a cube has a base with area of 324 meters squared . what is the volume of the cube, to the nearest unit?

The area of the rectangular animal pen with fencing of 200 m with a length of 60 m is 2400 sq m

Perimeter refers to the length of the boundary of a given shape.

Perimeter = 2(l + b)

where l is the length

b is the breadth

Given,

Perimeter = 200 m

l = 60 m

200 = 2(60 + b)

100 = 60 + b

b = 100 - 60

b = 40 m

The other side of the rectangle is 40 m.

The area is the expanse covered by a shape

Area = l * b

= 60 * 40

= 2400 sq m

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We can plot the vector r(t) and the vector N(T) at the given value of t = T.

To find the principal unit normal for the vector-valued function r(t) = sin(t)i + tcos(t)j + tk, we need to compute the derivative of r(t) with respect to t and then normalize it to obtain a unit vector.

First, let's find the derivative of r(t):

r'(t) = cos(t)i + (cos(t) - tsin(t))j + k

Next, we'll normalize the vector r'(t) to obtain the unit vector:

||r'(t)|| = sqrt((cos(t))^2 + (cos(t) - tsin(t))^2 + 1^2)

Now, we can find the principal unit normal vector by dividing r'(t) by its magnitude:

N(t) = r'(t) / ||r'(t)||

Let's evaluate the principal unit normal at t = T:

N(T) = (cos(T)i + (cos(T) - Tsin(T))j + k) / ||r'(T)||

To sketch the situation, we can plot the vector r(t) and the vector N(T) at the given value of t = T.

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Answer:

The missing step is 4x + 6 = -24. This step is justified by the additive property of equality. So the correct answer is B)

Step-by-step explanation:

The missing step in the given equation is 4x + 6 = -24. This step is justified by the additive property of equality. The additive property of equality states that if we add the same value to both sides of an equation, the equality remains true. In this case, 6 is added to both sides of the equation to isolate the term "4x" on the left side and move the constant term to the right side. Therefore, the correct answer is B: "4x + 6 = -24. This step is justified by the additive property of equality."

Answer:

non sequitur

Step-by-step explanation:

An argument in which the reasons do not support the conclusion so that the conclusion does not follow from the reasons offered is called a non sequitur.

Answer:

He earn approximately $2.14 everyday

Step-by-step explanation:

hope this helps :3

The margin of error is 2.695 for a sample size of 256 and a population variance of 484 at a 95% confidence level.



To find the margin of error, we need to use the formula:
Margin of error = z* (sigma / sqrt(n))
Where z* is the z-score corresponding to the desired confidence level, sigma is the population standard deviation, and n is the sample size.
In this case, we know that the population variance (sigma^2) is 484, which means the standard deviation (sigma) is sqrt(484) = 22.
The sample size (n) is 256.
The confidence level is 95%, which means the z-score is 1.96.
So, plugging these values into the formula, we get:
Margin of error = 1.96 * (22 / sqrt(256))
Simplifying, we get:
Margin of error = 1.96 * (22 / 16)
Margin of error = 2.695


Hence, we use the formula Margin of error = z* (sigma / sqrt(n)), where z* is the z-score corresponding to the desired confidence level, sigma is the population standard deviation, and n is the sample size. The margin of error is 2.695 for a sample size of 256 and a population variance of 484 at a 95% confidence level.

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To find the equation of the parabola with its vertex at the origin and its axis along one of the coordinate axes, we can use the following steps:

Step 1: Identify the axis of the parabola.
Since the parabola's vertex is at the origin, its axis will be one of the coordinate axes. In this case, it will be either the x-axis or the y-axis.

Step 2: Determine the focus of the parabola.
Given that the focus of the parabola lies on the line 3x + 4y = 12, we can rewrite this equation in terms of either x or y to find the coordinates of the focus. Let's rewrite it in terms of x:

3x = 12 - 4y
x = (12 - 4y) / 3

The x-coordinate of the focus is (12 - 4y) / 3. Since the parabola's vertex is at the origin, the y-coordinate of the focus will be 0.

So, the coordinates of the focus are [(12 - 4y) / 3, 0].

Step 3: Find the equation of the parabola.
Since the vertex is at the origin, the general equation of a parabola with its vertex at the origin and axis along the x-axis is given by:

x^2 = 4ay

where "a" is the distance between the focus and the vertex.

Using the coordinates of the focus we found in Step 2, we can substitute [(12 - 4y) / 3, 0] into the equation:

[(12 - 4y) / 3]^2 = 4a(0)

Simplifying the equation further:

(12 - 4y)^2 = 0

Expanding and solving for y:

144 - 96y + 16y^2 = 0

16y^2 - 96y + 144 = 0

Dividing the equation by 16:

y^2 - 6y + 9 = 0

Factorizing the quadratic equation:

(y - 3)^2 = 0

Taking the square root of both sides:

y - 3 = 0

y = 3

So, the equation of the parabola is x^2 = 4a(3), which simplifies to x^2 = 12a.

In conclusion, the equation of the parabola with its vertex at the origin and axis along one of the coordinate axes, where the focus lies on the line 3x + 4y = 12, is x^2 = 12a.

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Gibbs phase rule: F = C - P + 2, where F is degrees of freedom, C is components, and P is phases.

Starting with the expression for the Gibbs free energy of phase r, Gr = ∑(μirNir), where μir is the chemical potential of substance i in phase r and Nir is the number of moles of substance i in phase r. The chemical potential is a homogeneous function of temperature, pressure, and mole numbers.

Differentiating the expression for Gibbs free energy with respect to temperature, pressure, and mole numbers, we can obtain partial derivatives and use them to derive relationships between variables.

Using these relationships and considering the equilibrium conditions, we can derive the Gibbs phase rule: F = C - P + 2, where F is the number of degrees of freedom, C is the number of components (chemically independent substances), and P is the number of phases in the system.

When chemical reactions between different molecules are included, the phase rule can be generalized to account for additional constraints and variables arising from the stoichiometry of the reactions and the conservation of atoms.

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Answer

4z+5=

4*7+5=33

33

Step-by-step explanation:

Answer:

Step-by-step explanation:

You had the first part of the first question correct. The answer is 100:64

The sides of the squares

Area of e = 69% more than area of area of f

e^2: f^2 = ( 1 + 69/100 ) / 1

e^2 : f^2 = (1.69)/1            Take the square root of both sides

e:f  = 1.3:1

Answers:

\((f \circ g)(x) = 30x^2-18\\\\(g \circ f)(x) = 150x^2-180x+51\\\\\)

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

Work Shown:

\(f(x) = 5x-3\\\\f(g(x)) = 5(g(x))-3\\\\(f \circ g)(x) = 5(6x^2-3)-3\\\\(f \circ g)(x) = 30x^2-15-3\\\\(f \circ g)(x) = 30x^2-18\\\\\)

Those steps show we start with the outer function f(x) = 5x-3. Then we replace every x with g(x) in the second step. Afterward, we plug in g(x) = 6x^2-3 and we simplify.

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

We'll follow similar steps for (g∘f)(x)

But this time we started with g(x), plug in f(x) for every x, and then simplified.

\(g(x) = 6x^2-3\\\\g(f(x)) = 6(f(x))^2-3\\\\(g \circ f)(x) = 6(5x-3)^2-3\\\\(g \circ f)(x) = 6(25x^2-30x+9)-3\\\\(g \circ f)(x) = 150x^2-180x+54-3\\\\(g \circ f)(x) = 150x^2-180x+51\\\\\)

I'm probably doing nothing...

I might visit my grandparents tho because they recently moved near by

thanks for the points

Answer:

I might go see my cousins in a different state and most likely play with the snow out there!!

Step-by-step explanation:

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

Question: Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____

Current Progress: To express the given vector as a linear combination of u, v, and w, we need to find scalars a, b, and c such that (14, 9, 14) = a*u + b*v + c*w.

Step 1: Write the equation in component form:
(14, 9, 14) = (3a + b + 8c, a - b + 3c, 6a + 4b + 8c)

Step 2: Equate the corresponding components and solve for a, b, and c:
3a + b + 8c = 14
a - b + 3c = 9
6a + 4b + 8c = 14

Step 3: Solve the system of equations using any method (substitution, elimination, etc.). One possible solution is a = 1, b = -1, and c = 3.

Step 4: Plug the values of a, b, and c back into the linear combination equation:
(14, 9, 14) = 1*u + (-1)*v + 3*w

Step 5: Simplify the equation:
(14, 9, 14) = u - v + 3w

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

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The level of a line's slope indicates its steepness.

The slope is computed mathematically as "rise over run" (change in y divided by change in x).

In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.

The above equation is a standard straight-line equation, and we are asked to change it to slope-intercept form, which is given as y = mx + c. "m" denotes the slope of the line and "c" denotes its intercept.

Now, let's take an example ,

2x - 3y ≤ 12

or, - 3y ≤ 12 - 2x

or, 3y ≤ 2x - 12

or y ≤ (2/3)x - 4

So, here slope (m) = 2/3, graph is shown below:

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Answer: the last one on the right

Step-by-step explanation:

a)  Both the balloons will hit the ground at the same time.

b) The time taken by the second balloon to reach the ground : t'' = √(h/g)

c) The balloon B is moving with the fastest speed at impact (once it reaches the ground).

d) The balloon A has more chance to hit the car.

a) When the balloon A is thrown to the right horizontally, its vertical motion can be treated as if it is free fall motion under gravity. Therefore, it takes time, t for the balloon to hit the ground given as:

t = √(2h/g), where h is the height of the building and g is acceleration due to gravity.

Similarly, for the balloon B that is thrown down, the time taken to hit the ground is given by:

t' = √(2h/g),

since both the balloons are thrown from the same height. Thus, both the balloons will hit the ground at the same time.

b) For the second balloon, the time taken to reach the ground after the first balloon hits the ground is the time it takes to cover the distance h only.

Using the formula of distance covered, we can find the time taken to reach the ground after the first balloon hits the ground for the second balloon given as:

h = (1/2) g t''^2

where t'' is the time taken by the second balloon to reach the ground after the first balloon hits the ground.

Substituting t = √(2h/g) in the above equation, we get:

t'' = √(h/g)

c) When the balloon A reaches the ground, it is only moving horizontally with the speed v0.

On the other hand, when the balloon B reaches the ground, it is moving both horizontally and vertically with the speed √(2gh + v0^2), as it is thrown down with an initial velocity of v0 and accelerated downwards due to gravity.

d)As the balloon A is thrown horizontally to the right and the car is moving horizontally to the right, there is a chance that the balloon A can hit the car.

On the other hand, the balloon B is thrown downwards, so it has no chance of hitting the car.

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The original recipe had 0.9 cups of bananas.

Using only fresh ingredients, strawberry banana smoothie is a simple, nutritious dish. It is creamy, sweet, nutritious, and dairy- or dairy-free can be used to make it. The ideal summertime smoothie. Putting the strawberries, frozen banana, milk, and yoghurt in a blender and mixing until smooth and creamy is all that is required to make it.

Cups of strawberries = 1.75

No. of cups added of banana = 1/2

                                            = 0.5

No. of cups of banana smoothie have = 14.

The original recipe had = 1.4 - 0.5

                                   = 0.9

Hence, the original recipe had 0.9 cups of bananas.

Correct Question :

to make a strawberry banana smoothie, a recipe calls for 1.75 cups of strawberries and some bananas. to make the recipe taste more like banana, 1/2 cup more banana was added to the blender. the smoothie now has 1.4 cups of bananas. how many cups of bananas were in the original recipe?

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The spectral decomposition of matrix A is A = (-2)(u₁u₁ᵀ) + (0)(u₂u₂ᵀ) + (0)(u₃u₂ᵀ) + (-8)(u₃u₃ᵀ) + (-14)(u₃u₃ᵀ).

The spectral decomposition of matrix A involves expressing it as a sum of outer products of eigenvectors and corresponding eigenvalues. Given the matrices P and D, we have:

A = PDP⁻¹

Substituting the given values:

A = [-8 -4 4 -4 -10 0 4 0 -6]

P = [2/3 -1/3 2/3 -1/3 2/3 2/3 2/3 2/3 -1/3]

D = [-2 0 0 0 -8 0 0 0 -14]

We need to find the eigenvectors and eigenvalues from P and D to construct the spectral decomposition. The eigenvectors are the columns of P, and the eigenvalues are the diagonal elements of D.

Eigenvector u₁ corresponds to eigenvalue -2.

Eigenvector u₂ corresponds to eigenvalue 0.

Eigenvector u₃ corresponds to eigenvalue -14.

The spectral decomposition of A is then given by:

A = (-2)(u₁u₁ᵀ) + (0)(u₂u₂ᵀ) + (0)(u₃u₂ᵀ) + (-8)(u₃u₃ᵀ) + (-14)(u₃u₃ᵀ)

Simplifying, we can write it as:

A = (-2)(u₁u₁ᵀ) + (-8)(u₃u₃ᵀ) + (-14)(u₃u₃ᵀ)

Since the terms with u₂u₂ᵀ and u₃u₂ᵀ are multiplied by zero, they do not contribute to the spectral decomposition. The final expression is:

A = (-2)(u₁u₁ᵀ) + (-8)(u₃u₃ᵀ) + (-14)(u₃u₃ᵀ)

This completes the spectral decomposition of matrix A using the given matrices P and D.

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Answer:

Step-by-step explanation:

Given

\(x=4-t\)

and \(y=t^2-2\quad \ldots(i)\)

So, \(t=4-x\)

Substitute the value of \(t\) in \((i)\)

\(y=(4-x)^2-2\)

\(y+2=(4-x)^2\)

So it represent a parabola shown in the figure

Answer:

Step-by-step explanation:

The required t score would be determined from the t distribution table. In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 50 - 1 = 49

Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01

α/2 = 0.01/2 = 0.005

the area to the right of z0.005 is 0.005 and the area to the left of z0.005 is 1 - 0.005 = 0.995

Looking at the t distribution table,

t score = 2.678

a) Consider the experiment of picking 3 tax returns at random as 3 related experiments (due to the fact that it is without replacement); then, as for the first time one selects a tax return,

As for the second time we grab a tax return, there are 69 tax returns in total and 9 of them contain errors; thus,

Similarly, as for the third picking round,

Finally, the probability of experiment a) is

Rounded to one decimal place, the probability of event a) is 65.7%

b) Similarly, in the event of all three tax returns containing errors,

Thus,

The probability of event b) is 0.2%. It is quite unusual.

c) The condition 'at least one of those containing errors' includes the cases when 1, 2, or 3 tax returns of the ones selected have errors. Notice that

Therefore,

And we found the probability of picking 3 tax returns without any errors in part a); thus,

The probability of event c) is 34.3%.

d) Analogously to part c), the probability of selecting at least one without errors is

The probability of event d) is 99.8%, and it is not improbable at all.

H satisfies all three subspace properties, it is a subspace of R³.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur.

Let H be the set of all vectors of the form 4t, where t is any real number. We want to find a vector v in R³ such that H = Span{v}.

Let v = [4,0,0]. Then any scalar multiple of v will be of the form [4t,0,0], which is an element of H. Thus, H is contained in Span{v}.

Conversely, any vector in Span{v} can be written as a scalar multiple of v, which is of the form [4t,0,0] and therefore an element of H. Thus, Span{v} is contained in H.

Therefore, we have H = Span{v}.

This shows that H is a subspace of R³ because Span{v} is a subspace of R³ (since v is in R³) and H = Span{v}. To show that H is a subspace of R³, we need to verify the three subspace properties:

The zero vector of R³ is in H: The zero vector of R³ is [0,0,0], which is of the form [4t,0,0] when t = 0. Therefore, the zero vector is in H.

H is closed under vector addition: Let u and w be vectors in H. Then u = [4t₁,0,0] and w = [4t₂,0,0] for some t₁, t₂ in R. The sum u + w is [4t₁+4t₂,0,0], which is also an element of H. Therefore, H is closed under vector addition.

H is closed under scalar multiplication: Let u be a vector in H and let c be a scalar in R. Then u = [4t,0,0] for some t in R. The scalar multiple cu is [4ct,0,0], which is also an element of H. Therefore, H is closed under scalar multiplication.

Therefore H satisfies all three subspace properties, it is a subspace of R³.

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The largest open interval where f(x) is decreasing is (-2√(1/3), 2√(1/3)). In interval notation, this can be written as (-2√(1/3), 2√(1/3)).

To determine where the function f(x) = x^3 - 4x is decreasing, we need to find the intervals where the derivative is negative. Let's calculate the derivative of f(x) first:

f'(x) = 3x² - 4

To find where f'(x) < 0, let's solve the inequality:

3x² - 4 < 0

Adding 4 to both sides gives:

3x² < 4

Dividing both sides by 3 gives:

x² < 4/3

Taking the square root of both sides (and considering both the positive and negative square root) gives:

x < √(4/3) and x > -√(4/3)

Simplifying further, we have:

x < 2√(1/3) and x > -2√(1/3)

The largest open interval where f(x) is decreasing is (-2√(1/3), 2√(1/3)). In interval notation, this can be written as (-2√(1/3), 2√(1/3)).

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We need to investigate the behavior of the derivative of the feature. If the spinoff is negative inside a c program language period, then the quality is lowering over that c language.

Let's begin by finding the derivative of the function f(x) = x^3 - 4x:

f'(x) = 3x^2 - 4

we set f'(x) < zero:

3x^2 - four < zero.

Now, permit's remedy this inequality:

3x^2 < 4,

x^2 < four/three,

x^2 - 4/three < 0.

To find the critical points, we set x^2 - 4/three = zero:

x^2 = 4/three,

x = ±√(4/three),

x = ±2/√3.

We need to test the durations among the essential factors and beyond.

For x < -2/√3, allow's select x = -1. Plugging this cost into f'(x):

'(-1) = three(-1)^2 - four = -1.

Since f'(-1) < zero, the characteristic is decreasing for x < -2/√3.

For -2/√three < x < 2/√three, permits select x = zero. Plugging this price into f'(x):

f'(0) = 3(0)^2 - four = -four.

Since f'(0) < zero, the characteristic is lowering for -2/√three < x < 2/√3.

For x > 2/√three, permits choose x = 1. Plugging this cost into f'(x):

f'(1) = three(1)^2 - four = -1.

Since f'(1) < 0, the function is decreasing for x > 2/√3.

Therefore, the largest open c language in which the characteristic f(x) = x^3 - 4x is lowering is (-∞, 2/√three).

Answer:

8 cubes

If we want to cover the base of the prism having dimensions 2 cm × 1 cm with cm length of cube, then there will be (4 × 2) = 8 cubes that can occupy the base

Step-by-step explanation:

Answer:

(1, -4)

Step-by-step explanation:

if you rotate from quadrant 3 to 4, x=-y and y=x

After the rotation of 90° clockwise about the origin, the coordinates become P'(- 1, - 4).

Given is the coordinate of point as (-4, - 1). It is rotated by 90° clockwise about the origin.

When we rotate a figure 90 degrees clockwise about the origin, then the new coordinates will be -

A(x, y) → A(y, - x)

Then, we can write the new coordinates according to the rule as -

P(-4, - 1) → P'(- 1, - 4)

Therefore, after the rotation of 90° clockwise about the origin, the coordinates become P'(- 1, - 4).

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To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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