=41/5

=8.2

difference between A and B

8.2-8

=0.2

approximately

=0

Answer: Multiply the centimeters number by 10.

Step-by-step explanation: There are 10 millimeters in every centimeter.

The derivative of F(x) is \(F'(x) = x^{(1/3)\).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

To find the derivative of the given function F(x), we will apply the fundamental theorem of calculus and differentiate the integral with respect to x.

Let's compute F'(x):

F(x) = ∫[0 to x] \(t^{(1/3)} dt\)

To differentiate the integral with respect to x, we'll use the Leibniz integral rule:

F'(x) = d/dx ∫[0 to x] \(t^{(1/3)} dt\)

According to the Leibniz integral rule, we have to apply the chain rule to the upper limit of the integral.

\(F'(x) = x^{(1/3)} d(x)/dx - 0^{(1/3)} d(0)/dx\)   [applying the chain rule to the upper limit]

Since the upper limit of the integral is x, the derivative of x with respect to x is 1, and the derivative of 0 with respect to x is 0.

\(F'(x) = x^{(1/3)} (1) - 0^{(1/3)} (0)\)

\(F'(x) = x^{(1/3)\)

Therefore, the derivative of F(x) is \(F'(x) = x^{(1/3)\).

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Answer:

I think it's symmetric. I could be wrong, but its been 2 weeks since you posted this so if you have the correct answer can you tell me it please! :)

Step-by-step explanation:

Answer:

Z = 63º

Step-by-step explanation:

X = 180 - 61 - 31 = 88º Angles in a triangle add to 180º

Y = 180 - X = 180 - 88 = 92º Angles in a straight line add to 180º

Z = 180 - 25 - Y = 180 - 25 - 92 = 63º Angles in a triangle add to 180º

So Z = 63º

No, X or y-axis scale does not have to always start at zero. In a line chart, it's OK to start the axis at a number other than zero

A line that is used to take or mark measurements is known as an axis in mathematics. Two crucial axes of the coordinate plane are the x and y axes. A horizontal number line is the x-axis, while a vertical number line is the y-axis. The coordinate plane is created by the perpendicular intersection of these two axes.

Given,

No, X or y-axis scale does not have to always start at zero.

A line chart encodes data using location (x, y coordinates), whereas a bar chart represents data using length. In a line chart, it's OK to start the axis at a number other than zero despite many claims that they are always misleading since this minute difference influences how a reader utilizes the chart.

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P(X = 2) is not equal to P(X = 3)

To show that P(X = 2) = P(X = 3) in a binomial distribution with n = 5 and p = 0.5, we need to use the formula for the probability mass function (PMF) of a binomial distribution.

The PMF of a binomial distribution is given by the formula:

P(X = k) = C(n, k) *\(p^k * (1-p)^{(n-k)}\)

where n is the number of trials, k is the number of successes, p is the probability of success, and C(n, k) represents the binomial coefficient.

In our case, n = 5 and p = 0.5. Let's calculate P(X = 2) and P(X = 3) using the formula:

P(X = 2) = \(C(5, 2) * (0.5)^2 * (1-0.5)^{(5-2)}\)

        = 10 * 0.25 * 0.125

        = 0.3125

P(X = 3) = C(5, 3) * \((0.5)^3 * (1-0.5)^{(5-3)}\)

        = 10 * 0.125 * 0.125

        = 0.125

As we can see, P(X = 2) = 0.3125 and P(X = 3) = 0.125.

Therefore, P(X = 2) is not equal to P(X = 3) in this specific case of a binomial distribution with n = 5 and p = 0.5.

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Answer:

Step-by-step explanation:

For interval estimation of μ, the correct distribution to use is the standard normal distribution, assuming σ is known. The correct option is A.

Given that the interval estimation of μ foe the assumed known σ.

The first option is correct, as the sample is large too we can use normal.

The second, third and fourth options are wrong because t can be used only whenever the population standard deviation is unknown and the population has a normal or near-normal distribution.

For interval estimates, the t distribution applies only if the sample standard deviation is used to estimate the population standard deviation

Hence, the proper distribution to use for the interval estimation of μ when σ is assumed known is standard normal distribution.

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To find the polar coordinates (r, θ) corresponding to the Cartesian coordinates (-6, 6), we can use the following formulas:

r = √(x² + y²)

θ = arctan(y / x)

(a) For the given point (-6, 6):

x = -6

y = 6

First, let's find the value of r:

r = √((-6)² + 6²) = √(36 + 36) = √72 = 6√2

Next, let's find the value of θ:

θ = arctan(6 / -6) = arctan(-1) = -π/4 (since the point lies in the third quadrant)

Therefore, the polar coordinates of the point (-6, 6) are (6√2, -π/4).

(b) For r > 0 and 0 ≤ θ < 2:

In this case, the polar coordinates will remain the same: (6√2, -π/4).

(c) For r < 0 and 0 ≤ θ < 2:

Since r cannot be negative in polar coordinates, there are no valid polar coordinates for r < 0 and 0 ≤ θ < 2.

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Answer

Explanation

Debby has 15 yards in total to make pillow cases.

Each pillow case requires (8/9) yard.

How much yard is left after she makes as many pillowcases as she can.

1 pillowcase = (8/9) yard

We need to obtain how many pillowcases 15 yards can make.

That is obtainable by dividing 15 by (8/9).

Hence, 16.875 pillowcases of (8/9) yards each, are obtainable from 15 yards.

Since pillowcases cannot exist in fraction, the 0.875 pillowcase has to be extra yards of fabric.

1 pillowcase = (8/9) yard

0.875 pillowcase = 0.875 × (8/9) = (7/8) × (8/9) = (7/9) or 0.778 yards.

Hence, the number of yards that will be left after making as many

Answer:

90 degrees

Step-by-step explanation:

see image

make x A

y B

z C

AB=3 (given)

AC=9 (given)

measure of angel B or y, is 90

if

x= A

y= C

z= B

then the hypotenuse would be shorter than one of the legs

3<9

so B has to be the right angle (90 degrees)