a. Find the first four nonzero terms of the Maclaurin series for the given function. b. Write the power series using summation notation. c. Determine the interval of convergence of the series. ​f(x)equals​(4plusxsquared​)Superscript negative 1 a. The first nonzero term of the Maclaurin series is nothing. The second nonzero term of the Maclaurin series is nothing. The third nonzero term of the Maclaurin series is nothing. The fourth nonzero term of the Maclaurin series is nothing. b. Write the power series using summation notation. Choose the correct answer below. A. Summation from k equals 0 to infinity minus StartFraction 1 Over 4 Superscript k plus 1 EndFraction x Superscript 2 k B. Summation from k equals 0 to infinity StartFraction 1 Over 4 Superscript k plus 1 EndFraction x Superscript k C. Summation from k equals 0 to infinity StartFraction (negative 1 )Superscript k Over 4 Superscript k EndFraction x Superscript k D. Summation from k equals 0 to infinity StartFraction (negative 1 )Superscript k Over (4 )Superscript k plus 1 EndFraction x Superscript 2 k

Answer:

Plese read the complete procedure below:

Step-by-step explanation:

The polynomial is p(a) = (a^4 - 6a^3 + 3a^2 + 26a – 24)

a)

1   -6   3   26   -24    |  1    

     1   -5   -2    24

1   -5   -2   24    0

The remainder is zero, then (a-1) is a factor of the polynomial

b)

1   -6   3   26   -24    |  2    

     2  -8   10    72

1   -4   5   36    48

When p(a) is divided by (a-2) the remainder 28/p(a)

1   -6   3   26   -24    | - 4    

   -4  40  172  -792

1   -10  43  198  -816

When p(a) is divided by (a-2) the remainder -816/p(a)

c) I attached an image of the long division below:

Answer:

The answer is "14.625 ft"

Step-by-step explanation:

In the given question some information is missing that is attachment of file which can be described as follows:

Add products:

[tex]\rightarrow \ (\frac{1}{8})\times 1+(\frac{1}{4})\times 1+(\frac{1}{2})\times 3+(\frac{3}{4})\times8+(1)\times4+1 \frac{3}{8}\times (2)1 \frac{3}{8} \\\\ \rightarrow 11/8\\\\[/tex]

[tex]\rightarrow \frac{1}{8}\times 1+(\frac{1}{4})\times1+(\frac{1}{2})\times3+(\frac{3}{4})\times8+(1)\times4+\frac{11}{8}\times(2)\\\\[/tex]

[tex]\rightarrow (\frac{1}{8})+(\frac{1}{4})+(\frac{3}{2})+(6)+(4)+\frac{11}{4}\\\\\rightarrow (\frac{1+2+12+48+32+22}{8}) \\\\\rightarrow \frac{117}{8} \\\\ \rightarrow 14.625 \ ft \\[/tex]

Answer: The area of the new parallelogram is multiplied by 18

Step-by-step explanation: Let the base and the height of the original parallelogram be ' x '

Base of the parallelogram = x

Height of the parallelogram = x

Area of parallelogram = l × b = lb

= x × x = x²

∴ Area of the original parallelogram = x²

∴ The base is multiplied by 3 = 3x

The height is multiplied by 6 = 6x

∴ Area of new parallelogram = 3x × 6x = 18x²

∴ The area of the new parallelogram is multiplied by = 18x²/ x²

= 18

Please mark this as brainliest

Answer:

10

Step-by-step explanation:

Answer:

There is no error. This is a correct conclusion.

Step-by-step explanation:

If a sequence of rigid transformations

(translations, reflections, and rotations) and dilations can map △DCE onto △ABE, then the figures are similar.

Notice that both triangles are right triangles (at vertices B and C), with line AB and DC being the longer legs.

Therefore, if the triangles are similar, we should be able to map each pair of corresponding points onto each other with rigid transformations and dilations:

   D should be mapped onto A.

   C should be mapped onto B.

   E should be mapped onto itself.

Lennox used a reflection across line BE and a dilation about E to get △DCE as close as possible to △ABE. But still, point D did not map onto point A.

So we can conclude that it's not possible to map △DCE onto △ABE using a sequence of rigid transformations and dilations.

Lennox concluded:

"It's not possible to map △DCE onto △ABE using a sequence of rigid transformations and dilations, so the triangles are not similar."

There is no error. This is a correct conclusion.

Answer:

there is no error

Step-by-step explanation:

I took the quiz on Khan and got it correct!

Answer:

1

Step-by-step explanation:

(−4)−(−2)–{(−5)–[(−7)+(−3)–(−8)]}

PEMDAS

Work from the inside out

Change subtracting negatives to adding

(−4)+2–{(−5)–[(−7)+(−3)+8)]}

(−4)+2–{(−5)–[(-2)]}

(−4)+2–{-5+2}

(−4)+2–(−3)

Changing to adding

(−4)+2+3

-2+3

1

Answer: 1st and 3rd 2nd and fourth hope this helps :3

Step-by-step explanation:

Answer:

Mean of original test scores is 88.5

Mean of test scores , with three marks added to each score is 91.5

The mean of the test score with three marks added to each score is higher than the original mean of score is increased by three .

Explanation : hope it works out !!

Answer:

4

Step-by-step explanation:

[tex]256^{0.16}\cdot 256^{0.09}=\\256^{0.16+0.09}=\\256^{0.25}=\sqrt[4]{256}=4[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

Please check below in the attached, you will see answer to given questions, thank you, I hope it helps.

Answer:

Answer shown from explanation

Step-by-step explanation:

Area of trapezium =1/2 * sum of parallel side * height = 1/2. *(6+12) *4= 36sqft

Answer:

896+32=928in

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Since lines a, b, c, d, and XY are all parallel to each other, and are a part of the same triangle, they are all similar. Thus, we can compare rates -- the distance between P to Y is 12, and 2/3 of 12 is 8, so we need to find that length, which is C

The segment of line c shows the correct result of the dilation. Hence, the correct answer is option C.

Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.

Since lines a, b, c, d, and XY are all parallel and part of the same triangle, they are all similar. Thus, we can compare rates the distance between P to Y is 12, and 2/3 of 12 is 8, which is C.

Hence, the correct answer is option C.

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Answer:

(a) The mean and standard deviation of X is 2.6 and 1.2 respectively.

(b) The mean and standard deviation of T are 390 and 180 respectively.

(c) The distribution of T is N (390, 180²). The probability that all students’ requests can be accommodated is 0.7291.

Step-by-step explanation:

(a)

The random variable X is defined as the number of tickets requested by a randomly selected graduating student.

The probability distribution of the number of tickets wanted by the students for the graduation ceremony is as follows:

X      P (X)

0      0.05

1       0.15

2      0.25

3      0.25

4      0.30

The formula to compute the mean is:

[tex]\mu=\sum x\cdot P(X)[/tex]

Compute the mean number of tickets requested by a student as follows:

[tex]\mu=\sum x\cdot P(X)\\=(0\times 0.05)+(1\times 0.15)+(2\times 0.25)+(3\times 0.25)+(4\times 0.30)\\=2.6[/tex]

The formula of standard deviation of the number of tickets requested by a student as follows:

[tex]\sigma=\sqrt{E(X^{2})-\mu^{2}}[/tex]

Compute the standard deviation as follows:

[tex]\sigma=\sqrt{E(X^{2})-\mu^{2}}\\=\sqrt{[(0^{2}\times 0.05)+(1^{2}\times 0.15)+(2^{2}\times 0.25)+(3^{2}\times 0.25)+(4^{2}\times 0.30)]-(2.6)^{2}}\\=\sqrt{1.44}\\=1.2[/tex]

Thus, the mean and standard deviation of X is 2.6 and 1.2 respectively.

(b)

The random variable T is defined as the total number of tickets requested by the 150 students graduating this year.

That is, T = 150 X

Compute the mean of T as follows:

[tex]\mu=E(T)\\=E(150\cdot X)\\=150\times E(X)\\=150\times 2.6\\=390[/tex]

Compute the standard deviation of T as follows:

[tex]\sigma=SD(T)\\=SD(150\cdot X)\\=\sqrt{V(150\cdot X)}\\=\sqrt{150^{2}}\times SD(X)\\=150\times 1.2\\=180[/tex]

Thus, the mean and standard deviation of T are 390 and 180 respectively.

(c)

The maximum number of seats at the gym is, 500.

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e ∑X, will be approximately normally distributed.  

Here T = total number of seats requested.

Then, the mean of the distribution of the sum of values of X is given by,  

[tex]\mu_{T}=n\times \mu_{X}=390[/tex]  

And the standard deviation of the distribution of the sum of values of X is given by,  

[tex]\sigma_{T}=n\times \sigma_{X}=180[/tex]

So, the distribution of T is N (390, 180²).

Compute the probability that all students’ requests can be accommodated, i.e. less than 500 seats were requested as follows:

[tex]P(T<500)=P(\frac{T-\mu_{T}}{\sigma_{T}}<\frac{500-390}{180})\\=P(Z<0.61)\\=0.72907\\\approx 0.7291[/tex]

Thus, the probability that all students’ requests can be accommodated is 0.7291.

Answer:

Step-by-step explanation:

I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget ro thank me...

There are 41 white marbles in the bag.

Let's assume the number of green marbles is represented by "x". According to the given information, the number of white marbles is 3 less than 4 times the number of green marbles.

Number of white marbles = 4x - 3

The total number of marbles is given as 52, so we can write the equation:

Number of white marbles + Number of green marbles = Total number of marbles

(4x - 3) + x = 52

Combining like terms:

5x - 3 = 52

Adding 3 to both sides:

5x = 55

Dividing both sides by 5:

x = 11

Therefore, the number of green marbles is 11.

To find the number of white marbles:

Number of white marbles = 4x - 3

                       = 4 * 11 - 3

                       = 44 - 3

                       = 41

Hence, there are 41 white marbles.

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Answer:

6.5%

Step-by-step explanation:

305.5/4700=0.065=6.5%

Answer:

Step-by-step explanation:

Answer:

Supplementary angles are angles that add up to 180° so they need to add up to 180 degrees.

Step-by-step explanation:

Answer:

Decimal form: 0.00780379

Step-by-step explanation:

Used a calculator tbh.

Plz click the Thanks button!

<Jayla>

Answer:

A = 2x^2 + 17x -9

Step-by-step explanation:

A = LW

L = x + 9

W = 2x - 1

A = (x+9)(2x-1)

FOIL

A = 2x^2 + 18x - x - 9

A = 2x^2 + 17x -9

Answer:

The statements that are true for this equation are:

- The equation is an exponential growth equation.

- $228.000 represents the initial cost of a real estate that appreciates 3% per year over the course of years.

Step-by-step explanation:

We have the equation

[tex]V= 228,000(1.03)^t[/tex]

Where V: value of the real state and t: time in years.

As t is always positive in this case, and 1.03 is larger than 1, the value V will rise exponentially. The equation is an exponential growth equation.

The difference in value for each year is:

[tex]\dfrac{V_{t+1}}{V_t}=\dfrac{1.03^{t+1}}{1.03^t}=1.03^{t+1-t}=1.03\\\\\\V_{t+1}-V{t}=1.03V_t-V_t=0.03V_t[/tex]

We can conclude that the value increases each year 0.03 (3%) from the previous year value, starting from $228,000 in the year t=0.

$228.000 represents the initial cost of a real estate that appreciates 3% per year over the course of years.

Answer:

< 12,098

Step-by-step explanation:

Because yes

...........

It is <12,098

One of them is correct

Answer:

[tex] y= 7(x+5)^2 -4[/tex]

The vertex form for a parabola is given by this expression:

[tex] y = a(x-h)^2 +k[/tex]

By direct comparison we see that for this case:

[tex] a = 7, h = -5 and k=-4[/tex]

And we know from the general expression that the vertex is:

[tex] V= (h,k)[/tex]

So then the vertex for this case is:

[tex] V= (-5,-4)[/tex]

Step-by-step explanation:

For this case we have the following function:

[tex] y= 7(x+5)^2 -4[/tex]

And we need to take in count that the vertex form for a parabola is given by this expression:

[tex] y = a(x-h)^2 +k[/tex]

By direct comparison we see that for this case:

[tex] a = 7, h = -5 and k=-4[/tex]

And we know from the general expression that the vertex is:

[tex] V= (h,k)[/tex]

So then the vertex for this case is:

[tex] V= (-5,-4)[/tex]

Answer:

A: The expression is a trinomial with a degree of 4.

Step-by-step explanation:

The expression has three parts, so it's a tronomial.

The largest exponent is 4, so it has a degree of 4.  

Answer:

Yea he is right it is a

Step-by-step explanation:

Answer:

a) add x , subtract 1 and divide by 4

The solution of given equation [tex]x = \frac{3}{4}[/tex]

Step-by-step explanation:

Given equation  1+3 x  = -x +4

                 Add 'x' on both sides , we get

                     1 + 3 x + x = - x + x +4

                     1 + 4 x  = 4

       Subtract '1' on both sides , we get

                    1+4 x -1 = 4 -1

                         4 x = 3

      Dividing '4' on both sides, we get

                          [tex]\frac{4x}{4} = \frac{3}{4}[/tex]

                          [tex]x = \frac{3}{4}[/tex]

Final answer:-

The solution of given equation [tex]x = \frac{3}{4}[/tex]

Answer:

3

Step-by-step explanation:

1 / (1/3) = 3

Answer:

Step-by-step explanation:

Given the length(l), height(h) and width(w) of a rectangular prism.

Surface Area=2(lw+lh+wh)

For a rectangular prism with a height of h yards, a length of 2.6 yards, and a width of 3.5 yards.

Surface Area[tex]=2(2.6*3.5+2.6h+3.5h)[/tex]

[tex]=2(9.1+2.6h+3.5h)\\=18.2+5.2h+7h\\[/tex]

Surface Area= (18.2+12.2h) square yards

If the height, h=4 yards

Then the surface area of the rectangular prism

=18.2+12.2h

=18.2+12.2(4)

=18.2+48.8

=67 square yards

Answer:

  (x, y) = (4, 0)

Step-by-step explanation:

It looks like you want to solve ...

Adding the two equations gives ...

  2x = 8

  x = 4 . . . . divide by 2

Then ...

  y = 4 - x = 0

The solution is (x, y) = (4, 0).

_____

If you think about what you're seeing when you read the equations, you realize that adding or subtracting y gives the same result. Hence y=0 and x=4.

Answer:

A. a one-tailed paired t-test.

Step-by-step explanation: