Rewrite the expression in the form 3^n

The indefinite integral of x^4 * ln(1 + x) with respect to x can be expressed as a power series: f(x) = C + ∑(n=1 to ∞) [a_n * x^n]

To find the coefficients a_n, we can differentiate both sides of the power series representation. Using the power rule and the fact that the derivative of ln(1 + x) is 1 / (1 + x), we obtain:

f'(x) = ∑(n=1 to ∞) [n * a_n * x^(n-1)] = ∑(n=0 to ∞) [(n+1) * a_(n+1) * x^n]

Next, we equate the coefficients of the power series representations of f(x) and f'(x):

x^4 * ln(1 + x) = ∑(n=0 to ∞) [(n+1) * a_(n+1) * x^n]

Comparing the coefficients of corresponding powers of x, we can find a_n. By equating the coefficients of x^4 on both sides, we find a_5 = 1 / 5.

To determine the radius of convergence R, we use the ratio test. The ratio test states that if the limit of |a_(n+1) / a_n| as n approaches infinity is L, then the radius of convergence is R = 1 / L.

In this case, as n approaches infinity, the limit of |a_(n+1) / a_n| is 1. Therefore, the radius of convergence R is 1 / 1, which simplifies to R = 1.

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Answer: cos ( 390 ) − 4 cot ( − 45 ) sin (330 )

Step-by-step explanation: MAKE ME BRANLIEST!!!!!!

According to the conversation we can infer that the information focused on the conversation of two people; one of them is studing for an exam.

To identify what is the conversation about we have to consider who is talking and what are the ideas that they share. In this case, we can infer that the main idea of this conversation is that one of them is studying for an exam this week.

Also, the second person is apologizing because he considered that he is distracting the other person. So, the correc information about de conversation is a short conversation about study.

Note: This question is incomplete. Here is the complete information:

Conversation:
Hello

Hello, How are you?

I am fine, and you?

i am fine too, What are you doing?

I am studing for an exam this week.

Oh, sorry I won´t distract you.

Don´t worry.

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Answer:

Step-by-step explanation:

2x+4y=48

5x+2y=64

Adult ticket: $10    Child ticket: $7

For 2 adults and 3 children with the given price per ticket, the family having brought $40 as a budget, their budget would not be high enough as the total would come to be $41. They'd be a dollar short.

Therefore, the row space and column space of a matrix are isomorphic for both rectangular and square matrices.

(a) The row space of a matrix is isomorphic to the column space of its transpose.

(b) The row space of a matrix is isomorphic to its column space.

(a) The row space of a matrix is isomorphic to the column space of its transpose.

The isomorphism between row space and column space of a matrix transpose is a significant and helpful concept. The row space of a matrix A is the subspace that is spanned by the rows of A. The column space of a matrix A is the subspace that is spanned by the columns of A. The row space of A is equivalent to the column space of A transpose. The statement is denoted mathematically as row(A) ≅ col(A^T).

(b) The row space of a matrix is isomorphic to its column space.

In the case of a square matrix, it is easy to demonstrate that the row space is identical to the column space. Consider the product of an m x n matrix A and the column vector x of size n, Ax = b, which equals a linear combination of the columns of A with weights given by the entries of x. The solution b lies in the column space of A. Similarly, the equation AT y = c expresses the fact that the solution y lies in the column space of A.

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Answer:

B

Step-by-step explanation:

Formula

SA = 2*L*W + 2*L*H + 2*H*W

Givens

L = 14

W = 7

H = 7

Solution

SA = 2*14*7 + 2*14*7 + 2*7*7

SA = 196 + 196 + 98

SA = 490

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{2}[/tex] x + 4 ← is in slope- intercept form

Thus

y = [tex]\frac{1}{2}[/tex] x + 4 is the equation of a straight line

with slope m = [tex]\frac{1}{2}[/tex] and y- intercept c = 4

Answer:

C, A and D

Step-by-step explanation:

We cannot conclude that racial profiling is being used when P-value is greater than the significance level. Therefore, the correct option is A. No, because the P-value is greater than the significance level.

Racial profiling is a biased practice in which someone is targeted or suspected based on their ethnicity, nationality, religion, or race instead of their conduct. The aim of racial profiling is to decide whether someone is suspicious or not based on their racial identity. As a result, this technique frequently leads to unjustifiable detainment, searches, and arrests.

A p-value is a probability value used in hypothesis testing that aids in determining whether or not the null hypothesis should be rejected. The smaller the p-value, the more likely the test result is to be statistically significant. In other words, it is less probable that the null hypothesis is true.

Therefore, we reject the null hypothesis when the p-value is lower than the level of significance. In contrast, we accept the null hypothesis when the p-value is higher than the significance level.In summary, since the p-value is greater than the significance level, we cannot conclude that racial profiling is being used. Therefore, the correct option is A. No, because the P-value is greater than the significance level.

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1. Finite: A set is considered finite if it contains a specific number of elements. In other words, a set is finite if you can count its elements and reach a finite number. For example, a set containing {1, 2, 3} is finite because it has three elements.

2. Infinite: A set is considered infinite if it has an uncountable number of elements. This means that the set cannot be put into a one-to-one correspondence with the natural numbers (1, 2, 3, ...). For example, the set of all integers {..., -3, -2, -1, 0, 1, 2, 3, ...} is infinite.

3. Denumerable: A set is denumerable (also called countable) if its elements can be put into a one-to-one correspondence with the natural numbers (1, 2, 3, ...). In other words, a denumerable set has a countable number of elements. For example, the set of all natural numbers is denumerable.

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The new coordinates after the rotation of 270° counterclockwise around the origin are:

J'(8, -10)

K'(3, -10)

L'(9, -5)

There are different types of transformation of geometry such as:

Translation

Reflection

Rotation

Dilation

The original coordinates before transformation are:

J(10, 8)

K(10, 3)

L(5, 9)

Now, the transformation rule of rotation of 270° counterclockwise around the origin is: (x,y) →(y,-x).

Thus, the new coordinates are:

J'(8, -10)

K'(3, -10)

L'(9, -5)

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Answer:

The answer is 5 years

Step-by-step explanation:

50+(3x5)=65

75-(2x5)=65

Answer:

A. y=-2x+6

Step-by-step explanation:

Hello again!

Answer:

The correct answer is B. 18 months.

Step-by-step explanation:

I just typed in "credit card payoff calculator" in g00gle, and it should be the first one you see.

That was the website I used to solve this problem. You can use that for other problems you need to solve too.

Hope this helps :)

Answer: The initial value for Z= 8 * 3w is 8 and the growth factor for it is 3. The initial value for A= 6(2.5)t is 6 and the growth factor for it is 2.5.

Step-by-step explanation: Exponential growth equations.

Answer:

1) a , b , c , e are ans....

2) a.F b.T c.F d.T

The distance between your ship and the port is approximately 8 units. To arrive at the port, you need to take a bearing of 135 degrees. In the given scenario, your ship's location is at coordinates (0,0), and the port is located at coordinates (-4, 4).

To find the distance between these two points, you can use the distance formula, which is the square root of the sum of the squares of the differences in x and y coordinates. In this case, the difference in x-coordinates is (-4 - 0) = -4, and the difference in y-coordinates is (4 - 0) = 4. Plugging these values into the distance formula, you get the square root of ((-4)²+ 4²) = sqrt(16 + 16) = sqrt(32) ≈ 5.66. Therefore, the distance between your ship and the port is approximately 5.66 units or rounded to 8 units.

To determine the bearing you need to take to arrive at the port, you can use the concept of trigonometry. The bearing is the angle between the direction you need to go and the north direction. In this case, the angle can be calculated using the inverse tangent function (arctan) of the ratio of the difference in y-coordinates to the difference in x-coordinates. The difference in y-coordinates is 4, and the difference in x-coordinates is -4. Taking the arctan(4 / -4), you get an angle of -45 degrees. Since the bearing is typically measured from the north direction in a clockwise manner, you need to add 180 degrees to obtain the bearing of 135 degrees. Therefore, you need to take a bearing of 135 degrees to arrive at the port.

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Answer:

B. Addition Property of Equality

Step-by-step explanation:

B addition property of equality

Answer:

34% in favor of the new dress code

Step-by-step explanation:

Because it has a higher percentage and when there is only 16% of students that doesn't really prove the claim or statement. But, when there is more participating or voting that claim or statement is supported.

Answer:

7:3

Step-by-step explanation:

Convert one of the measurements to the other before attempting to solve the question.

1 yard = 3 feet

Multiply both sides by 3 to get:

3 yards = 9 feet

Therefore the ratio would be

21:9

Simplify to 7:3 length to height.

Answer:

Nwm miałem to dawno powodzenia

Answer:

8

Step-by-step explanation:

First add all the terms together.

[tex]8+7+5+9+6+13=48[/tex], so the total is 48.

Then you divide the total by the number of terms (which is 6) to get the mean.

[tex]\frac{48}{6}=8[/tex], so the mean is 8.

Answer:  x=6

The two angles shown in each are complementary because they add up to 90°.

10 & 12 would be supplementary to one another because they would add up to 180°.

Step-by-step explanation:

We know that on both 10 & 12 the angles add up to equal 90° so...

10.  8x+7x=90

15x=90

x=6

12.  it's the same in pic as 10

The two angles shown in each are complementary because they add up to 90°.

10 & 12 would be supplementary to one another because they would add up to 180°.

Answer:

22.5 pounds

Step-by-step explanation:

The computation of the weight of the block of gel is shown below:

As we know that

Volume = (length) (width) (height)

= (20) (6 ) (6)

= 720 cubic inches

Now we have to convert into cubic foot

As we know that

1 ft = 12 inches

So 1ft^3 = 12 inches^3

= 1728 inches ^3

Now

= 720 × 1 cubic foot ÷ 1728 cubic inches

= 5 ÷ 12

Now the weight is

= 54 × 5 ÷ 12

= 22.5 pounds

Answer:

ok

Step-by-step explanation:

Answer: [tex]\dfrac{1}{220}[/tex]

Step-by-step explanation:

Given

There are 3 marbles of red, blue, green and orange

Total marbles are 12

No of ways of choosing 3 green marbles out of 3 green marbles is [tex]^3C_3[/tex]

Total no of ways of selecting 3 marbles out of 12 are [tex]^{12}C_3[/tex]

So, the probability is

[tex]\Rightarrow P=\dfrac{^3C_3}{^{12}C_3}=\dfrac{1\times 3\times 2\times 1}{12\times 11\times 10}\\\\\Rightarrow P=\dfrac{1}{220}[/tex]

Answer:

x is 120.104121495

Step-by-step explanation:

because you can square out the equation and get x

Answer:

The first one should be right but if you’re from K12 then it’ll be 12/5, and just that again except had a negative.

Step-by-step explanation:

Answer:

what do you mean? is there another part of the problem?

Step-by-step explanation: