Select the correct answer. Which expression is a prime polynomial?

A.
\( {x}^{3} - {b}^{3} \)
B.
\( {x}^{2} - 4x - 12\)
C.
\( {x}^{4} + 8x {y}^{3} \)
D.
\( {x}^{2} - {b}^{3} \)
​

True , Every matrix transformation is a linear transformation.

Is there a linear transformation for every matrix operation?

Despite the fact that every linear transformation is a matrix transformation, not all linear transformations are matrix transformations.      

                                    Because of this, it's possible that we'll encounter a linear transformation in which we're unable to locate a matrix to carry out the mapping.

What alteration does matrix entail?

In a two-dimensional or three-dimensional space, the transformation matrix converts one vector into another vector, which may be comprehended geometrically.

                                    Stretching, squeezing, rotation, reflection, and orthogonal projection are some of the often utilized transformations.

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Step-by-step explanation:

the answer is in the above image

Answer:

61°

Step-by-step explanation:

(x+18)°=(4x-15)°alternate angles, because BC is parallel to AD

x°+18°=4x°-15°

18°+15°=4x°-x°

33°=3x°

33°/3°=3x°/3°

11=x

angle ABD

90°-(x+18)°. the sides of a rectangle meet at 90°

90°-(11+18)°

90°-(29)°

90°-29°

61°

Answer:

a = 3

Step-by-step explanation:

We can start by cross multiplying, which is a method to help solve proportions. We get:

5 * a = 3 * (a + 2)

Now, we can distribute the 3 and solve:

5a = 3a + 6

-3a  -3a

2a = 6

/2    /2

a = 3

Answer:

\(a = 3\)

Step-by-step explanation:

\(a \times 5=(a+2) \times 3\)

\(5a=(a+2) \times 3\)

\(5a=3a+6\)

\(5a−3a=6\)

\(2a=6\)

\(a = 3\)

Answer:

a and b

Step-by-step explanation:

they're both equal to 25%; 100 reduced by 75 is 25

The probability that two random people being born on the same day is thus 1/365 or about 0.3%

We apply our probability model above to the task at hand.

First, we suppose Person 1. This person is born on a certain date of the year.

Since this is a random person, we can fix this person's birthday to a specific date (a number between 1 and 365) without loss of generality for the problem.

Let's say this person is born on 10. (i.e. January 10th)

Now, we take Person 2. In order to achieve the event that Person 2 is born on the same date as Person 1,

we need them to be born on 10. In other words, we seek the probability of Person 2 being born on 10.

Based on our model, we have that this probability is 1/365.

The probability that two random people being born on the same day is thus 1/365 or about 0.3%

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Answer:

1.5kg

Step-by-step explanation:

The mean for the packages on day 1 will be:

= (1 + 8 + 1 + 12 + 1 + 11 + 7 + 6)/8

= 47/8

= 5.875

The mean for day 2 will be:

= (47 + 12)/8

= 59/8

= 7.375

The increase in mean:

= 7.375 - 5.875

= 1.5

Answer:

\(=\frac{1}{2}\)

Step-by-step explanation:

\(= -6/12+9/12+3/12\)

\(=\frac{-6}{12}+\frac{9}{12}+\frac{3}{12}\)

\(=\frac{-6+9+3}{12}\)

\(=\frac{6}{12}\)

\(=\frac{1}{2}\)

Answer:

1/2

Step-by-step explanation:

Words words words words

Answer:

Come on... Not enough evidence given.

Step-by-step explanation:

Answer:

Step-by-step explanation:

You need to do math to solve for the answer.

Work Shown:

\(a^2 + b^2 = c^2\\\\a^2 + 23^2 = 30^2\\\\a^2 + 529 = 900\\\\a^2 = 900 - 529\\\\a^2 = 371\\\\a = \sqrt{371}\\\\a \approx 19.26136\\\\a \approx 19.3\)

For more information, search out "pythagorean theorem" to see other examples. The pythagorean theorem only works for right triangles.

Answer:

18 units²

Step-by-step explanation:

Solve for height:

4² + x² = 5²

16 + x² = 25

9 = x²

x = 3

Solve for area:

Formula = (base1+base2)h / 2

(4 + 8)* 3 ÷ 2

12 * 3 ÷ 2

36 / 2 = 18

If my answer is incorrect, pls correct me!

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

-Chetan K

Option A. AA Similarity Postulate. The AA Similarity Postulate is a geometric principle that states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

This means that their corresponding sides are in proportion, and the triangles have the same shape, but not necessarily the same size. This postulate is one of the ways to prove the similarity of two triangles. In the case of the given question, if we know that two angles of one triangle are congruent to the two angles of another triangle, then we can use the AA Similarity Postulate to prove that the triangles are similar. This principle is widely used in geometry and helps to establish relationships between different shapes and figures.

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Area of a rectangle = height × width

= 5b × 3a

= 15ab

Answer:

Mayzle at 8th game and madison at the 12th game

Answer:

3.5 un

Step-by-step explanation:

to find the new length of the square using a scale factor of 1/7 you can just multiply 24.5 by 1/7

this is basically dividing 24.5 by 7

24.5 / 7 = 3.5

that is your answer

The correct answer regarding the volume of the pyramid has been explained and given below.

The volume of the pyramid shape is given by the product of its base area and its height and then the product is divided by 3.

i.e.V = (1/3)a²h

So, the options which are correct are, (a) XY and ST , (b) VU and TW  and (d) TX and WX.

From the given figure we can clearly see that,

a=XY=YZ=ZU=UV=VW=WX

h=ST

Firstly, the volume of the pyramid can be easily determined by XY and ST.

and also, VU and WX can be used to calculate the area of the base and YZ and TX can be used to calculate height.

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37.

Add all the distances .

3/4 + 1/2 + 2/3 + 3/4 = 8/3 miles

To add fractions you need equal bottom numbers

find the LCM ( Least common multiple of the denominators )

4 , 2 , 3 , 4 = LCM = 12

Multiply each fraction by the same numerator and denominator, to obtain 12 as a bottom number

(3/4 * 3/3) + (1/2 * 6/6) + (2/3 * 4/4) + (3/4 * 3/3)

9/12 + 6/12 + 8/12 + 9/12

Now that all fractions have the same denominator ( bottom number) you can add them.

Add the numerators ( top numbers ) and put 12 as a denominator.

(9 + 6 + 8 + 9 ) / 12 = 32/12

Simplify ( divide both numbers by 4 )

32/12 = 8/3

Answer:

see the photo

Step-by-step explanation:

hope this helps

A parking sign is in the shape of a square. The area in square centimeters, is given by the equation: l^(2)=400 The length, l, of one side of the sign is  20 centimeters.

The equation l^2 = 400 represents the relationship between the length of one side of the square (l) and its area. To find the length of one side, we need to solve for l. In this case, we can take the square root of both sides of the equation to isolate l.

Taking the square root of 400, we get l = √400 = 20.

Therefore, the length of one side of the parking sign is 20 centimeters.

By substituting the value of l back into the equation, we can verify that it satisfies the equation: (20)^2 = 400, which is true.

Hence, the length of one side of the square parking sign is 20 centimeters.

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Answer:

You can form a proportion to solve this problem.

Step-by-step explanation:

The proportion can look like this (there are other ways to write an equal proportion but this is just one of the ways you could go about it :)

\(\frac{2.25}{12}\)=\(\frac{x}{32}\)

12x=72

x=6 cups of flour

Hope this helps!! :)

Answer:

You can form a proportion to solve this problem.

Step-by-step explanation:

The proportion can look like this (there are other ways to write an equal proportion but this is just one of the ways you could go about it :)

=

12x=72

x=6 cups of flour

To solve this problem, we first need to understand that a rhombus is a quadrilateral with all sides equal in length. Also, the diagonals of a rhombus bisect each other at right angles. Let's assume that the angle between one of the sides and a diagonal is x degrees. Then, the angle between the other diagonal and the same side is 180-x degrees. Since the difference between these two angles is given as 32 degrees, we can set up an equation:
(180-x) - x = 32
Solving this equation, we get:
2x = 148
x = 74
Therefore, the angles of the rhombus are 74 degrees and 106 degrees.

A rhombus is a special type of quadrilateral where all sides are equal in length. Also, the diagonals of a rhombus bisect each other at right angles. In this problem, we are given that the difference of the measures of 2 angles between a side and the diagonals is 32 degrees. To solve for the angles of the rhombus, we need to use the fact that the sum of the interior angles of a quadrilateral is 360 degrees. We assume that one of the angles between a side and a diagonal is x degrees, and set up an equation using the difference given in the problem. Solving this equation gives us the value of x, which allows us to find the other angle.

In a rhombus, the angles between a side and the diagonals are equal. If we are given the difference between these angles, we can use an equation to solve for the measures of these angles. In this problem, we found that the angles of the rhombus are 74 degrees and 106 degrees.

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The percentage of students who played video games in the survey is 52%.

To find this percentage, we first need to calculate the fraction of students who played video games. This can be done by dividing the number of students who played video games by the total number of students surveyed:

Fraction of students who played video games = 130/250

Simplifying this fraction by dividing both the numerator and denominator by 10, we get:

Fraction of students who played video games = 13/25

To convert this fraction to a percentage, we can multiply it by 100:

Percentage of students who played video games = (13/25) * 100

Simplifying this expression, we get:

Percentage of students who played video games = 52%

Therefore, 52% of the students in the survey played video games.

Hence, to find the percentage of students who played video games in a survey, we divide the number of students who played video games by the total number of students surveyed and then multiply the resulting fraction by 100 to get the percentage.

In this case, 130 out of 250 students played video games, so the percentage is 52%.

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The height of the office building casting a shadow of 107ft is approximately 124.83 ft.

A ratio is simply the relation between two amounts showing how many times a value is contained within another value.

Given the data in the question;

Ratio of height of office building and its height = x / 107

Ratio of height of post and its height = 7 / 6

Equate the two to get the height of the office building.

x / 107 = 7 / 6

Solve for x

x × 6 = 7 × 107

6x = 749

x = 746 / 6

x = 124.83 ft

Therefore, the height of the building is 124.83 ft.

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Answer: 375

Step-by-step explanation:

Since we are given the information that there are 250 bricks used to build a wall 20 feet high, the number of brick used per feet will be:

= 250/20

= 12.5 bricks per feet.

Therefore, the number of bricks that will be used to buld a wall that is 30 fet high will be:

= 12.5 × 30

= 375 bricks.

Therefore, 375 bricks would be used.

The fraction of the students in Siena's class are girls with brown eyes is 5/12.

Let the fraction of students in Siena's class with brown eyes be a=5/8.

And the fraction of students in Siena's class with brown eyes are girls be b=2/3.

Then, the fraction of students in Siena's class are girls with brown eyes be z=a×b

Therefore, by substituting the fraction values, we get

z=(5/8)×(2/3)

z=5/12.

Hence, 5/8 of the students in Siena's class have brown eyes. 2/3 of the students with brown eyes are girl. Then, the fraction of students in Siena's class are girls with brown eyes is 5/12.

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(a) Confidence interval: The sample size is n = 40, the mean is x¯ = 70 and the standard deviation is s = 3.4. Since the sample size is greater than 30, we can use the normal distribution to find the confidence interval at 99% confidence level.

So, we have z0.005 = 2.576 (two-tailed test)

Now, we can calculate the confidence interval as follows:

Confidence interval = [x¯ - zα/2(σ/√n) , x¯ + zα/2(σ/√n)][70 - 2.576(3.4/√40), 70 + 2.576(3.4/√40)]

Confidence interval = [68.2, 71.8]

Therefore, the 99% confidence interval for the mean height of all men is between 68.2 and 71.8 inches.  

Conclusion: We are 99% confident that the mean height of all men is between 68.2 and 71.8 inches. (b) Hypothesis test: The null hypothesis is that the average height of all men is exactly 6 feet tall, i.e. µ = 72 inches. The alternative hypothesis is that the average height of all men is less than 6 feet tall, i.e. µ < 72 inches. The level of significance is α = 0.10. The sample size is n = 40, the mean is x¯ = 70 and the standard deviation is s = 3.4. Since the population standard deviation is unknown and the sample size is less than 30, we can use the t-distribution to perform the hypothesis test.

So, we have t0.10,39 = -1.310 (left-tailed test)

Now, we can calculate the test statistic as follows:

t = (x¯ - µ) / (s/√n)= (70 - 72) / (3.4/√40)=-3.09

Therefore, the test statistic is t = -3.09.

Since t < t0.10,39,

we can reject the null hypothesis and conclude that the average height of all men is less than 6 feet tall.

Conclusion:

At the 10% significance level, we have found that the data provide evidence to conclude that the average height of all men is less than 6 feet tall. That is, we reject the null hypothesis.

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1. sinh(2x) = 2sinh(x)cosh(x) Using Osborne's rule, replace sin^2(x) with (1-cos^2(x)). Apply the hyperbolic definitions of sin(2x), sin^2(x), and cos^2(x) to obtain the hyperbolic counterpart.

2. sinh(x-y) = sinh(x)cosh(y) - cosh(x)sinh(y) Apply Osborne's rule to the trigonometric identity sin(x-y) = sin(x)cos(y) - cos(x)sin(y), replacing sin(x), cos(x), sin(y), and cos(y) with their hyperbolic counterparts.

3. cosh(2x) = 2cosh^2(x) - 1Substitute cos^2(x) with (1+cos^2(x)) using Osborne's rule. cosh(2x) and cos^2(x) to derive the hyperbolic identity.

4. cosh(x-y) = cosh(x)cosh(y) - sinh(x)sinh(y) Replace cos(x), sin(x), cos(y), and sin(y) in the trigonometric identity cos(x-y) = cos(x)cos(y) + sin(x)sin(y) with their hyperbolic counterparts using Osborne's rule.

5. tanh(2x) = (2tanh(x))/(1 + tanh^2(x))

Use Osborne's rule to replace sin^2(x) and cos^2(x) in the trigonometric identity tan^2(x) = (1 - cos^2(x))/(cos^2(x)). tanh(2x) and tan^2(x) to obtain the hyperbolic counterpart.

6. sinh(3t) = 3sinh(t) - 4sinh^3(t) Apply Osborne's rule to the trigonometric identity sin(3t) = 3sin(t) - 4sin^3(t), replacing sin(t) with sinh(t) to derive the hyperbolic counterpart.

7. 2sinh(x)cosh(x) = sinh(2x)Use the hyperbolic definitions of sinh(2x), sinh(x), and cosh(x) to calculate both sides.

8. cosh(x)cosh(y) + sinh(x)sinh(y) = cosh(x+y)Substitute the hyperbolic definitions of cosh(x), cosh(y), sinh(x), and sinh(y) into the left side. Simplify the expression to cosh(x+y) to establish the equality.

9. tanh(ln(3)) = 1/8 Replace the natural logarithm with its corresponding hyperbolic function. Evaluate tanh(ln(3)) using the hyperbolic tangent of the logarithm of 3, resulting in 1/8.

10. 4cosh^3(t) = cosh(3t) + 3cosh(t)

11. d/dx(coth(x)) = -cosech^2(x)

Take the derivative of coth(x) using the derivative of its hyperbolic counterpart. Simplify the expression to -cosech^2(x) to establish the equality.

12. d/dx(sech(x)) = -sech(x)

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We have counted all the edges in the graph and there are no additional edges, which justifies our answer of 195 edges.

Now, First, let's consider the number of edges in the complete graph formed by the first 16 vertices.

A complete graph of size n has n(n-1)/2 edges.

Therefore, the complete graph formed by the first 16 vertices has,

= (16 x 15)/2

= 120 edges.

Now, let's add the remaining vertices to this graph.

Each of the remaining 5 vertices in V17 - V21 is connected to each vertex in the first 16 vertices, except for the vertices in its own clique.

Therefore, each of the remaining vertices contributes 16-1 = 15 edges to the graph.

This gives us a total of 5×15 = 75 edges.

Therefore, the total number of edges in G is,

120 + 75 = 195.

To justify this answer, we need to show that there are no other edges in G besides the ones we have counted.

Since the graph is formed only by the two cliques and the edges between the cliques, we only need to check if there are any additional edges that connect vertices within the same clique.

However, we know that the first 16 vertices form a complete graph, which means that there are no additional edges that can be added between them.

Similarly, the last 11 vertices form a complete graph, which means that there are no additional edges that can be added between them.

Therefore, we have counted all the edges in the graph and there are no additional edges, which justifies our answer of 195 edges.

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Answer:

(b) reduce the variability of the poll result.

Step-by-step explanation:

when the sample size of an opinion poll is increased, more data will be gathered about the population, and when there is enough data present, The estimates that is made afterward base on the gathered data will be more accurate compare with when there is small sample size. It should be noted that when the sample size of an opinion poll is increased, it will reduce the variability of the poll result.

The angles are x is 35° and y is 17° when the angles on protractor ∠QUT=74°, ∠RUS=22° and ∠QUS=57°.

Given that,

The angles are given ∠QUT=74°, ∠RUS=22° and ∠QUS=57°.

We have to find the angles.

An angle is formed when two straight lines or rays meet at a single terminal. The vertex of an angle is the point at which two points converge. ​The name "angle" comes from the Latin word "angulus," which meaning "corner." ​

The ∠QUS = ∠QUR + ∠RUS

57°=x+22°

x=57°-22°

x=35°

Now, ∠QUT = ∠QUR + ∠RUS + ∠SUT

74°=35°+22°+y
y=74-35-22

y=17°

Therefore, The angles are x is 35° and y is 17° when the angles are given ∠QUT=74°, ∠RUS=22° and ∠QUS=57°.

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