Please look at the picture and answer. Thanks! :)

Answer:

P₄(x) = ln3 + 1/3 (x-3) - 1/9*2! (x-3)² + 2/27*3! (x-3)³ - 2/27*4! (x - 3)⁴

Step-by-step explanation:

Given:

f(x) = ln(x)

n = 4

c = 3

To find:

nth Taylor polynomial for the function, centered at c

Solution:

The Taylor series for f(x) = ln x centered at 3 is:

[tex]P_{n}(x) = f(c) + \frac{f'(c)}{1!}(x-c)+\frac{f''(c)}{2!}(x-c)^{2} +\frac{f'''(c)}{3!}(x-c)^{3}+...+\frac{f^{n} (c)}{n!}(x-c)^{n}[/tex]

Since c = 3 So,

[tex]P_{4}(x) = f(3) + \frac{f'(3)}{1!}(x-3)+\frac{f''(3)}{2!}(x-3)^{2} +\frac{f'''(3)}{3!}(x-3)^{3}+...+\frac{f^{n} (3)}{n!}(x-3)^{n}[/tex]

Now

f(3) = ln 3

f'(x) = 1/x ⇒ f'(3) = 1/3

f''(x) = -1/x² ⇒ f''(3) = -1/3² = -1/9

f'''(x) = 2/x³  ⇒ f'''(3) = 2/3³ = 2/27

f[tex]^{(4)}[/tex] (x) = -6/x⁴ ⇒ f[tex]^{(4)}[/tex] (3) = -6/3⁴ = -6/81 = - 2/27

So Taylor polynomial for n=4 is:

P₄(x) = ln3 + 1/3 (x-3) - 1/9*2! (x-3)² + 2/27*3! (x-3)³ - 2/27*4! (x - 3)⁴

Answer:

PQ = 2

Step-by-step explanation:

We know that OQ = OP + PQ. Since OQ = 16 and OP = 14, we know that 16 = 14 + PQ, therefore, PQ = 2.

Answer:

13 hours

Step-by-step explanation:

8:00 plus 4 is twelve ( 12 o'clock )

then you have 9hrs left.

( 4+9=13 )

Answer:

7

Step-by-step explanation:

:)

it's so easy :))))))))

Answer:

Half of 14 is 7

Step-by-step explanation:

Answer:

a number with a non repeating and non terminating decimal expansion.

Step-by-step explanation:

Irrational numbers are numbers which cannot be expressed as fractions, they are real numbers which cannot be expressed as rational numbers such as the square root of natural numbers other than perfect squares.

Irrational numbers are non repeating, non terminating decimal numbers with no group of the digits repeated. Therefore the decimal expansion does not terminate but continues without repetition example is π.

Answer:

60in^2

Step-by-step explanation:

Area of a triangle = Height x Base X 1/2

Base = 10

Other 2 sides = 13

Now, let's split the Base into 2 parts.

=> 1 part = 5 and 2 part = 5

We can find the height using Pythagorean theorem

=> Isosceles triangle

=> (1 part of the base)^2 + Height^2 = The Hypotenuse^2  = the longer side of a triangle = 13^2

=> 5^2 + Height ^2 = 13^2

=> 25 + Height^2 = 169

=> 25 - 25 + Height ^2 = 169 - 25

=> Height^2 = 144

=> Height = Square root of 144

=> Height = 12

Area = 12 x 10 x 1/2

=> 12 x 5

=> 60 in^2

So, the Area is 60 in ^2

Answer:

Option (D)

Step-by-step explanation:

Total hours worked of Monday= 4:45 hours + 5:00 hours = 9:45 hours

Total hours worked of Tuesday= 4:45 hours + 4:45 hours = 9:30 hours

Total hours worked of Wednesday= 4:30 hours + 4:30 hours = 9:00 hours

Total hours worked of Thursday= 4:45 hours + 4:15 hours = 9:00 hours

Total hours worked of Friday= 4:45 hours + 4:15 hours = 9:00 hours

Total hours worked = 9:45 + 9:30 + 9:00 + 9:00 + 9:00

                                 = 46:15 hours

                                 ≈ 46 hours 15 minutes

Option (D) will be the answer.

Answer:

(6, -17)

Step-by-step explanation:

Given the coordinate of a midpoint, (5, -12), and one endpoint, (4, -7), the other endpoint can be determined as follows:

The midpoint formula is given as [tex] M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) [/tex].

Since we are given ordered pairs of the midpoint and one endpoint, we would find the other ordered pair of the endpoint as shown below.

Let the other endpoint be [tex] (x_1, y_1) [/tex]

Midpoint = M(5, -12)

Let the given endpoint = [tex] (4, -7) = (x_2, y_2) [/tex]

Thus:

[tex] M(5, -12) = (\frac{x_1 + 4}{2}, \frac{y_1 +(-7)}{2}) [/tex]

Rewrite the equation to find the coordinates of the other endpoints

[tex] 5 = \frac{x_1 + 4}{2} [/tex] and [tex] -12 = \frac{y_1 - 7}{2} [/tex]

Solve for each:

[tex] 5 = \frac{x_1 + 4}{2} [/tex]

[tex] 5*2 = \frac{x_1 + 4}{2}*2 [/tex]

[tex] 10 = x_1 + 4 [/tex]

[tex] 10 - 4 = x_1 + 4 - 4 [/tex]

[tex] 6 = x_1 [/tex]

[tex] x_1 = 6 [/tex]

[tex] -12 = \frac{y_1 - 7}{2} [/tex]

[tex] -12*2 = \frac{y_1 - 7}{2}*2 [/tex]

[tex] -24 = y_1 - 7 [/tex]

[tex] -24 + 7 = y_1 - 7 + 7 [/tex]

[tex] -17 = y_1 [/tex]

[tex] y_1 = -17 [/tex]

Ordered pair of the other endpoint is (6, -17)

Answer:

Larger number = 37

Smaller Number = 11

Step-by-step explanation:

Lets take x as the bigger number and y as the smaller number

x + y = 48

What do we know?

The larger number is 7 less than four times the smaller number

so 4y - 7 = x

Lets replace the equation obove with x

4y - 7 + y = 48

5y - 7 = 48

5y = 48 + 7

y = 55/5

y = 11

Then multiply 11 by 4 11 times 4 = 44 and subtract by 7 44 - 7 = 37

To recheck add 37  to 11 and u should get 48

Answer:

  4 years

Step-by-step explanation:

The formula for simple interest is useful here.

  I = Prt

where P is the principal invested at rate r for t years.

Fill in the given values and solve for t:

  81 = 450×0.045×t

  81/20.25 = t = 4

It will take 4 years for 450 to yield 81.

Remove the parentheses and combine the like terms:

7 - -9 = 7+ 9 = 16

6i - -8i = 6i +8i = 14i

The answer is 16 + 14i

Answer:

14322 * 10¹²

1.4322 * 10¹⁶

Step-by-step explanation:

14322000000000000

14322 * 10¹²

1.4322 * 10¹⁶

Answer:

7g-100%

x-38,25

38,25*7:100=2,6775g

7g-2,6775g=4,4325g

Step-by-step explanation:

Answer: (3x+2)(x+3)

Step-by-step explanation: Factor by grouping.

I hope this helps you out.

Answer:

[tex](3x+2)(x+3)[/tex]

Step-by-step explanation:

[tex]3x^{2} +11x+6[/tex]

Let's factor.

[tex]3x^{2}+11x+6[/tex]

This equals

[tex](3x+2)(x+3)[/tex]

Now you got your answer!

Hope this helps!

Answer:

that is the outsider part.of something

the sum of the areas of all the faces of a three dimension figure or in 3-D shapes

Answer:

Step-by-step explanation:

36/12 = 3

12 x 3 = 36

Answer:  11.0  or 11

Step-by-step explanation:

To find the distance first find the difference between the coordinates. find the change in the x and y coordinates and square them to add them to get a number and find the square root of that same number to find the distance.

x coordinates:   5-(-6)= 11

y coordinate:  7-6 =  -1  

Now square them

11^2 + 1^2 = l^2    where l is the distance

121 + 1 = l^2

 122 =l^2

 l =  [tex]\sqrt{122}[/tex]

  l  =  11.045   Rounded to the nearest tenth is 11.0

Answer:

Sarah answered 7 multiple choice questions and 3 free response questions correctly.

Step-by-step explanation:

Given that: she has 36 points.

                   3 points each for the multiple choice question (MCQ)

                   5 points each for the free response question (FRQ)

To determine how many of each question was answered correctly. Let the number of MCQ she answered be represented by x and FRQ by y.

  3x + 5y = 36   ............ 1

Since she answered a total of 10 question, then;

  x + y = 10

 x = 10 - y  ................  2

Substitute equation 2 into 1,

3(10 - y) + 5y = 36

30 - 3y + 5y = 36

2y = 6

y = 3

Substitute the value of y in equation 2,

x = 10 - y

  = 10 - 3

  = 7

x = 7, y = 3

Therefore, Sarah answered 7 multiple choice questions and 3 free response questions.

Answer:

-10+4=-6

Step-by-step explanation:

Answer:

38°

Step-by-step explanation:

∠4=∠2

∠2=∠6

∠6=38°

So ∠4=38°

Answer:

The answer is 38°

Step-by-step explanation:

When both lines are parallel, their vertical opposite angles will be the same. So ∠4 = 38°.

Answer:

v=15.625ft³ or 15.63ft³

Step-by-step explanation:

v=s³

v=2.5³

v=15.625

round off to the nearest hundredth

v=15.63ft³

Answer:

I THINK IT WILL BE HELPFUL

Answer:

y = 3x +8

Step-by-step explanation:

[tex](-5 ,-7)=(x_1,y_1) \\m = 3\\[/tex]

Plug in values into point-slope form

[tex]y -y_1 =m(x-x_1)\\y - (-7) = 3(x - (-5))\\y +7 =3(x+5)\\y+7 =3x+15\\y = 3x +15-7\\y = 3x +8[/tex]

Answer:

Step-by-step explanation:

=-3-i-5-3i

=-8-4i

Answer:

The mean of the sampling distribution  [tex]\mu_{\overline x}[/tex] is 86

The standard deviation of the sampling distribution  [tex]\sigma_x[/tex]  is 2

The mean of the sampling distribution  [tex]\mu_{\overline x}[/tex] is 71

The standard deviation of the sampling distribution  [tex]\sigma_x[/tex]  is 1

B) The distribution is approximately normal.

[tex]\mathbf{P(\overline x >73) = 0.0228}[/tex]

Therefore, the probability that the sample mean is greater than 73 = 0.0228

[tex]\mathbf{P(\overline x \leq 69) = 0.0228}[/tex]

The probability that the sample mean is less than or equal to 69 is 0.0228

[tex]\mathbf{P( 69.8 \leq \overline x \leq 72.5) = 0.8181}[/tex]

Thus, the probability that the sample mean is between 69.8 and 72 is 0.8181.

Step-by-step explanation:

We are to determine the [tex]\mu_{\overline x}[/tex] and [tex]\sigma_x[/tex] from the given parameters of a population and sample size.

Given that :

population mean [tex]\mu[/tex] = 86

population standard deviation [tex]\sigma[/tex] = 16

sample size n = 64

From the central limit theorem's knowledge, we know that as the sample distribution approximates a normal distribution, the sample size gets larger. Thus, the mean of the sampling distribution [tex]\mu_{\overline x}[/tex]  is equal to the population mean [tex]\mu[/tex]

∴

[tex]\mu_{\overline x}[/tex]  = [tex]\mu[/tex] = 86

The standard deviation of the sampling distribution can be computed by using the formula:

[tex]\sigma_{\overline x } = \dfrac{\sigma }{\sqrt{n}}[/tex]

[tex]\sigma_{\overline x } = \dfrac{16 }{\sqrt{64}}[/tex]

[tex]\sigma_{\overline x }= \dfrac{16 }{8}[/tex]

[tex]\mathbf{\sigma_{\overline x } = 2}[/tex]

∴

The mean of the sampling distribution  [tex]\mu_{\overline x}[/tex] is 86

The standard deviation of the sampling distribution  [tex]\sigma_x[/tex]  is 2

Suppose a simple random sample of size n = 36  is obtained from a population with mu = 71 and sigma = 6.

i.e

sample size n = 36

population mean [tex]\mu[/tex] = 71

standard deviation [tex]\sigma[/tex] = 6

From the central limit theorem's knowledge, we know that as the sample distribution approximates a normal distribution, the sample size gets larger. Thus, the mean of the sampling distribution [tex]\mu_{\overline x}[/tex]  is equal to the population mean [tex]\mu[/tex]

∴

[tex]\mu_{\overline x}[/tex]  = [tex]\mu[/tex] = 71

The standard deviation of this sampling distribution [tex]\sigma_{\overline x}[/tex] can be estimated as :

[tex]\sigma_{\overline x }= \dfrac{\sigma }{\sqrt{n}}[/tex]

[tex]\sigma_{\overline x }= \dfrac{6 }{\sqrt{36}}[/tex]

[tex]\sigma_{\overline x } = \dfrac{6 }{6}[/tex]

[tex]\mathbf{\sigma_{\overline x } = 1}[/tex]

∴

The mean of the sampling distribution  [tex]\mu_{\overline x}[/tex] is 71

The standard deviation of the sampling distribution  [tex]\sigma_x[/tex]  is 1

A)

The correct option from the  given question is:

B) The distribution is approximately normal.

B) What is P (xbar > 73)?

i.e

[tex]P(\overline x >73) = P \begin {pmatrix} \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}} > \dfrac{73 -71 }{\dfrac{6}{\sqrt{36}}} \end {pmatrix}[/tex]

[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{73 -71 }{\dfrac{6}{\sqrt{36}}} \end {pmatrix}[/tex]

[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{2 }{\dfrac{6}{6}} \end {pmatrix}[/tex]

[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{2 \times 6 }{6} \end {pmatrix}[/tex]

[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{12 }{6} \end {pmatrix}[/tex]

[tex]P(\overline x >73) = P \begin {pmatrix} Z > 2 \end {pmatrix}[/tex]

[tex]P(\overline x >73) = 1- P \begin {pmatrix} Z < 2 \end {pmatrix}[/tex]

Using the Excel Function ( =NORMDIST(2) )

[tex]P(\overline x >73) = 1- 0.9772[/tex]

[tex]\mathbf{P(\overline x >73) = 0.0228}[/tex]

Therefore, the probability that the sample mean is greater than 73 = 0.0228

C) What is P (xbar ≤ 69)?

i.e

[tex]P(\overline x \leq 69) = P \begin {pmatrix} \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{69 -71 }{\dfrac{6}{\sqrt{36}}} \end {pmatrix}[/tex]

[tex]P(\overline x \leq 69) = P \begin {pmatrix}Z \leq \dfrac{-2 }{\dfrac{6}{6}} \end {pmatrix}[/tex]

[tex]P(\overline x \leq 69) = P \begin {pmatrix} Z \leq \dfrac{-2 \times 6 }{6} \end {pmatrix}[/tex]

[tex]P(\overline x \leq 69) = P \begin {pmatrix} Z \leq \dfrac{-12 }{6} \end {pmatrix}[/tex]

[tex]P(\overline x \leq 69) = P \begin {pmatrix} Z \leq -2 \end {pmatrix}[/tex]

Using the EXCEL FUNCTION ( = NORMSDIST (-2) )

[tex]\mathbf{P(\overline x \leq 69) = 0.0228}[/tex]

The probability that the sample mean is less than or equal to 69 is 0.0228

NOTE: This text editor can't contain more than 5000 characters so the last part of the question is attached in the image below.

Answer:

0.001km

1km is 1000m

So, 1m is 1m divided by 1000km

Which gives 0.001km

There are 0.001 kilometres in 1 metre.

1000 metre =1 kilometre

1 metre=1/1000 kilometre

Answer:

-0.66666666666

Step-by-step explanation:

1/3-5/5

8^15 ÷ 1/8^3 = 8^15 x 8^3=8^18

1.8014399e+16

Step-by-step explanation:

So before you can divide the numbers you have to simplify the exponents. You probably learned P(parentheses) E(exponents) M(multiply) D(divide) A(add) S(subtract.

Answer:

Step-by-step explanation:

343

Answer:

7^3

Step-by-step explanation:

7 to the power of 3. Because there are 3, 7's so you are multiplying 7 3 times