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The similarity theorem that proves the two given triangles are similar is: B. AA similarity theorem.

Recall:

The angle-angle similarity theorem (AA) states that if two angles in one triangle are of the same measure with two corresponding angles in another triangle, both triangles are similar to each other.

In the image given:

\(\angle F\) in \(\triangle ETF\) is congruent to \(\angle U\) in \(\triangle VTU\) (\(\angle F = \angle U = 78\))

\(\angle ETF = \angle VTU\) (vertical angles are equal)

This implies that two angles in \(\triangle ETF\) are congruent to two corresponding angles in \(\triangle VTU\).

Therefore, both triangles can be proven to be similar by the angle-angle similarity theorem (AA).

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The expression x to the power of 3 times x to the power of 3 times x to the power of 3 is not equivalent to an expression x to the power of 3 times 3 times 3.

For given question,

We have been given a statement 'x to the power of 3 times x to the power of 3 times x to the power of 3 '

We can write above statement in expression form as,

x³ × x³ × x³

Now, we simplify above expression.

We know that the product rule of exponents states that, 'To multiply expressions with the same base, add the exponents while keeping the base the same.'

So, x³ × x³ × x³ = \(x^{3+3+3}\)

⇒  x³ × x³ × x³ = \(x^{9}\)                    ....................................(1)

Also, we have been given a statement that 'x to the power of 3 times 3 times 3'

We can write above statement in expression form as,

\(x^{3\times 3\times 3}\)

Now we simplify above expression.

By power of a product rule of exponents,

\(x^{3\times 3\times 3}=x^{27}\)                           .....................................(2)

From (1) and (2),

x³ × x³ × x³ ≠ \(x^{3\times 3\times 3}\)

Therefore, the expression x to the power of 3 times x to the power of 3 times x to the power of 3 is not equivalent to an expression x to the power of 3 times 3 times 3.

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The surface integral ∬S F⋅dS, where F =  <1, y², -(1 - z - x)²> , and S is part of the plane x+y+z=1 where x² + y² ≤ 1, oriented upwards, is equal to 2/3 + 1/2 (2π - 1).

To compute the surface integral ∬S F⋅dS, where F = <1, y², -(1 - z - x)²> and S is part of the plane x + y + z = 1 where x² + y² ≤ 1, oriented upwards, we can use the divergence theorem.

Calculate the divergence of F:

∇ · F = ∂/∂x(1) + ∂/∂y(y²) + ∂/∂z(-(1 - z - x)²)

= 0 + 2y + 2(1 - z - x)(-1)

= 2y - 2(1 - z - x)

= -2x - 2y + 2z

Determine the unit normal vector to the surface S:

The plane x + y + z = 1 has a normal vector given by <1, 1, 1>. Since we want the surface to be oriented upwards, we use the unit normal vector <1, 1, 1>/√3.

Calculate the magnitude of the normal vector:

|n| = √(1² + 1² + 1²) = √3

Step 4: Evaluate the surface integral using the divergence theorem:

∬S F⋅dS = ∭V (∇ · F) dV

= ∭V (-2x - 2y + 2z) dV

Determine the limits of integration for the volume V:

The volume V is determined by the region x² + y² ≤ 1 and the plane x + y + z = 1. Since the plane intersects the unit circle in the xy-plane, we can use polar coordinates to represent the volume.

In polar coordinates, we have x = r cos(θ), y = r sin(θ), and z = 1 - r cos(θ) - r sin(θ), where r varies from 0 to 1 and θ varies from 0 to 2π.

Rewrite the surface integral in terms of polar coordinates:

∬S F⋅dS = ∫θ=0 to 2π ∫r=0 to 1 ∫z=0 to 1 -2r cos(θ) - 2r sin(θ) + 2(1 - r cos(θ) - r sin(θ)) r dz dr dθ

Evaluate the integral:

∬S F⋅dS = ∫θ=0 to 2π ∫r=0 to 1 [-2r cos(θ) - 2r sin(θ) + 2(1 - r cos(θ) - r sin(θ))] r dz dr dθ

Since the integrand does not depend on z, the innermost integral with respect to z evaluates to 1:

∬S F⋅dS = ∫θ=0 to 2π ∫r=0 to 1 [-2r cos(θ) - 2r sin(θ) + 2(1 - r cos(θ) - r sin(θ))] r dr dθ

Next, evaluate the integral with respect to r:

∬S F⋅dS = ∫θ=0 to 2π [-2/3 r³ cos(θ) - 2/3 r³ sin(θ) + 1/2 r² (1 - r cos(θ) - r sin(θ))]|r=0 to 1 dθ

Simplifying further:

∬S F⋅dS = ∫θ=0 to 2π [-2/3 cos(θ) - 2/3 sin(θ) + 1/2 (1 - cos(θ) - sin(θ))] dθ

Integrating with respect to θ:

∬S F⋅dS = [-2/3 sin(θ) + 2/3 cos(θ) + 1/2 (θ - sin(θ) - cos(θ))]|θ=0 to 2π

Evaluating the expression:

∬S F⋅dS = [-2/3 sin(2π) + 2/3 cos(2π) + 1/2 (2π - sin(2π) - cos(2π))] - [-2/3 sin(0) + 2/3 cos(0) + 1/2 (0 - sin(0) - cos(0))]

Simplifying further:

∬S F⋅dS = [-2/3 (0) + 2/3 (1) + 1/2 (2π - 0 - 1)] - [-2/3 (0) + 2/3 (1) + 1/2 (0 - 0 - 1)]

Finally, we have:

∬S F⋅dS = 2/3 + 1/2 (2π - 1)

Therefore, the surface integral ∬S F⋅dS, where F=<1,y²,-(1-z-x)²> and S is part of the plane x+y+z=1 where x² +y² ≤1, oriented upwards, is equal to 2/3 + 1/2 (2π - 1).

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Answer:

1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

4(x+2)+2=14

4x+8+2=14

4x+10=14

4x=14 - 10

4x=4

x=4/4

x = 1

dimensions of the poster with margin are L  =  12 in and h  = 24 in

The shape/polygon of a rectangle is two dimensional, having four sides, four vertices, and four right angles. The rectangle's two opposing sides are equal and parallel to one another. The space a rectangle occupies is known as its area. The area of a rectangle can also be defined as the region inside its border.

We utilise the unit squares to calculate a rectangle's area. Rectangle ABCD should be divided into unit squares. The total number of unit squares that make up a rectangle ABCD is its area.

Rectangle area equals length times width.

Let call length of printed area of the poster be " x "  and  height of printed area of the poster be " y ".

Area of the poster = length and height

200 = x*y  

y = 200/x

We also know that dimensions of the poster with margin is:

L  =  x + 2   in  and     H  =  y + 4 in

Therefore area of the poster is:

A(p)  = ( x + 2 ) * ( y + 4 )

And area as function of x is:

A(x)  =   ( x + 2 ) * ( 200/x + 4 )

A(x)  =  200 + 4*x + 400 /x  + 8

Taking derivatives on both sides of the equation we have:

A´(x)  =  4 - 400/x²

By taking A´(x)  = 0

4 - 400/x² = 0 ⇒ 4*x² - 400 = 0

x² = 400 / 4

x² = 100

x = 10 in

and y = 200/x ⇒ y = 20

The second derivative A´´(x) = 400/x4 which is > 0

there is a minimum for the function at the point x = 10

As x and y are dimensions of the printing area of the poster, dimensions of the poster with margin are

L  = x  +  2   =   10  + 2  =  12 in   and

h = y  +  4   =   20  + 4  =  24  in

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\(\tt \dfrac{3}{8}\times 28.7=10.7625=10.76~kg\)

Answer: which one do you prefer

Step-by-step explanation:

Answer:

0 over 12

Step-by-step explanation:

3/4 is equal to 9/12

so your basically taking 9/12 from 9/12

Here, we use the property of multiplication of exponential expression which states when we multiply two exponential expressions with the same base, we keep the base and add the exponents.

Therefore,

\(x^(3+5) = x^8\)

Now,

\(x^(3+5) = x^8\)

is of the form:

\(x^b = x^p\)

When we have two equal expressions on either side of the equation, the power of the base remains the same. Therefore,

p = 8

There we have it. The value of p is 8. The full solution is shown below:

\(x^3 × x^5 \\= x^px^8\\ = x^p\)

We can see that the base of the exponential expression on either side is equal.

Therefore, the power of the base must be equal as well. In other words

,p = 8.

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The rectangle that has the maximum area when the length is 5.5 and the width is 5.5.

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

To find the rectangle with the maximum area among all rectangles with a perimeter of 22, we need to consider the relationship between the perimeter and the dimensions of the rectangle.

Let's assume the width of the rectangle is represented by "w". Since a rectangle has two equal pairs of sides, the length of the rectangle will also be "w".

The perimeter of the rectangle is given by:

Perimeter = 2(length + width)

Given that the perimeter is 22, we can set up the equation:

22 = 2(2w)

Simplifying:

22 = 4w

Dividing both sides by 4:

w = 5.5

So, the width of the rectangle is 5.5, and since the length is equal to the width, the length is also 5.5.

Now, let's define the objective function in terms of the width, w, and the area, A.

The area of the rectangle is given by:

Area = length × width

Substituting the values:

A = (5.5)(5.5) = 30.25w²

So, the objective function in terms of the width of the rectangle, w is A = 30.25w²

hence, the rectangle that has the maximum area when the length is 5.5 and the width is 5.5

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Complete question:

Of all rectangles with a perimeter of 29​, which one has the maximum​ area? (Give the​ dimensions.) Let A be the area of the rectangle. What is the objective function in terms of the width of the​ rectangle, w? Aequals 14.5 w minus w squared ​(Type an​ expression.) The interval of interest of the objective function is nothing. ​(Type your answer in interval notation. Use integers or simplified fractions for any numbers in the​ expression.) The rectangle that has the maximum area has length nothing and width nothing. ​

The value of the standard error of the mean in each of the following cases are as follows: a) = 1.414213562 = 1.41, b) = 1.41, c) = 1.41 and d) = 1.34.

As standard error (SE) = s × fpc /sqrt (n) and fpc = sqrt [(N-n) / (N-1)] where,

N = population size

n = sample size

then,

a) The population size is infinite (to 2 decimals).

If N = infinity, then fpc = 1.

Thus, SE = 10×1/sqrt (50) = 1.414213562 = 1.41  

b) The population size is N = 50,000 (to 2 decimals).

If N = 50000, then

fpc = sqrt [(50000-50)/(50000-1)] = 0.99950987

Thus, SE = 10*0.99950987/sqrt (50) = 1.413520414 = 1.41  

c) The population size is N = 5000 (to 2 decimals).

If N = 5000, then

fpc = sqrt [(5000-50)/ (5000-1)] = 0.995086951

Thus, SE = 10*0.995086951/sqrt (50) = 1.407265462 = 1.41

d) The population size is N = 500 (to 2 decimals).

If N = 500, then

fpc = sqrt [(500-50)/ (500-1)] = 0.949633407

Thus, SE = 10*0.949633407/sqrt (50) = 1.342984443 = 1.34

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Answer:

-5 2

Step-by-step explanation:

Answer:

if it's a test then don't cheat mate

4\(4\sqrt{3}\)Answer: 4 radical 3

Step-by-step explanation

Answer:

12

200+50=250

3,000/250=12

The sample proportion who prefer balancing the budget is 0.59

The sample proportion is the ratio of a sample's number of successes to its overall sample size. A single dataset may contain many sample proportions, some of which may or may not be equal; yet, the sample proportion is roughly normally distributed because it is a random variable.

P=X/N, where X represents the number of successes and N represents the sample size, yields the sample proportion.

How to calculate Sample Space?

Count the total number of successes in the sample as well as its size to determine the sample proportion. This could entail resolving challenging combinatorial puzzles. After that, calculate the sample size to the total number of successes. This is a sample percentage.

So, our sample proportion will be 702/1190 = 0.59

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Answer:it will be 20 inches long at the end of 5 weeks

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

i got it wrong and it showed me the real answer

Answer:

x = 13

Step-by-step explanation:

\(\huge{ \frac{x - 5}{2} + \frac{x - 1}{8} = \frac{x - 3}{4} + \frac{x - 4}{3}} \)

\(\huge{24( \frac{x - 5}{2} + \frac{x - 1}{8} ) = 24( \frac{x - 3}{4} + \frac{x - 4}{3} )}\)

\(\huge{24( \frac{x - 5}{2} + \frac{x - 1}{8} ) = 24( \frac{x - 3}{4} + \frac{x - 4}{3} )}\)

\(\huge{24 \times \frac{x - 5}{2} + 24 \times \frac{x - 1}{8} = 24 \times \frac{x - 3}{4} + 24 \times \frac{x - 4}{3}} \)

\(12(x - 5) + 3(x - 1) = 6(x - 3) + 8(x - 4)\)

\(12x - 60 + 3x - 3 = 6x - 18 + 8x - 32\)

\(15x - 63 = 14x - 50\)

\(15x - 14x = - 50 + 63\)

\(x = - 50 + 63\)

\(\boxed{\green{x = 13}}\)

Answer:

A

Step-by-step explanation:

:)

Answer:

x = 30

Step-by-step explanation:

30 - -2 = 32

16 /=/ 32

(A) The leading term is -8x^5.
(B) The limit of p(x) as x approaches 0 is 16.
(C) The limit of p(x) as x approaches infinity is negative infinity.

(A) The leading term of a polynomial is the term with the highest degree.

In this case, the highest degree term is -8x^5.

Therefore, the leading term of the polynomial p(x) = 16+2x^4-8x^5 is -8x^5.

(B) To find the limit as x approaches 0, we can simply substitute 0 for x in the polynomial p(x).

Doing so gives us:

p(0) = 16 + 2(0)^4 - 8(0)^5
p(0) = 16

Therefore, the limit of p(x) as x approaches 0 is 16.

(C) To find the limit as x approaches infinity, we need to look at the leading term of the polynomial.

As x gets larger and larger, the other terms become less and less significant compared to the leading term.

In this case, the leading term is -8x^5. As x approaches infinity, this term becomes very large and negative.

Therefore, the limit of p(x) as x approaches infinity is negative infinity.

In summary:

(A) The leading term is -8x^5.
(B) The limit of p(x) as x approaches 0 is 16.
(C) The limit of p(x) as x approaches infinity is negative infinity.

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Answer:

\(x = \sqrt{ {17}^{2} - {15}^{2} } = \sqrt{289 - 225} = \sqrt{64} = 8\)

So x = 8 = 8.0

The probability that exactly 4 out of 6 selected students own a computer is approximately 0.3493, or 34.93%.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about how probable an event is to happen, or its chance of happening.

To calculate the probability of exactly 4 out of 6 selected students owning a computer, we can use the binomial probability formula:

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

where:

- P(X = k) is the probability of exactly k successes (4 students owning a computer),

- C(n, k) is the number of combinations of selecting k items from a set of n items (also known as the binomial coefficient),

- p is the probability of success (the proportion of students owning a computer), and

- n is the total number of trials (number of students selected).

In this case, n = 6, k = 4, and p = 0.82.

Using the formula, we can calculate the probability:

\(P(X = 4) = C(6, 4) * 0.82^4 * (1 - 0.82)^{(6 - 4)\),

C(6, 4) = 6! / (4! * (6-4)!) = 15,

\(P(X = 4) = 15 * 0.82^4 * 0.18^2\),

P(X = 4) ≈ 0.3493.

Therefore, the probability that exactly 4 out of 6 selected students own a computer is approximately 0.3493, or 34.93%.

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Answer:

A= B= C= D= E= F=

Step-by-step explanation:

Answer:

The number y decreased by 12.

Step-by-step explanation:

Answer

the answer is b y decreased by 12

Step-by-step explanation:

that is what y-12 is

Answer:

\(f(x)=\dfrac25x+\dfrac35\)

Step-by-step explanation:

The data in the table means that if you input the value of x into the function, the output will be f(x).

The first two answer options are linear functions.  If a function is linear, the ratio of the difference in y-values to the difference in x-values is always constant.

We can see that the x-values in the table increase by 3 each time, so the difference in x-values is 3.

By calculation, we can also see that the y-values increase by 6/5 each time, so the difference in y-values is 6/5.

Therefore, the ratio of differences is 6/5 ÷ 3 = 2/5 and is constant.

So the function is linear and has a slope (gradient) of 2/5

Therefore, the function is: \(f(x)=\dfrac25x+\dfrac35\)

Answer:

I think it would be 7:28 P.M but it's not in choice so maybe I'm wrong.

Step-by-step explanation

To solve this problem, we just add them together...

Change to minutes: 3h51'=231mins ; 3h37'=217mins.

<=>231+217= 448 mins = 7hours28mins

Answer:

Step-by-step explanation:

No its A dont listen to anyone else but me

To draw the digital circuit corresponding to the expression x(yz' + z), we can break it down into logical operations.

The given expression involves the logical operations of NOT, AND, and OR. In the circuit diagram, we would have three inputs: x, y, and z. Firstly, we need to calculate the complement of z (represented as z') using a NOT gate. The output of the NOT gate would then be connected to one input of the AND gate. The other input of the AND gate would be connected directly to the input y.

The output of the AND gate would be connected to one input of the OR gate. Finally, the input x would be directly connected to the other input of the OR gate. The output of the OR gate would be the result of the expression x(yz' + z).

The circuit would consist of an input x connected directly to an OR gate, while an input y would be connected to one input of an AND gate along with the complement of input z (z') obtained through a NOT gate. The output of the AND gate would be connected to the other input of the OR gate, and the output of the OR gate would represent the result of the given expression x(yz' + z).

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The co-ordinate of the point of trisection of the line joining the (25,10) (-5,-5)​ is (15,5).

Given - Line joining the points (25,10) (-5,-5)​

To find - The co-ordinate of the point of trisection

The points that divide a line segment AB in a ratio of 1:2 or 2:1 are known as points of trisection.

The point that splits a line segment AB in the ratio m:n is determined by the following formula,

\(\frac{mx_{2}+ nx_{1} }{m+ n}\) , \(\frac{my_{2} + ny_{1} }{m + n}\)

Accordingly,

\(\frac{1(-5) + 2(25)}{3}\) , \(\frac{1(-5) + 2(10)}{3}\)

\(\frac{-5 +50}{3}\) , \(\frac{-5 + 20}{3}\)

Solving,

\(\frac{45}{3}\) , \(\frac{15}{3}\)

(15, 5)

The co-ordinate of the point of trisection of the line joining the (25,10) (-5,-5)​ is (15,5).

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