Find the area of the trapezoid

The nth Maclaurin polynomial for the function f(x) = -5 - x + 4x² - 5x³ + 4x⁴ + ...

The nth Maclaurin polynomial for the function f(x) = (4x − 5)/(x + 1), we need to expand the function as a power series centered at x = 0 (the Maclaurin series) and then truncate it to the desired degree.

First, let's find the Maclaurin series expansion of f(x):

f(x) = (4x − 5)/(x + 1)

To expand this as a power series, we'll use the concept of geometric series expansion. We'll start by expressing f(x) as a product of two functions:

f(x) = (4x − 5)×(x + 1)⁻¹

Now, let's find the power series expansion for each factor separately.

1.The power series expansion for (4x - 5) centered at x = 0 is given by:

(4x - 5) = -5 + 4x

2.The power series expansion for (x + 1)⁻¹ centered at x = 0 is given by the geometric series formula:

(x + 1)⁻¹ = 1 - x + x² - x³ + x⁴ - ...

Note that this expansion is valid when |x| < 1 since it's based on a geometric series.

Now, we'll multiply these two expansions together to get the expansion for f(x). We'll keep terms up to the fourth degree (n = 4).

f(x) = (4x - 5) × (x + 1)⁻¹ = (-5 + 4x) × (1 - x + x² - x³ + x⁴)

Expanding this expression:

f(x) = -5 + 4x - 5x + 4x² - 5x³ + 4x⁴ + ...

Simplifying the terms:

f(x) = -5 - x + 4x² - 5x³ + 4x⁴ + ...

This is the Maclaurin series expansion for f(x). The nth Maclaurin polynomial, we'll truncate the series at the fourth degree (n = 4):

f(x) ≈ -5 - x + 4x² - 5x³ + 4x⁴

Therefore, the fourth Maclaurin polynomial for f(x) is given by:

P₄(x) = -5 - x + 4x² - 5x³ + 4x⁴

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Multiply 6 by 1/2 to get 3

Ow you have :

3( h + 1) = 18

Distribute the 3:

3h + 3 = 18

Subtract 3 from both sides:

3h = 15

Divide both sides by 3:

H = 5

Answer:

the answer is 120 degree

Answer:

(A) 30 degree

Step-by-step explanation:

Just subtract 180 with 120 = 60

then add 60 and 90 = 150

after that 180 - 50 = 30

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Answer:

Complementary

x= 60

Step-by-step explanation:

Answer:

The angles are complementary.

X =  60

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Hello There!

This is the formula for volume of a cylinder

[tex]V=\pi r^2h[/tex]

where r = radius and h = height

we are given the height and diameter height - 10 ft diameter - 22 ft

we are not give the radius directly but we can easily convert the diameter to the radius by dividing by 2

22/2=11 so the radius is 11

now having found the radius and height we plug in the values into the formula (note: it says leave answer in terms of pi so we will not apply pi to the final answer.)

[tex]V=\pi 11^210\\11^2=121\\121*10=1210\\V=1210\pi[/tex]

so we can conclude that the answer is A

Answer:

$135,000

Step-by-step explanation:

108000*1.25

Answer: Common factor

common factor. a whole number that is a factor of two or more nonzero whole numbers

Step-by-step explanation:

[tex] \purple{ \tt{ \huge{ \: ✨Answer ✨ \: }}}[/tex]

[tex] \: \: \: \red{ \boxed{ \boxed{ \huge{ \tt{ \: common \: factor \: }}}}}[/tex]

Answer:

volume=1yd x 1yd = q cubic yard

Answer:

19x−14y

Steps:

7x-3y+4x-5y+8x-6y

=19x-3y-5y-6y

= 19x−14y

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Answer:

19x-14y

Step-by-step explanation:

rearrange

7x+4x+8x-3y-5y-6y

solve the coefficient and add the variables

The assumption which is not true for multiple linear regression is that there will be a multi-collinearity effect. What is multiple linear regression? Multiple linear regression is a regression method where the response variable is dependent on more than one independent variable. Multiple linear regression is an extension of linear regression, where one response variable is dependent on one independent variable. It helps to determine the nature of the relationship between dependent variables and independent variables in the form of linear equations. It is used to find out the relationship between variables and make predictions based on that relationship. Assumptions of multiple linear regression1. Linearity, It is assumed that the relationship between the independent variables and dependent variables is linear. This implies that as the value of the independent variable changes, the change in the dependent variable is constant.2. Independence, There should be independence among the observations. This implies that there should not be any relationship between the residuals of the observations.3. Homoscedasticity implies that the variance of residuals should remain constant across all levels of the independent variable.4. Multicollinearity, It is the condition where the independent variables are highly correlated with each other. If there is perfect collinearity, it will not be possible to obtain the estimates of regression coefficients.5. Normality, The residuals should follow a normal distribution with mean zero and constant variance. The residuals should be normally distributed and centered on zero. The assumptions that are true for multiple linear regression are: The independent variables are not correlated. The residuals are normally distributed. The relationship between dependent and independent variables is linear. The assumption which is not true for multiple linear regression is that there will be a multi-collinearity effect. Hence, the correct option is D) There will be a multi-collinearity effect.

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Answer:

11 Seconds

Step-by-step explanation:

Swimming pool volume:

25.8 × 11.9 × 1.1 = 337.722

Time to empty pool:

337.722 ÷ 29.8 = 11.3329530201 ≈ 11 seconds

The correct answer is option A which is y = 25x + 100.

Given the following:

To join a local square dancing group, Jan has to pay a $100 sign-up fee plus $25 per month

We need to write an equation for the cost (y) based on the number of months.

To solve the above problem, the answer is;a. y = 25x + 100

Explanation; Let's break down the problem

The $100 sign-up fee is a fixed cost that is added only once to the monthly fee which is $25. Thus the equation for the cost (y) based on the number of months can be expressed as; y = 25x + 100 where:y is the cost for the number of monthsx is the number of months

Therefore the correct answer is option A which is;y = 25x + 100.

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To join a local square dancing group,

Jan has to pay a $100 sign-up fee plus $25 per month.

The equation for the cost (y) based on the number of months is

y = 25x + 100,

where x is the number of months.

Option A is the correct equation for the cost based on the number of months.

Writing the equation:

y = 25x + 100

Where:

y = Cost based on the number of months

x = Number of months

Therefore, when Jan has been part of the local square dancing group for 1 month, the total cost will be:

$25 * 1 + $100 = $125

And if Jan has been a part of the group for 4 months, then the total cost would be:

$25 * 4 + $100 = $200

Therefore, option A is the correct answer.

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Answer:

Step-by-step explanation:

(-3)x + (3)(-12)

= -3x -36

or -3(x + 12)

Answer:

Step-by-step explanation:

(-3)x + 3(-12) = (-3) (x + 12)

(-3) is both the two terms. So we can take (-3) as common

Answer:

b

Step-by-step explanation:

Answer:

Both commutative and associative

The expression that shows a difference of squares is option B, i.e., 16y² − x². We can represent it as (4y - x)(4y + x).Therefore, the correct option is B.

Difference of Squares is a squared quantity that can be represented as the difference of the squares of two variables or numbers. In simple terms, when two squares are subtracted, a difference of squares is produced. The squares of the two quantities, x and y, are subtracted from each other in the Difference of Squares.Here, the expression that shows a difference of squares is option B, i.e., 16y² − x². We can represent it as (4y - x)(4y + x).Therefore, the correct option is B. In this expression, we have the square of two quantities subtracted, which results in the Difference of Squares.Checking the other options, we can say that option A (10y² − 4x²) cannot be considered a difference of squares because there is no squared quantity subtracted from it. Similarly, option C (8x² − 40x + 25) and option D (64x² − 48x + 9) do not show the Difference of Squares as they do not have two squared quantities subtracted from each other.

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Answer:

Step-by-step explanation:

True. A rational expression is undefined whenever its denominator is zero. This is because division by zero is not defined.

In mathematics, a rational expression is defined as the quotient of two polynomials, where the denominator represents the divisor. When the denominator of a rational expression becomes zero, it results in division by zero, which is undefined. Division by zero is not a valid operation in mathematics, and it leads to an undefined value. Therefore, to determine if a rational expression is undefined, we need to check if its denominator evaluates to zero. If the denominator is zero, the rational expression is undefined. Also there is division by zero, or related concepts in mathematics.

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To find the volume of the glass formed by rotating the shaded region about the y-axis, we can use the method of cylindrical shells.

The volume of a solid of revolution using cylindrical shells is given by the integral:

V = ∫[a,b] 2πx * f(x) * dx

In this case, the function representing the curve that forms the inside of the glass is y = x^4/2. We need to find the limits of integration, a and b, which correspond to the x-values where the shaded region begins and ends.

From the graph, it appears that the shaded region begins at x = -1 and ends at x = 1. So, the limits of integration are -1 to 1.

Now, we can calculate the volume of the glass using the integral formula:

V = ∫[-1,1] 2πx * [tex](x^4/2) * dx[/tex]

V = π * ∫[-1,1] [tex]x^5 dx[/tex]

Using the power rule of integration, we integrate x^5:

V = π * [x^6/6] from -1 to 1

V = π * [[tex](1^6/6) - (-1^6/6)][/tex]

V = π * [(1/6) - (1/6)]

V = π * 0

Therefore, the volume of the glass is 0 cubic units.

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Answer:

the second one is 20 i think

Step-by-step explanation:

Answer:

6(2x+3)

Step-by-step explanation:

There's really no way to explain this. Take the number that all of the numbers in the equation can be divisible by and then single it out and then yeah.

Hope this helped! :)

Approximately 12.5% percentage of the students could be expected to score between 80 and 90.

To determine the percentage of students who could be expected to score between 80 and 90, we need to calculate the z-scores for these scores and use the standard normal distribution.

First, we need to calculate the z-scores for 80 and 90 using the formula:

z = (x - μ) / σ

where x is the individual score, μ is the mean, and σ is the standard deviation. Plugging in the values of μ = 100, σ = 60, and x = 80 or x = 90, we can calculate the z-scores.

For x = 80:

z = (80 - 100) / 60 = -0.3333

For x = 90:

z = (90 - 100) / 60 = -0.1667

Next, we need to find the area under the standard normal distribution curve between these two z-scores. This represents the percentage of students who scored between 80 and 90.

Using a standard normal distribution table or calculator, we can find that the area between -0.3333 and -0.1667 is approximately 0.1210 or 12.1%.

Therefore, approximately 12.5% of the students could be expected to score between 80 and 90.

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Answer:

5+5=10

Step-by-step explanation:

5+5=10

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Answer:

Answers is D

Step-by-step explanation:

2x = 60° because they are vertically opposite angles.

x=60÷2=30°

Answer:

[tex]x = \frac{20}{ \sqrt{3} } \\ y = \frac{40}{ \sqrt{3} } [/tex]

Step-by-step explanation:

[tex]for \: \: x \\ \tan(60) = \frac{20}{x} \\ \sqrt{3} = \frac{20}{x} \\ x = \frac{20}{ \sqrt{3} } \\ \\ for \: y \: \\ \sin(60) = \frac{20}{y} \\ \frac{ \sqrt{3} }{2} = \frac{20}{y} \\ \sqrt{3} \: y = 20 \times 2 \\ y = \frac{40}{ \sqrt{3} } [/tex]

I hope that is useful for you :)

Answer:

1. 1/4

2. 43/10 or 4 3/10 either are correct.

3. 67/12 or 5 7/12 either are correct.

Step-by-step explanation:

I hope this helped.

Answer:

If you add teacher plus students which is 490+10=500

you get 500 people in total after that you divide 500 by 50 and you get 10 so you will need 10 busses in total hope this helped!

Step-by-step explanation:

I will come back to this question when it has been further clarified.

(Honestly I just really need to delete this answer since I misread the question but it doesn't give me an option to delete it).

Answer:

- 22719559.

Step-by-step explanation:

Answer:

y=4x+2

Step-by-step explanation: