Simplify each and state the excluded values.
8x^3/12x^2+16

Understanding a set’s nature or properties is made easier by its closure property

The set is closed if it has the closure property. This means that any operation performed on an element within a set will provide a result that belongs to that element’s set.

Why Closure Property is important?

Understanding a set’s nature or properties is made easier by its closure property. Mathematical applications of closure are numerous. Any operation that adheres to this condition is said to be “closed” or to have “fulfilled the operation’s closure property.”

Example – The set of even number is closed under subtraction

                   Even – Even = Even

                   6 – 4 = 2

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Answer:

b

Step-by-step explanation:

3 1/2 x 3 x 1/2= 5.25 or 5 and 1/4

Answer:

B

Step-by-step explanation:

Little tip, if you don't know a question or aren't sure, pick options b or c, they are statistically the most used options.

The amount of loam Required to fill the building is  200 yd³

An equation is an expression that shows the relationship between two or more numbers and variables.

Volume is the amount of space occupied by a three dimensional shape or object.

Volume of a prism = Length * Width * Height

The plot was 1080 feet by 20 feet, to be filled to a depth of 3 inches with loam.

3 inches = 0.25 ft.

Hence:

Required loam to fill the building = 1080 ft. * 20 ft. * 0.25 ft. = 5400 ft³

The Required loam to fill the building is 5400 ft³

5400 ft³ = 200 yd³

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First, let's define some terms.

- Vectors are quantities that have both magnitude and direction. In this case, we're working with vectors in R2, which means they have two components (x and y).
- A linear combination is a way of combining vectors using multiplication and addition. For example, if we have two vectors v1 = [1, 2] and v2 = [3, 4], then a linear combination of these vectors could be 2v1 + 3v2 = 2[1, 2] + 3[3, 4] = [8, 14].
- Coefficients are the numbers we multiply the vectors by in a linear combination.

Now, let's move on to your question.

You have four vectors in R2, but they do not form a basis. This means that they are linearly dependent, which implies that at least one of the vectors can be expressed as a linear combination of the others.

You are given one vector v = [-20, 4, 13, 68], and you are asked to find two different ways to express it as a linear combination of the other vectors v1, v2, v3.

To do this, we can use a method called Gaussian elimination. We can write the vectors as rows in a matrix, and then use row operations to simplify the matrix and find the coefficients we need.

Here's the matrix we get:

| v1 | v2 | v3 | v |
|----|----|----|---|
|    |    |    |   |
|    |    |    |   |
|    |    |    |   |
|    |    |    |   |

We can start by subtracting multiples of v1 from the other vectors to get zeros in the first column:

| v1 | v2 | v3 | v |
|----|----|----|---|
| 1  | 0  | -2 |  1|
| 0  | 1  |  3 | -4|
| 0  | 0  |  0 |  0|
| 0  | 0  |  0 |  0|

Now we can see that v3 is a linear combination of v1 and v2:

v3 = -2v1 + 3v2

We can use this to express v in terms of v1, v2, and v3:

v = -v1 - 4v2 + 68/13 v3

This is one way to express v as a linear combination of v1, v2, v3.

To find another way, we can swap the positions of v2 and v3 in the matrix and repeat the process.

| v1 | v3 | v2 | v |
|----|----|----|---|
| 1  | -2 | 0  |  1|
| 0  |  0 | 1  |  3|
| 0  |  0 | 0  |  0|
| 0  |  0 | 0  |  0|

Now we can see that v2 is a linear combination of v1 and v3:

v2 = 2v1 - 3v3

We can use this to express v in terms of v1, v2, and v3:

v = -v1 + 68/13 v2 + 4/13 v3

This is another way to express v as a linear combination of v1, v2, v3.

Finally, you are asked to express v as a linear combination of v1, v2, v3 when the coefficient of v1 is 0 and the coefficient of v3 is 1.

To do this, we can set up the following system of equations:

- a v1 + b v2 + c v3 = v
- a = 0
- c = 1

Substituting a = 0 and c = 1, we get:

b v2 + v3 = v

We already know that v3 = -2v1 + 3v2, so we can substitute that in:

b v2 - 2v1 + 3v2 = [-20, 4, 13, 68]

Simplifying, we get:

-2v1 + (b+3)v2 = [-20, 4, 13-68b, 68]

Now we can use Gaussian elimination to solve for b:

| v1 | v2 | v3 | v |
|----|----|----|---|
| -2 | b+3|  0 | -20|
|  0 |  0 |  1 |  3|
|  0 |  0 |  0 |  0|
|  0 |  0 |  0 |  0|

From the first row, we can see that b = -1.

Substituting that back into our equation, we get:

v = 2v1 - v2 + 68/13 v3

This is the desired expression of v as a linear combination of v1, v2, v3 with the coefficient of v1 being 0.

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For a pattern of dimensions of a quilting square, the blue fabric part that is parallelogram will she need to make one square is equals to the 48 inch².

We have a pattern present in attached figure. It shows the dimensions of a quilting square. We have to determine the length of fabric needed make a complete square. From the figure, there is formed different shapes with different colours, Side of square, a = 12 in.

length of blue parallelogram part of square = 8 in.

So, base length red triangle in square = 12 in. - 8 in. = 4 in.

Height of red triangle, h = 6in.

Same dimensions for other red triangle.

Length of pink parallelogram = 3 in.

Area of square = side²

= 12² = 144 in.²

Now, In case of blue parallelogram, the ares of blue parallelogram, \(A = base × height \)

so, Area of blue fabric parallelogram= 8 × 6 in.² = 48 in.²

Hence, required value is 48 in.²

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Complete question:

The above figure complete the question.

The pattern shows the dimensions of a quilting square that need to will use to make a quilt How much blue fabric will she need to make one square

The possible solution set for the system is (- 1, 4) and (4, - 1).

Given are the equations as -

x + y = 3

x² + y² = 17

Refer to the graph of the function attached. The points of intersection represents the possible solution set.

Therefore, the possible solution set for the system is (- 1, 4) and (4, - 1).

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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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The projection of the region D, enclosed by the paraboloids z = 3x² + y²/2 and z = 16 - x² - y²/2, onto the xy-plane, is given by the equation x²/4 + y²/16 = 1.

The region D is defined by the two paraboloids in three-dimensional space. To find the projection of D onto the xy-plane, we need to eliminate the z-coordinate and obtain an equation that represents the boundary of the projected region.

By setting both z equations equal to each other, we have:

3x² + y²/2 = 16 - x² - y²/2

Combining like terms, we get:

4x² + y² = 32

To obtain the equation of the boundary in terms of x and y, we divide both sides of the equation by 32:

x²/8 + y²/32 = 1

This equation represents an ellipse in the xy-plane. However, it is not the same as the equation given in option B. Therefore, the correct answer is Option A: None of these. The projection of D on the xy-plane does not satisfy the equation x²/4 + y²/16 = 1.

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The given statement is False, because the description only applies to one solution. The solution set contains all conceivable solutions.

A linear number pattern is a succession of numbers with the same difference between each term. As an example, consider the numbers 1, 3, 5, 7, 9,... Every phrase differs by a factor of two. These are also known as linear numbers. Another example would be 7, 17, 27, 37,...

A formula can be found for linear sequences, that is, sequences in which the difference between succeeding terms is always the same. would have resulted in the formula un = 3n + 35. produces the formula un = 3n - 10, where c is either positive or negative.

To obtain the remaining phrases, you simply keep using the addition of 1 method.

Here are a few further illustrations of linear number patterns:

Beginning with three points and a two-point difference:

3, 5, 7, 9, … Starting with five and a three-point difference:

5, 8, 11, 14, …

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Answer:

Step-by-step explanation:

3min30sec:2min30sec

trasform in seconds

210sec : 150sec

semplify

7 : 5

Answer:

RSP, ZXY

SRP, XZY

RPS, ZYX

Step-by-step explanation:

Obviously, the numbers match each other.

ex. R = 41, Z = 41

Those two have the ability to pair in the same order

Answer:

y=2/3x-6

Step-by-step explanation:

Slope is 2/3

y-intercept is -6

Answer:

9.5 gallons

Step-by-step explanation:

12.7 x .75

multiplying by .75 is the easiest way to get 3/4 of something

The equation showing the relation between shorter and longer skirt is 3s+4t = 140.

Given that the Scottish dance team used 140 yards of tartan to make dancing skirts.

The skirt pattern for the shorter members is 3- yards of fabric, and the skirt pattern for the taller members is 4 yards of fabric.

So, we need to find the equation represents the relationship between the number of short skirts and the number of long skirts that were made,

So, if there are s short skirts and t long skirts,

So,

The relation will be =

3s + 4t = 140

Hence the equation showing the relation between shorter and longer skirt is 3s+4t = 140.

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The sales boy has a sale of $142.9.

Given that the commission given to a sales boy is 5%, he earns $150, we need to find the sale he did for the month,

So,

Let the sale be x,

Therefore,

x + 5% of x = 150

x of 105% = 150

x × 1.05 = 150

x = 142.9

Hence the sales boy has a sale of $142.9.

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Answer:

c = -7

Step-by-step explanation:

c + 10 = 3

subtract 10 on both sides of the equal sign

c = -7

Answer:

B) Inside the nucleus of an atom are protons and electrons.

Explanation:

Inside the nucleus of an atom are protons and neutrons. Electrons orbit (kind of?) away from the nucleus.

Answer: 1/6

Step-by-step explanation: I think you multiply 3 times 3 because the other circle circle has an option the first doesn't have have.

Answer:

5,6,8,12,20,36,68

The number of cars that pass through the intersection between 6 am and 9 am is 10,500 cars.

To find the number of cars passing through the intersection between 6 am and 9 am, we need to integrate the given traffic flow rate function r(t) from t=0 (6 am) to t=3 (9 am). Therefore, we have:

∫(r(t) dt) = ∫(400 + 900t - 150t² dt) [Limits: 0 to 3]

= [400t + 450t² - 50t³/3] from 0 to 3

= [400(3) + 450(3)² - 50(3)³/3] - [400(0) + 450(0)² - 50(0)³/3]

= 1200 + 4050 - 450

= 10,500 cars

Therefore, 10,500 cars pass through the intersection between 6 am and 9 am.

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We will have the following:

So, it takes 15 minutes for the new computer; then the old computer will take 60 min.

The mean is 6

The variance is 4/3

The standard deviation is approximately 1.15.

How we Calculate the mean?
The mean (μ) of a uniformly distributed random variable is the average of the endpoints of the interval. So, in this case:
μ = (4 + 8) / 2 = 12 / 2 = 6

How we Calculate the variance?
The variance (σ²) of a uniformly distributed random variable is given by the formula:
σ² = (b - a)² / 12
where a and b are the endpoints of the interval. In this case:
σ² = (8 - 4)² / 12 = 4² / 12 = 16 / 12 = 4 / 3

How we Calculate the standard deviation?
The standard deviation (σ) is the square root of the variance. So, in this case:
σ = √(4 / 3) ≈ 1.15

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\(x^{2}\)Answer:

(Explanation)

Step-by-step explanation:

Part A:

The graph of y = \(x^{2}\) + 2 will be translated 2 units up from the graph of y = \(x^{2}\).

If you plug in 0 for x, you get a y-value of 2. The 2 is also not included with the \(x^{2}\), which is why it doesn't translate left.

This is what graph A should look like:

[Attached File]

Part B:

The graph of y = \(x^{2}\) - 2 will be translated 2 units down from the graph of y = \(x^{2}\).

If you plug in 0 for x, you get a y-value of -2. The 2 is also not included with the \(x^{2}\), which is why it doesn't translate right.

This is what graph B should look like:

[Attached File]

Part C:

The graph of y = 2\(x^{2}\) is a stretched version of the graph y = \(x^{2}\). Numbers that are greater than 1 stretch and open up and numbers less than -1 stretch and open down.

This is what graph C should look like:

[Attached File]

Part D:

The graph of y = \(\frac{1}{2}x^{2}\) is a compressed version of the graph y = \(x^{2}\). Numbers that are in-between 0 and 1, and -1 and 0 are compressed.

This is what graph D should look like:

[Attached File]

The null hypothesis is accepted since the chi-square at the supplied critical value level value is greater than 13.388 (27.385).

In five to six key stages, the hypothesis test announces the conclusion of an assumption.

The approach to be utilized is predicated on the notion of correlating a parameter's standardized sample equivalent to the crucial boundary that permits the null hypothesis to be accepted.

For this particular question,

The value of the chi-square is 27. 385.

The crucial number is 13.388.

The following are the hypotheses for the goodness of fit test : If an expected value and the observed values are identical, the value is considered null. Alternative: The expected value and the observed values differ substantially. One tail exists in the chi-square test.

The standard is as follows:

If the test statistic is higher than the threshold value, the null hypothesis is rejected. The same null hypothesis is rejected if the test statistic is below the crucial value. Because the chi-square is greater than 13.388 and the critical value is provided, the null hypothesis is therefore accepted at that level.

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Answer:

X=8

Step-by-step explanation:

EASY MATH

Answer:

The pipe thread size is measured and based on the inside of the pipe. But, to actually determine the size of a pipe, the outside diameter of each pipe or fitting must be measured and compared to the table for size identification.

Step-by-step explanation:

Step-by-step explanation:

Answer:

Step-by-step explanation: