Consider the following function.
f(x) = x sin(x), a = 0, n = 4, −0.5 ≤ x ≤ 0.5
(a) Approximate f by a Taylor polynomial with degree n at the number a.
T4(x) =
(b) Use Taylor's Inequality to estimate the accuracy of the approximation
f(x) ≈ Tn(x) when x lies in the given interval. (Round your answer to four decimal places.)
|R4(x)| ≤
(c) Check your result in part (b) by graphing |Rn(x)|.

Answer:

Hope It helps

Step-by-step explanation:

Recall that

[tex]1 + \tan^2 x = \sec^2 x[/tex]

and

[tex]\dfrac{d}{dx}(\tan x) = \sec^2 x[/tex]

so that

[tex]\displaystyle \int \tan^2 x = \int (\sec^2 x - 1)dx[/tex]

[tex]\:\:\:\:\:\:\:\:\:=\int \sec^2 xdx - \int dx[/tex]

[tex]\:\:\:\:\:\:\:\:\:=\tan x - x + C[/tex]

where C is the constant of integration.

Answer:

a) By the Central Limit Theorem, it has an approximately normal shape, with mean(center) 0.9 and standard deviation(spread) 0.035.

b) Average numbers of children between 0.83 and 0.97 are reasonably likely in the sample.

c) 0.0021 = 0.21% probability that the average number of children per family in the sample will be 0.8 or less

d) 0.9958 = 99.58% probability that the average number of children per family in the sample will be between 0.8 and 1.0

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean 0.9 and standard deviation 1.1.

This means that [tex]\mu = 0.9, \sigma = 1.1[/tex]

Suppose a television network selects a random sample of 1000 families in the United States for a survey on TV viewing habits.

This means that [tex]n = 1000, s = \frac{1.1}{\sqrt{1000}} = 0.035[/tex]

a. Describe (as shape, center and spread) the sampling distribution of the possible values of the average number of children per family.

By the Central Limit Theorem, it has an approximately normal shape, with mean(center) 0.9 and standard deviation(spread) 0.035.

b. What average numbers of children are reasonably likely in the sample?

By the Empirical Rule, 95% of the sample is within 2 standard deviations of the mean, so:

0.9 - 2*0.035 = 0.83

0.9 + 2*0.035 =  0.97

Average numbers of children between 0.83 and 0.97 are reasonably likely in the sample.

c. What is the probability that the average number of children per family in the sample will be 0.8 or less?

This is the p-value of Z when X = 0.8. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.8 - 0.9}{0.035}[/tex]

[tex]Z = -2.86[/tex]

[tex]Z = -2.86[/tex] has a p-value of 0.0021

0.0021 = 0.21% probability that the average number of children per family in the sample will be 0.8 or less.

d. What is the probability that the average number of children per family in the sample will be between 0.8 and 1.0?

p-value of Z when X = 1 subtracted by the p-value of Z when X = 0.8.

X = 1

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{1 - 0.9}{0.035}[/tex]

[tex]Z = 2.86[/tex]

[tex]Z = 2.86[/tex] has a p-value of 0.9979

X = 0.8

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.8 - 0.9}{0.035}[/tex]

[tex]Z = -2.86[/tex]

[tex]Z = -2.86[/tex] has a p-value of 0.0021

0.9979 - 0.0021 = 0.9958

0.9958 = 99.58% probability that the average number of children per family in the sample will be between 0.8 and 1.0

Step-by-step explanation:

guess

Dependent variable: y and Independent variable: x

gauthammath dot com 

Answer:

The graphs below have the same shape. What is the equation of the blue graph? A. G(x) = (x + 3)^3 B. G(x) = x^3 + 3 C. G(x) = x^3 - 3 D. G(x) = (x - 3)^3

The blue graph is a horizontal shift to the left by 3 units of F(x) = x³.

G(x) = (x + 3)³.

In mathematics, translation is the process of moving an object from one position to another without changing its shape, size, or orientation.

It involves sliding the object in a particular direction by a certain distance.

We have,

From the graph, the blue graph is G(x) = (x + 3)³.

The function f(x) = (x + 3)³ is a transformation of the function f(x) = x³.

Specifically, it is a horizontal shift to the left by 3 units.

To see why,

Let's consider the effect of replacing x with x + 3 in the original function f(x) = x³.

f(x + 3) = (x + 3)³

Notice that f(x + 3) is equal to f(x) translated horizontally to the left by 3 units.

For example, when x = 0, we have:

f(0) = 0³ = 0

f(0 + 3) = 3³ = 27

So the point (0, 0) on the graph of f(x) = x³ is transformed to the point

(-3, 27) on the graph of f(x) = (x + 3)³.

Similarly, we can see that every point on the graph of f(x) = x³ is shifted horizontally to the left by 3 units to obtain the graph of f(x) = (x + 3)³.

Therefore,

The blue graph is G(x) = (x + 3)³.

Learn more about translation here:

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Answer:

no.1 answer 0

Step-by-step explanation:

3x + 1= 4

or; 3x = 4 - 1

or; x = 3 ÷ 3

x = 0

Answer:

Step-by-step explanation:

Answer:

t = [tex]\frac{75}{n}[/tex]

Step-by-step explanation:

Use the inverse variation equation, y = [tex]\frac{k}{x}[/tex]

Replace y with t, and replace x with n, since those are the variables in this situation:

t = [tex]\frac{k}{n}[/tex]

Plug in 3 as t and 25 as n, and solve for k:

3 = [tex]\frac{k}{25}[/tex]

75 = k

Create the equation by plugging in 75 as k:

t = [tex]\frac{75}{n}[/tex]

So, the equation is t = [tex]\frac{75}{n}[/tex]

Given:

Consider the below figure attached with this question.

The table represents a proportional relationship.

To find:

The missing value from the table.

Solution:

If y is proportional to x, then

[tex]y\propto x[/tex]

[tex]y=kx[/tex]                 ...(i)

Where, k is a constant of proportionality.

The relationship passes through the point (-3,-1). Substituting [tex]x=-3,y=-1[/tex] in (i), we get

[tex]-1=k(-3)[/tex]

[tex]\dfrac{-1}{-3}=k[/tex]

[tex]\dfrac{1}{3}=k[/tex]

Putting [tex]k=\dfrac{1}{3}[/tex] in (i), we get

[tex]y=\dfrac{1}{3}x[/tex]           ...(ii)

We need to find the y-value for [tex]x=-12[/tex].

Substituting [tex]x=-12[/tex] in (ii), we get

[tex]y=\dfrac{1}{3}(-12)[/tex]

[tex]y=-4[/tex]

Therefore, the missing value in the table is -4. Hence, option D is correct.

Answer:

A FORMULA is an expression that uses variables to state a rule.

Answer:

B. angle with the greatest measure

opposite the largest angle

Answer:

The correct answer is:

(a) Mean = 170,

    Standard deviation = 30

(b) 1700

Step-by-step explanation:

Given:

(a)

Mean of monthly expenses will be:

= [tex]\frac{\mu}{2}[/tex]

= [tex]\frac{2040}{2}[/tex]

= [tex]170[/tex]

Standard deviation will be:

= [tex]\frac{\sigma}{12}[/tex]

= [tex]\frac{360}{12}[/tex]

= [tex]30[/tex]

(b)

The total amount of monthly expenses will be:

= [tex]n\times \frac{\mu}{12}[/tex]

= [tex]100\times 170[/tex]

= [tex]1700[/tex]

Answer:

Step-by-step explanation:

shape Sides Sum of interior angles Each Angle

Triangle         3 180°         60°

Quadrilateral 4 360° 90°

Pentagon 5 540° 108°

Hexagon         6 720° 120°

Heptagon  7 900° 128.57...°

Octagon         8 1080° 135°

Nonagon 9 1260° 140°

Answer:

n= -10

Step-by-step explanation:

-20+n=1+2n which simplifies to -21n+n=2n which simplifies to -20n=2n which simplifies to

n= -10

Answer:

27

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

x = -3

y = 3

y - 8x

Step 2: Evaluate

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{y - 8x}\\\\\large\textsf{= 3 - 8(-3)}\\\\\large\textsf{8(-3) = \bf -24}\\\\\large\textsf{= 3 - \bf 24}\\\\\large\textsf{= \bf 27}\\\\\boxed{\boxed{\large\textsf{\huge\textsf{Answer: \bf 27}}}}\huge\checkmark\\\\\\\\\large\textsf{Good luck on your assignment and enjoy your day!}\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]

Answer:

0.38 = 38% probability that it is neither red nor blue​.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

100 cars.

Of those, 28 + 34 = 62 are either blue or red.

100 - 62 = 38 are neither blue of red.

What is the probability that it is neither red nor blue​?

38 out of 100, so:

[tex]p = \frac{38}{100} = 0.38[/tex]

0.38 = 38% probability that it is neither red nor blue​.

Answer:

For the perimeters, x must be equal to 2.

For the areas, it is either undefined, or something.

Step-by-step explanation:

You can first find the perimeters for both sides.

For the left shape, we add the two sides of 6 and x + 4 to get x + 10.

Then we multiply x + 10 by 2 because there are 4 sides, and we only got 2 sides.

The perimeter of the first shape is 2x + 20.

The second shape can be solved by doing the same thing by adding 2 and 3x + 4 to get 3x + 6.

3x + 6 times 2 is 6x + 12.

The second perimeter is 6x + 12.

If both sides are supposed to be equal, then we can write these two expressions we solved for like:

6x + 12 = 2x + 20.

Subtraction property of equality

6x + 12 - 12 = 2x + 20 - 12

Simplify

6x = 2x + 8

Again

6x - 2x = 2x - 2x + 8

Simplify

4x = 8

Division property of equality

4/4x = 8/4

Simplify

x = 2

So if x = 2, the perimeters will be the same.

You can confirm this by plugging it back into either equation.

For the areas, we just multiply the length and width for both shapes, so we get

6(x+4)  =  2(3x+4)

Since they are supposed to be equal.

We simplify and get

6x + 24 = 6x + 8

We know this is false and is not possible, since we can remove the 6x because it is on both sides.

We also know that 24 is not equal to 8 (who thought!)

:D

24 ≠ 8

So it is undefined or whatever you call it.

Answer:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2". 1 more similar replacement(s).

Step by step solution :

STEP

1

:

Equation at the end of step 1

(((x3) - 2x2) + 2x) - 1 = 0

STEP

2

:

Checking for a perfect cube

2.1 x3-2x2+2x-1 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: x3-2x2+2x-1

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: 2x-1

Group 2: -2x2+x3

Pull out from each group separately :

Group 1: (2x-1) • (1)

Group 2: (x-2) • (x2)

Answer:

70

Step-by-step explanation:

the answer is 35*2=70

Answer:

70

yhsdhjbfjdfjdfhdfh

Answer:

（2,1）

Step-by-step explanation:

the graph intersects at 2 and 1

Answer:

AAS

Step-by-step explanation:

It will be angle angle side because you are given a side and two angles, and when you put them in the correct order, you will get AAS, or SAA (not the correct way to say it)

Answer:

20 million = 2 crore

Step-by-step explanation:

Here we will show you how to convert 20 million to crores (twenty million in crores). This may be useful if you for example want to convert 20 million rupees to crore rupees or 20 million dollars to crore dollars.

In some parts of the world like the United States, large numbers are separated with commas in three-digit-interval format like this:

...,BBB,MMM,TTT,HHH

BBB = billions

MMM = millions

TTT = thousands

HHH = hundreds

In certain parts of Asia, the format is a little different. From right to left, it starts out with three digits followed by a comma like the US, but after that, it is in intervals of two digits like this:

..,AA,CC,LL,TT,HHH

AA = arabs

CC = crores

LL = lakhs

TT = thousands

HHH = hundreds

Below we have displayed 20 million with the two number systems, based on the information above:

MM,TTT,HHH

20,000,000

=

C,LL,TT,HHH

2,00,00,000

When you match up 20 million with the C,LL,TT,HHH format above, you can see what 20 million is in crores. The answer to 20 million in crores is as follows:

20 million

= 2 crore

Answer:

Gary is now 24years

Step-by-step explanation:

let the age of Jan be x and that of Gary be x+15

in six years time they will be as follows

Jan =x+6

Gary=x+15+6=x+21

2(x+6)=x+21

2x+12=x+21

collect the like terms

2x-x=21-12

x=9

Gary =9+15=24years

Answer:

pretty sure it could

Step-by-step explanation:

Answer:

What it's asking is for 2 angles at different angles of attack, are parallel

Step-by-step explanation:

for example, // these two slashes are parallel because they wont ever touch, it wants you to find if the angles are parallel or not.

Answer:

The sampling distribution of the sample mean is approximately normal with mean 72 and standard deviation 1.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Normally distributed with mean 72 and standard deviation 6.

This means that [tex]\mu = 72, \sigma = 6[/tex]

A random sample of size 36

This means that [tex]n = 36, s = \frac{6}{\sqrt{36}} = 1[/tex]

The sampling distribution of the sample mean is

By the Central Limit Theorem, it is approximately normal with mean 72 and standard deviation 1.

Common difference: 6

First term: 7

Second term: 13

Third term: 19

Fourth term: 25

Fifth term: 31

I hope this is correct and helps!

Answer to the following question is as follows;

Number of term in AP (N) = 10

Step-by-step explanation:

Given:

Sum of arithmetic progression (Sn) = 340

First term of AP (a) = 7

Common difference of AP (d) = 6

Find;

Number of term in AP (N)

Computation:

Sn = [n/2][2a + (n-1)d]

340 = [n/2][2(7) + (n-1)6]

340 = [n/2][14 + 6n - 6]

680 = n[6n + 8]

6n² + 8n - 680

Using Quadratic Formula

n = 10

Number of term in AP (N) = 10

Learn more:

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Answer: 1, 4

Step-by-step explanation:

[tex]\frac{1}{4} x+x=5\\\\\frac{1}{4} x+\frac{4}{4} x=5\\\\\frac{5}{4} x=5\\\\5x=4*5\\5x=20\\x=4[/tex]

Answer:

-∞ <y<5

Step-by-step explanation:

The range of the graph is the values that y can take.  The graph can go from negative infinity to 5

-∞ <y<5

Answer:

A, C and D are not polynomials

Step-by-step explanation:

A because the variable has a negative power.

C because the variable is in the denominator

D because the variable has a root.

When a variable has a root, it's power is 1/2 which does not count as an ideal polynomial. You might be wondering then that why E is a polynomial?

E is a polynomial because because the root is not on the variable but on the constant.

B and E are polynomials while A,C and D are not.

Please mark me as brainliest.