3x3(2+3)x4 I need this asap

Partial fractions refer to a method of evaluating complex fractions by breaking them down into simpler fractions that can be easily integrated. A partial fraction is the sum of a constant numerator divided by a linear denominator in the form

\(\frac{A}{x-k} + \frac{B}{(x-k)^2} + \frac{C}{(x-k)^3} +...\), where k is the root of the denominator of the fraction and A, B, and C are constants.

A partial fraction can be expressed in the following way:

Partial Fraction =\(A\frac{1}{x} + A\frac{2}{x-2} + A\frac{3}{(x-2)^2 }+ A\frac{4}{(x-2)^3} + B\frac{1}{(x^2 + 4)} + B\frac{2x}{(x^2 + 4)} +\)∫\((-2x^2+8x+8) (x^2+4)(x-2)^3dx\)

= ∫\((A\frac{1}{x} + A\frac{2}{x-2} + A\frac{3}{(x-2)^2} + A\frac{4}{(x-2)^3} + B1\frac{1}{(x)^2+4} + B2\frac{x}{(x)^2+4}) dx\)

Let us assume that the given integral can be expressed as the sum of the six partial fractions mentioned above.

Therefore,

∫ \((-2x^2+8x+8) (x^2+4)(x-2)^3dx\)

\((A\)∫\(\frac{1}{x}+\)\(A\)∫\(\frac{2}{x-2}+\)\(A\)∫\(\frac{3}{(x-2)^2}+\)\(A\)∫\(\frac{4}{(x-2)^3}+\)\(B1\)∫\(\frac{1}{(x)^2+4}+\)\(B2\)∫\(\frac{x}{(x)^2+4}) dx\)

Each integral can be calculated separately using the integral formulas, with the exception of \(B2\) ∫ \(\frac{x}{x^2+4}dx\). This integral may be evaluated by substitution.

The following are the steps:

\(u = x^2 + 4\)

\(\frac{du}{dx} = 2x\)

\(dx= \frac{du}{2x}\)

Substituting this into the integral, we get:

∫\(\frac{x}{x^2+4} dx\) = ∫ \((\frac{1}{2} ) * (\frac{1}{u} )du\)

Now we will substitute the value of u and solve the integral.

∫\((\frac{1}{2} ) * (\frac{1}{u} )du=\frac{1}{2}ln|x^2 + 4|\)

Therefore, the integral will be:

∫ \((-2x^2+8x+8) (x^2+4)(x-2)^3dx\)

\(= A1 ln|x| + A2 ln|x-2| + A3 (\frac{1}{x-2} ) + A4 (\frac{1}{2}) * (\frac{1}{2}) * (\frac{1}{(x-2)^2}) + B1 (\frac{1}{2}) * tan^-1(\frac{x}{2} ) + B2 (\frac{1}{2}) * ln|x^2 + 4|\)

Therefore, this is how we can express the integrand as a sum of partial fractions and evaluate the integral.

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In the context of measurement, accuracy and precision refer to two related but distinct concepts. Accuracy is the degree to which a measurement is close to the true value of what is being measured, while precision is the degree to which repeated measurements of the same quantity are close to each other.

The uncertainty of a measurement refers to the degree of doubt or lack of confidence in the result obtained from a measuring instrument. It is typically represented by an interval around the measured value that indicates the range within which the true value is likely to lie.

The accuracy of a measuring device is related to its ability to provide measurements that are close to the true value. If a measuring device is highly accurate, then its measurements will be close to the true value, and the uncertainty associated with those measurements will be relatively small. On the other hand, if a measuring device is not very accurate, then its measurements may be far from the true value, and the uncertainty associated with those measurements will be relatively large.

The precision of a measuring device is related to its ability to provide measurements that are close to each other when measuring the same quantity repeatedly. A measuring device that is highly precise will give measurements that are very close to each other, and the uncertainty associated with those measurements will be relatively small. Conversely, a measuring device that is not very precise will give measurements that are far apart, and the uncertainty associated with those measurements will be relatively large.

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Answer and Step-by-step explanation:

The measure of angle D is 64.

This is true by the vertical angles theorem, which states that angles that are vertical to each other, they are equal.

#teamtrees #WAP (Water And Plant)

The output of the following code snippet will be 1, 2, 3, and 4.

The reason is that the while loop runs infinitely until the break statement is executed. The break statement terminates the loop if the value of x is divisible by 5. However, the value of x is incremented at each iteration of the loop before checking the condition. Here is the step-by-step explanation of how this code works:

Step 1: Assign 1 to x.x = 1

Step 2: Start an infinite loop using the while True statement.

Step 3: Check if the value of x is divisible by 5 using the if x % 5 == 0 statement.

Step 4: If the value of x is divisible by 5, terminate the loop using the break statement.

Step 5: Print the value of x to the console using the print(x) statement.

Step 6: Increment the value of x by 1 using the x += 1 statement.

Step 7: Repeat steps 3-6 until the break statement is executed.

Therefore, the output of the code will be: 1 2 3 4.

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The numerical length of GH would be 4 and the obtained value of x = 2.

A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.

The figure given below shows a line segment GI, where the length of line segment GI refers to the distance between its endpoints, G and I.

Given that Point H is on line segment

GH = 5x - 6, HI = 2, and  GI = 3x

G______________H______________I

⇒ GI = GH + HI

Substitute the values of GH = 5x-6 and  GI = 3x,

⇒ 3x = 5x - 6 + 2

⇒ 5x - 3x =  6 - 2

⇒ 2x = 4

⇒ x = 4/2

⇒ x = 2

Substitute the value of x = 2 in GH = 5x-6.

So GH = 5(2) - 6 ⇒ GH = 4.

Therefore, the numerical length of GH is 4.

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Answer:

the anwser is 180

Step-by-step explanation:

Home prices are probably skewed to the right and not symmetric. So the correct option would be A.

This makes the median a better representation of the center than the mean which would be influenced by the extremely high-priced homes.

Reporting the mean would give the impression that the​ "typical" home price is higher than it is.

they substitute the median for the mean. The median is unaffected by severe outliers or asymmetric score distributions because it only takes one or two values. In contrast, skewed distributions might have different mean and mode values.

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Answer:

Exact Form:

1215 / 2

Decimal Form:

607.5

Mixed Number Form:

607  1/2

Answer:

16 million

Step-by-step explanation:

see the explanation attached above

Answer:

0.1 and 0.11...

Ok, to compare them as a fractions we can write:

0.1 we multiply the numerator and denominator by the same number, 10^n where n depends on the number of digits after the decimal point, in this case only one, so n = 1.

0.1 = 0.1*(10/10) = 1/10.

now, for 0.1...

First, we only multiply by 10^n same as before, in this case n = 1.

0.11...*10 = 1.11...

Now, we can subtract the initial number:

1.11... - 0.111... = 1

So we have that:

0.11...*(10 - 1) = 0.11...*9 = 1

0.11... = 1/9

So the 0.1 is written as 1/10

and 0.1 repeating is written as 1/9.

So the denominator is one unt smaller in the case of the repeating decimals.

now, with 0.13 and 0.13...

Same as before, but in this case we have two digits after the decimal point, so we use n = 2 and 10^2 = 100.

0.13 = 0.13*(100/100) = 13/100.

and

0.13...*100 = 13.13....

we subtract the initial number:

13.13... - 0.13... = 13

Then:

0.13...*(100 - 1) = 13

0.13...*99 = 13

0.13... = 13/99

So again, the difference between 0.13 and 0.13... is that in the fraction notation, the repeating one has a denominator that is one unit smaller.

And finally, for:

0.157 and 0.157...

We do the same as before, but here we have 3 digits after the decimal point, so n = 3.

10^3 = 1000.

then:

0.157 = 0.157*1000/1000 = 157/1000.

And for:

0.157...*1000 = 157.157...

we subtract the initial number.

157.157... - 0.157... = 157

then:

0.157...*(1000 - 1) = 157

0.157... = 157/999

And again, in the case of the repeating decimals the denominator is one unit smaller than in the other case.

The general solution of the differential equation y''(x) + y(x) = sec(x) tan(x) is y(x) = c₁cos(x) + c₂sin(x) + (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x); here c₁ and c₂ are constants.

To solve the differential equation y''(x) + y(x) = sec(x) tan(x) using variation of parameters, we first need to find the solutions to the homogeneous equation y''(x) + y(x) = 0.

The auxiliary equation for the homogeneous equation is r² + 1 = 0, which has complex roots r = ±i.

The corresponding solutions to the homogeneous equation are y₁(x) = cos(x) and y₂(x) = sin(x).

Next, we need to find the particular solution using the method of variation of parameters. Let's assume the particular solution has the form y_p(x) = u(x)cos(x) + v(x)sin(x).

Now, we need to find u(x) and v(x) by substituting this form into the original differential equation and solving for u'(x) and v'(x).

Differentiating y_p(x), we get y_p'(x) = u'(x)cos(x) - u(x)sin(x) + v'(x)sin(x) + v(x)cos(x).

Taking the second derivative, y_p''(x) = -u(x)cos(x) - u'(x)sin(x) + v(x)sin(x) + v'(x)cos(x).

Substituting these derivatives into the original differential equation, we have:

(-u(x)cos(x) - u'(x)sin(x) + v(x)sin(x) + v'(x)cos(x)) + (u(x)cos(x) + v(x)sin(x)) = sec(x)tan(x).

Simplifying, we get:

u'(x)sin(x) + v'(x)cos(x) = sec(x)tan(x).

To find u'(x) and v'(x), we solve the following system of equations:

u'(x)sin(x) + v'(x)cos(x) = sec(x)tan(x),

u(x)cos(x) + v(x)sin(x) = 0.

We can solve this system using various methods such as substitution or elimination.

Solving the system, we find:

u'(x) = sin(x)sec(x),

v'(x) = -cos(x)sec(x).

Integrating these expressions, we obtain:

u(x) = -ln|sec(x) + tan(x)| + C₁,

v(x) = -ln|sec(x) + tan(x)| + C₂.

Finally, the particular solution is given by:

y_p(x) = (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x).

The general solution to the differential equation is the sum of the homogeneous and particular solutions:

y(x) = c₁cos(x) + c₂sin(x) + (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x).

Here, c₁ and c₂ are constants.

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The probability that he makes the first and second free throw, but misses the third free throw is 7.7 %.

Given :

suppose steph curry is fouled while shooting a three-point goal and misses his shot. the probability of steph curry making a free throw is 90%.

probability :

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

P ( makes 2 then misses 1 ) = P ( make 1st ) and P ( make 2nd ) and P ( miss 3rd )

= 0.906 *0.906 * 0.094

= 0.077

= 7.7 %

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The statement "the standard deviation is equal to the square of the variance" is False.

In statistics, both the standard deviation and the variance are measures of variability or dispersion within a dataset.

However, they are distinct measures and not equal to each other.

The variance (σ²) is the average of the squared deviations from the mean.

It is calculated by summing the squared differences between each data point and the mean, and then dividing by the total number of data points. The variance is expressed in squared units of the original data.

On the other hand, the standard deviation (σ) is the square root of the variance.

It represents the average amount of deviation or dispersion of data points from the mean.

By taking the square root of the variance, the standard deviation is expressed in the same units as the original data, making it more interpretable and easier to compare across different datasets.

In summary, the standard deviation is not equal to the square of the variance. Rather, it is the square root of the variance.

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There 6 number of bags and each bag will have 4 marbles in it.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

4 x 6 = 24

If 24 represents total bof marbles.

So, we can assume that there 6 number of bags and each bag will have 4 marbles in it.

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Answer: A. 4/3 x

Step-by-step explanation:

x miles in 90 minutes to ? miles in 120 minutes

90 miles to 120 miles is 1.3333 which is equal to 4/3.

Multiply it to x and you have A. 4/3x

The required expression would be 18 + 56/(15/3) - 64 which represents subtracting 64 from the sum of 18 and 56 divided by the quotient of 15 and 3.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

To determine the expression which represents subtract 64 from the sum of 18 and 56 divided by the quotient of 15 and 3.

As per the given condition, we can write the word problem as an expression like this:

⇒ 18 + 56/(15/3) - 64

Hence, the required expression would be 18 + 56/(15/3) - 64.

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Answer:

18.3

Step-by-step explanation:

Answer:

69

Step-by-step explanation:

let the first term be n

second term = 2 + n

third term = 3 + second term so we can conclude that the other term will be:

forth term = 4 + third term

fifth term = 5 + forth term etc.

eleventh term will be 11 + 10 term

based on observations the tenth term is 58 so

eleventh term= 11 + 58

= 69

Answer:

The chances are 36.8% that a random student has an A

Step-by-step explanation:

There are 19 total students and 7 of them have an A. Divide 7 by 19 and convert the decimal value into a percentage.

Since quadrilateral PQRS was transformed using the rule (x, y) → (x + 4, y),a graph that shows this transformation is: D. graph D.

In Mathematics, the translation of a graph to the left is a type of transformation that simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph to the right is a type of transformation that simply means adding a digit to the value on the x-coordinate of the pre-image.

By translating the pre-image of quadrilateral PQRS horizontally right by 4 units, the coordinates of quadrilateral PQRS include the following:

(x, y)                               →                  (x + 4, y)

P (-4, 5)                        →                  (-4 + 4, 5) = P' (0, 5).

Q (-3, 3)                        →                  (-3 + 4, 3) = Q' (1, 3).

R (-4, 1)                        →                  (-4 + 4, 1) = R' (0, 1).

S (-5, 3)                        →                  (-5 + 4, 3) = S' (-1, 3).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Quadrilateral PQRS is transformed using the rule (x, y) → (x + 4, y). Which graph shows this transformation?

Answer:

12 miles

Step-by-step explanation:

2.25+3.50x=44.25

3.50x=42

x=12

The equation relating x, y, and z is:

z = 0.5 * x * y.

In the given problem, the relationship between x, y, and z can be expressed by the equation z = k * x * y, where k represents the constant of proportionality. By substituting the values of x = 4 and y = 5, when z is equal to 10, we can determine the value of the constant of proportionality, k, and further define the relationship between the variables.

To find the constant of proportionality, we substitute the known values of x = 4, y = 5, and z = 10 into the equation z = k * x * y. This gives us the equation 10 = k * 4 * 5. By simplifying the equation, we have 10 = 20k. To isolate k, we divide both sides of the equation by 20, resulting in k = 0.5. Therefore, the equation relating x, y, and z is z = 0.5 * x * y, meaning that z is directly proportional to the product of x and y with a constant of proportionality equal to 0.5.

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Answer:

360

Step-by-step explanation:

Answer:

360

Step-by-step explanation:

120% of 300

Answer: She bowled 4 games

Step-by-step explanation:

21 - 3 = 18
18 ÷ 4.50 = 4

Answer:

Shakira bowled 4 games.

Step-by-step explanation:

If Shakira paid $3 for rent, we can subtract 3 from 21.

21-3=18.

Now, find out how much 4.50 can go into 18.

First, multiply 4.50 by 2.

4.50x2=9

Now, Since 2 games is $9, multiply 9 by 2.

9x2=18

Now that we found out that 9x2=18, we can see that Shakira bowled 4 games.

Hope this helps! :D

The cost of the apples is 2.9 dollars.

The cost of the bananas is 5.7 dollars.

The total cost is 6 dollars, each apple cost $1.50 each banana cost $.30 and there’s two more bananas then apples.

Therefore,

let

x = number of apples

y = 2x

where

Therefore, using equations,

1.5(x) + y(0.30) = 6

Hence,

where

y = 2x

1.5(x) + 2x(0.30) = 6

1.5x + 0.6x = 6

2.1x = 6

divide both sides by 2.1

x = 6 / 2.1

x = 2.9 dollars

y = 2(2.9) = 5.7 dollars

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(a) If f(x) is a convex function with x ∈ ℝⁿ, then all local minima of f(x) are also global minima. In other words, if there exists a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo, then f(x) ≥ f(xo) for all x ∈ ℝⁿ.

(b) A graph of a non-convex function can be visualized to understand why the statement in part (a) is not true. It will show a scenario where a local minimum is not a global minimum.

(a) To prove that all local minima of a convex function are also global minima, we can utilize the property of convexity. Suppose there is a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo. We assume that xo is a local minimum. Now, consider any arbitrary point x in ℝⁿ. We can express x as a convex combination of xo and another point y in the neighborhood, using the convexity property: x = λxo + (1 - λ)y, where λ is a scalar between 0 and 1. Using this expression, we can apply the convexity property of f(x) to get f(x) ≤ λf(xo) + (1 - λ)f(y). Since f(x) ≥ f(xo) for all x in the neighborhood, we have f(y) ≥ f(xo). Therefore, f(x) ≤ λf(xo) + (1 - λ)f(y) ≤ λf(xo) + (1 - λ)f(xo) = f(xo). This inequality holds for all λ between 0 and 1, implying that f(x) ≥ f(xo) for all x ∈ ℝⁿ, making xo a global minimum.

(b) A graph of a non-convex function can demonstrate a scenario where the statement in part (a) is not true. In such a graph, there may exist multiple local minima, but one or more of these local minima are not global minima. The non-convex nature of the function allows for the presence of multiple valleys and peaks, where one of the valleys may contain a local minimum that is not the overall lowest point on the graph. This occurs because the function may have other regions where the values are lower than the local minimum in consideration. By visually observing the graph, it becomes apparent that there are points outside the neighbourhood of the local minimum that have lower function values, violating the condition for a global minimum.

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The best sample frame when studying the nature of product defects generated by two types of stamping machines is a D) list of all stamping machines in the factory, divided into two groups by type of machine.

When studying the nature of product defects generated by two types of stamping machines, the best sample frame is the list of all stamping machines in the factory divided into two groups by the type of machine. A sample frame refers to a list of items or individuals from which a sample is drawn.

The sample frame is an important element of a research study as it forms the basis for choosing the sample. It should be inclusive, accurate, and up-to-date. It is also critical to define the sampling unit and the population so that the correct sample frame can be selected.

The list of all machines in your factory would not be an appropriate sample frame because not all machines would be involved in the production of the stamped products.

A list of all serial numbers of stamping machine output during one month would not be suitable as the sample frame as it would be biased towards a specific time period and may not represent the entire population of the stamping machines in the factory.

None of the options listed above provide the best sample frame.

Therefore, the best sample frame when studying the nature of product defects generated by two types of stamping machines is a list of all stamping machines in the factory divided into two groups by the type of machine.

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Barbara has 10 shirts with long sleeves

100% of Barbara's shirts is 25

Given: 60% of Barbara's shirts are short sleeves.

That means, 1.0 - 0.6 = 0.4 --> 40% of Barbara's shirts are long sleeves.

We need to find: 40% of 25

0.4 * 25 = 10

10 long sleeved shirts