Find a power series representation for the function. (Give your power series representation centered at x = 0.)
f(x) = x2 x 4 + 81
f(x) = [infinity] n = 0.

Answers

Answer 1

Answer:

attached below

Step-by-step explanation:

The Function; F(x) = x^2 / (x^4 + 81 )

power series representation

F(x) = x^2 / ( 81 + x^4 )

      = ( x^2/81 ) / 1 - ( -x^4/81 )

attached below is the remaining part of solution

Find A Power Series Representation For The Function. (Give Your Power Series Representation Centered

Related Questions

what is the inverse of the function shown

Answers

Step-by-step explanation:

the down function clearly is

y = x - 5, -2 <= x <= 8

the reasons :

1. it is linear. so, we have only a form of ax+b

2. x=0 => y=-5

x=5 => y=0

so, with these 2 points alone we can see

y = ax + b

-5 = a×0 +b = b

0 = a×5 - 5

5 = a×5

1 = a

the inverse function is based on

y = x - 5

=>

x = y + 5

now renaming the variables so that y is the result and x the input variable delivers

y = x + 5

and because the original function only delivered y- values between -7 and +3, this is also the defined domain for the inverse function.

so,

y = x + 5, -7 <= x <= +3

so, we have the points

x=-7 => y=-2

x=+3 => y=8

you need to draw the line between these 2 points with filled dots at the end points (as they are included in the function).

There are 92 students enrolled in an French course and 248 students enrolled in a Spanish course. Construct a ratio comparing students enrolled in a French course to students enrolled in a Spanish course. Write your answer as a decimal, rounded to the thousandths place.

Answers

Answer:

0.371

Step-by-step explanation:

The ratio comparing students enrolled in a French course to students enrolled in a Spanish course rounded to the thousandths place is 0.371.

What is the ratio?

A ratio indicates how many times one number contains another. If a and b are to objects then ratio of a to the b is given as a : b.

Now it is given that,

Students enrolled in a French course = 92

Students enrolled in a Spanish course = 248

So, Ratio comparing students enrolled in a French course to students enrolled in a Spanish = Students enrolled in a French course / Students enrolled in a Spanish course

Ratio comparing students enrolled in a French course to students enrolled in a Spanish = 92/248

Ratio comparing students enrolled in a French course to students enrolled in a Spanish = 0.370967

To rounded to the thousandths place, the digit at the thousandth place is 0 and right to it is 9 which is greater than 5 so round up the place value at thousandths place.

Ratio comparing students enrolled in a French course to students enrolled in a Spanish = 0.371

Thus, the ratio comparing students enrolled in a French course to students enrolled in a Spanish course rounded to the thousandths place is 0.371.

To learn more about ratio:

https://brainly.com/question/1504221

#SPJ2


Now actually compute 2 - 8

Answers

Answer:

the answer is -6. you just subtract 2 with 8

You want to buy a $203,000 home. You plan to pay 10% as a down payment, and take out a 30 year loan for the rest. or a) How much is the loan amount going to be? $ b) What will your monthly payments be if the interest rate is 6%? $ c) What will your monthly payments be if the interest rate is 7%?​

Answers

Answer:

The amount of the loan is going to be $ 182,700, and the monthly payments, if the interest is 6%, are going to be $ 537.95, while if the interest is 7%, are going to be $ 543.02.

Step-by-step explanation:

Given that you want to buy a $ 203,000 home, and you plan to pay 10% as a down payment, and take out a 30 year loan for the rest, for A) determine how much is the loan amount going to be, B) determine what will your monthly payments be if the interest rate is 6%, and C) determine what will your monthly payments be if the interest rate is 7%, the following calculations must be made:

A) 100 - 10 = 90

203,000 x 0.90 = X

182,700 = X

B) (182,700 x 1.06) / (30 x 12) = X

193,662 / 360 = X

537.95 = X

C) (182,700 x 1.07) / (30 x 12) = X

195,489 / 360 = X

543.025 = X

Therefore, the amount of the loan is going to be $ 182,700, and the monthly payments, if the interest is 6%, are going to be $ 537.95, while if the interest is 7%, are going to be $ 543.02.

The three methods used to classify costs into their fixed and variable components includes:_____.
a. high-low method.
b. scatter diagrams.
c. most-squares regression.
d. least-squares regression.
e. variable-fixed method.

Answers

Answer:

a. high-low method.

b. scatter diagrams.

d. least-squares regression.

Step-by-step explanation:

Costing is a measurement of the cost of production of goods and services by assessing the fixed costs and variable costs associated with each step of production.

Fixed cost can be defined as predetermined expenses in a business that remain constant for a specific period of time regardless of the quantity of production or level of outputs. Some examples of fixed costs in business are loan payments, employee salary, depreciation, rent, insurance, lease, utilities etc.

On the other hand, variable costs can be defined as expenses that are not constant and as such usually change directly and are proportional to various changes in business activities. Some examples of variable costs are taxes, direct labor, sales commissions, raw materials, operational expenses etc.

In Financial accounting, the three methods used to classify costs into their fixed and variable components includes high-low method, scatter diagrams and least-squares regression.

The high-low method is a quick and easy way to estimate costs by using historical accounting information from a range of reporting periods.

A scatter diagram (scattergraph) estimate costs by considering all the data points and not just the lowest or highest point.

A least squares regression line is a standard technique in regression analysis used to make the vertical distance obtained from the data points running to the regression line to become very minimal or as small as possible.

Generally, the sum of the residuals of a least squares regression line is always equal to zero.

Answer:

a. high-low method.

b. scatter diagrams.

d. least-squares regression.

Step-by-step explanation:

The three methods used to classify costs into their fixed and variable components includes:

high-low method.

scatter diagrams.

least-squares regression.

A modified roulette wheel has 36 slots. One slot is​ 0, another is​ 00, and the others are numbered 1 through 34​, respectively. You are placing a bet that the outcome is an even number.​ (In roulette, 0 and 00 are neither odd nor​ even.) a. What is your probability of​ winning?

Answers

Answer:

[tex]P(win) = 0.4722[/tex]

Step-by-step explanation:

Given

[tex]n = 36[/tex] --- slots

[tex]Even = 17[/tex] i.e. even numbers between 1 and 34 (inclusive)

Required

[tex]P(win)[/tex]

The probabiity of winning is the number of even numbers divided by the total slot;

i.e.

[tex]P(win) = \frac{Even}{n}[/tex]

So, we have:

[tex]P(win) = \frac{17}{36}[/tex]

[tex]P(win) = 0.4722[/tex]

Two groups were moving from one campsite to another. The first group traveled the distance in 5 hours. The second group finished in 7 hours. Find the distance between the campsites if the first group was going 4mph faster than the second group.

Answers

Answer:

The distance between the campsites was 70 miles.

Step-by-step explanation:

Since two groups were moving from one campsite to another, and the first group traveled the distance in 5 hours while the second group finished in 7 hours, to find the distance between the campsites if the first group was going 4mph faster than the second group, the following calculation must be performed:

X + 4 = 5

X = 7

4 x 7 = 28

(4 + 4) x 5 = 40

10 x 7 = 70

(10 + 4) x 5 = 70

Therefore, the distance between the campsites was 70 miles.

What is the value of the function when x = -2 in the
piecewise function
g(x) =
3x when x > 1
-2x when x <1

Answers

Answer:

[tex]g(2) = 6[/tex]

Step-by-step explanation:

Given

[tex]g(x) = 3x[/tex] --- [tex]x > 1[/tex]

[tex]g(x) = -2x[/tex] -- [tex]x < 1[/tex]

Required

[tex]g(2)[/tex]

[tex]2 > 1[/tex]

So, we use:

[tex]g(x) = 3x[/tex]

Substitute [tex]2[/tex] for x

[tex]g(2) = 3 * 2[/tex]

[tex]g(2) = 6[/tex]

Answer:g(-2)=4

Step-by-step explanation:

Since x = -2, use the piece of the function when x ≤ 1. Therefore, use g(x) = -2x and substitute -2 in for x to get g(-2) = -2(-2), which simplifies to g(-2) = 4.

The amount of tax on a chair was $3.60. The tax rate was 5%. Find the original price of the chair.

Bianca solved the problem below. Find Bianca’s error.

0.05(3.60) = Original price

The original price is $0.18.

Answers

9514 1404 393

Answer:

  $72.00

Step-by-step explanation:

The relationship between price and tax is ...

  tax amount = (tax rate) × (price)

Then the price can be found by dividing by the tax rate:

  price = (tax amount)/(tax rate)

  price = $3.60 / 0.05 = $72.00

The original price of the chair was $72.00.

__

Bianca apparently did not pay any attention to the way tax is computed. Nor did she check her work. The original price is not a small fraction of the tax. It is the other way around. Bianca used a wrong relationship between tax and price.

Which table represents a direct variation function?

Answers

9514 1404 393

Answer:

  (b)  the correct table is marked

Step-by-step explanation:

Direct variation is characterized by the ratio of y to x being a constant for all values in the table. That constant is the constant of proportionality. For the values in the second table (marked), the ratio is ...

  y/x = 8/6 = 12/9 = 16/12 = 4/3

The constant of proportionality is 4/3.

Rewrite in simplest terms: (9x+5)-(-2x+10)(9x+5)−(−2x+10) . Someone please help me

Answers

Answer:

18x^(2)-69x-55

Step-by-step explanation:

dont have the time to rn

Answer:

[tex]{ \bf{(9x + 5) - ( - 2x + 10)(9x + 5) - ( - 2x + 10)}} \\ = { \tt{(9x + 5) - ( - {18x}^{2} + 80x + 50) - ( - 2x + 10)}} \\ = { \tt{(9 - 80 + 2)x + {18x}^{2} + 5 - 50 - 10 }} \\ = { \tt{ {18x}^{2} - 69x - 55}}[/tex]

1.3 hectoliters is how many liters

Answers

Answer: 130 liters

Step-by-step explanation:

1 hectoliter = 100 liters

1.3 hectoliters = 1.3 · 100 = 130 liters

Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 83% of all defectives that are present, and the second inspector does likewise. At least one inspector does not detect a defect on 34% of all defective components. What is the probability that the following occur

Answers

Complete question is;

Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 83% of all defectives that are present, and the second inspector does likewise. At least one inspector does not detect a defect on 34% of all defective components. What is the probability that the following occurs?

(a) A defective component will be detected only by the first inspector?

b) A defective component will be detected by exactly one of the two inspectors?

(c) All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)?

Answer:

A) 0.17

B) 0.34

C) 0

Step-by-step explanation:

a) We are told that the first inspector(A) detects 83% of all defectives that are present, and the second inspector(B) also does the same.

This means that;

P(A) = P(B) = 83% = 0.83

We are also told that at least one inspector does not detect a defect on 34% of all defective components.

Thus;

P(A' ⋃ B') = 0.34

Also, we now that;

P(A ⋂ B) = 1 - P(A' ⋃ B')

P(A ⋂ B) = 1 - 0.34

P(A ⋂ B) = 0.66

Probability that A defective component will be detected only by the first inspector is;

P(A ⋂ B') = P(A) - P(A ⋂ B)

P(A ⋂ B') = 0.83 - 0.66

P(A ⋂ B') = 0.17

B) probability that a defective component will be detected by exactly one of the two inspectors is given as;

P(A ⋂ B') + P(A' ⋂ B) = P(A) + P(B) - 2P(A ⋂ B)

P(A) + P(B) - 2P(A ⋂ B) ; 0.83 + 0.83 - 2(0.66) = 0.34

C) Probability that All three defective components in a batch escape detection by both inspectors is written as;

P(A' ⋃ B') - (P(A ⋂ B') + P(A' ⋂ B))

Plugging in the relevant values, we have;

0.34 - 0.34 = 0

if x+y=12 and xy =27,then find the value of x^2+y^2
PLEASE HELP !​

Answers

Answer:

90

Step-by-step explanation:

=> x + y = 12

=> x² + y² + 2xy = 144

=> x² + y² + 2 * 27 = 144

=> x² + y² = 144 - 54

=> x² + y² = 90

which of the following is the median of 19, 31, 15, 50, 20​

Answers

the answer would be 20

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

[tex]\large\text{19, 31, 15, 50, \& 20}[/tex]

[tex]\large\text{When you see or hear the word \underline{median}, think of the question}\\\large\text{asking you \bf what is the MIDDLE NUMBER.}\large\text{To find the}\\\large\text{middle number you have to put the numbers from descending}\\\large\text{(least/decreasing) or ascending (greatest/increasing) order}[/tex]

[tex]\large\text{15, 19, 20, 31, \& 20}[/tex]

[tex]\large\text{Make sure it is even on BOTH SIDES of the DATA SET}[/tex]

[tex]\large\text{It seems to be even on both sides of the number \bf 20}\large\text{ so \underline{20}}\\\large\text{can be your median/middle number in this given set}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Answer: the median is \bf 20}}}\huge\checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]

15. Dravid is a famous cricket player. He has
so far scored 6980 runs in the test matches.
He wishes to complete 10,000 runs: How
many more runs does he need? *
4020 runs
3220 runs
2820 runs
O 3020 runs

Answers

Answer:

3020 runs

Step-by-step explanation:

Because he wants 10000 but only has 6980 so you have to minus 6980 from 10000. 10000-6980=3020

so 3020 is the answer

Answer:

3020 runs

Step-by-step explanation:

10,000-6980=3020

A multiple regression model is ^Y = 8.114 + 2.005X1 + 0.774X2. Which of the following values is the estimate for the intercept parameter?
a. 0.774.
b. 8.114.
c. 1.000.
d. 2.005.

Answers

Answer:

B. 8.114

Step-by-step explanation:

The intercept parameter is the zero-grade component of the multilinear equation, that is, the component independent from [tex]x_{1}[/tex] and [tex]x_{2}[/tex]. Hence, the intercept parameter of the multilinear regression is 8.114. (Correct answer: B)

You are charged $9.33 total for a meal, assume the 7% sales tax, how much was the menu price of this item?

I have already tried
$8.68
$8.71
$8.67
all were wrong ​

Answers

Answer:

$8.71.

Step-by-step explanation:

Given that you are charged $ 9.33 total for a meal, assuming the 7% sales tax, to determine how much was the menu price of this item, the following calculation must be performed:

100 + 7 = 107

107 = 9.33

100 = X

100 x 9.33 / 107 = X

933/107 = X

8.71 = X

Therefore, the menu price of this item was $ 8.71.

The manager of a fast-food restaurant determines that the average time that her customers wait for service is 2.5 minutes. (a) Find the probability that a customer has to wait more than 4 minutes. (Round your answer to three decimal places.)

Answers

Answer:

0.758

explaination

using poisson distribution

0.08208+0.2052+0.2565+0.2138

0 .758

5. What is the value of x if the quadrilateral is a kite? B X+2 C С 13 A Xth12 D​

Answers

Answer: just had this problem! X = 11

Which problem has a greater (bigger) answer? Solve both, choose the one that has the bigger answer and explain (1-2 sentences) how you found your
answer.
1) (2 + 3) (5 + 5)
2)2 + 3 x 5 + 5 =



I need so much helppppp pleaseeeee

Answers

Answer:

Problem 1 has a greater answer.

Step-by-step explanation:

Solve problem 1 using the order of operatiobs PEMDAS (Parentheses, Exponents, multiplication/division, and addition/subtraction):

Multiplication/division depends from left to right of the expression, the same goes to addition/subtraction.

(2 + 3) (5 + 5)

= (5)(10)

= 50

SOLVE problem 2 using PEMDAS:

2 + 3 x 5 + 5

= 2 + 15 + 5

= 17 + 5

= 22

Answer 1 (50) compared to Answer 2 (22):

50 > 22

HOPE THIS HELPS!

Aaron used ordinary electrical wire to connect the lights around the new factory. He ended up using 3 entire spools of wire, which totaled 1,380 feet. What is the number of feet of wire contained on one spool, written as a ratio? Type your ratio using a : between the numbers

Answers

Answer:

There are 460 feet of wire contained on one spool.

Step-by-step explanation:

Since Aaron used ordinary electrical wire to connect the lights around the new factory, and I have ended up using 3 entire spools of wire, which totaled 1,380 feet, to determine what is the number of feet of wire contained on one spool, written as a ratio, the following calculation must be performed:

1380/3 = X

460 = X

So there are 460 feet of wire contained on one spool.

Convert the following to a simplified fraction. Show all your work.

Answers

Answer:

11/6

Step-by-step explanation:

Your friend is looking at laptops for college, and is comparing the different
screen sizes. Use the diagram and formula below to find the height of the
laptop screen. Round your answer to the tenths place.
d - VW
d= 72.7mn
h
W 026

Answers

Answer:

B. h = 7.4 inches

Step-by-step explanation:

height of the laptop screen = h

d = 12.1 in.

w = 9.6 in.

We are given the formula,

d = √(w² + h²)

Plug in the values and solve for h

12.1 = √(9.6² + h²)

Square both sides

12.1² = 9.6² + h²

146.41 = 92.16 + h²

146.41 - 92.16 = h²

54.25 = h²

√54.25 = h

7.4 = h (nearest tenth)

h = 7.4 inches

Suppose X and Y are two independent exponential variables. The mean of X is twice the mean of Y. If the probability of X exceeding 50 is 0.7788, what is the probability of Y exceeding 40

Answers

If X ~ Exponential(µ), then the mean of X is 1/µ. So if the mean of X is twice the mean of Y, then the mean of Y is 1/(2µ), so that Y ~ Exponential(2µ).

We're given that

P(X > 50) = 1 - P(X ≤ 50) = 1 - Fx (50) ≈ 0.7788

==>   Fx (50) = P(X ≤ 50) ≈ 0.2212

where Fx is the CDF of X, which is given for 0 ≤ x < ∞ to be

Fx (x) = 1 - exp(-µx)

Solve for µ :

1 - exp(-50µ) ≈ 0.2212   ==>   µ ≈ -ln(0.7788)/50 ≈ 0.005

Then we have

P (Y > 40) = 1 - P (Y ≤ 40) = 1 - Fy (40)

where Fy is the CDF of Y,

Fy (y) = 1 - exp(-2µy)

so that

P (Y > 40) ≈ 1 - exp(-2 × 0.005 × 40) ≈ 0.3297

Suppose that 20° of boys opted for mathematics and 40% of girls opted for mathematics. What is the probability that a student opted for mathematics if half of the class is girls?​

Answers

Answer: 30%

Step-by-step explanation:

Let A be the probability of a student opting for mathematics - it consists of either boy opting for mathematics or girl opting for mathematics. As there is "or" we need to sum these probabilities.

[tex]P(A) = P(B)* P(M|G) + P(G)*P(M|G)[/tex]

[tex]P(A) = \frac{1}{2} * \frac{20}{100} + \frac{1}{2} * \frac{40}{100}[/tex]

[tex]P(A) = 3/10 = 0.3[/tex]

=> 30%

Answer:

30% Chance

Step-by-step explanation:

This one is rather simple. If half the class is girls, split 40 into half. Do the same with 20 if half is boys. Add 10 and 20 and you get 30.

Please help ASAP. No links

Answers

Hello my dear friend of USA !!!

DB/AD = BE/EC

=> 6/4 = x+1/x

=> 6x = 4x + 4

=> 2x = 4

=> x = 2

So x = 2

I am from INDIA.

Lots of love ❤️!!!

Have a great day ahead!

Answer:

x = 2

Step-by-step explanation:

[tex]\frac{6}{4} = \frac{x+1}{x}[/tex]

6x = 4x + 4

2x = 4

x = 2

if a=(1 2 3 4) find A×A and the relation determined by (I) y=2x (II) x+y​

Answers

Answer:

HOPE IT HELPS PLZ MARK ME BRAINLIEST

Step-by-step explanation:

A={1,2,3,4,5,6}

R={(x,y):y is divisible by x}

We know that any number (x) is divisible by itself.

(x,x)∈R

∴R is reflexive.

Now,(2,4)∈R [as 4 is divisible by 2]

But,(4,2)∈ /

R. [as 2 is not divisible by 4]

∴R is not symmetric.

Let (x,y),(y,z)∈R. Then, y is divisible by x and z is divisible by y.

∴z is divisible by x.

⇒(x,z)∈R

∴R is transitive.

Hence, R is reflexive and transitive but not symmetric.

Create a quadratic equation in one variable of the form ax^2+bx+c=0 that meets the following criteria. A=1, b=0 , c=-100. 20 points.

Answers

Answer:

Equation is x^2-100=0

Step-by-step explanation:

I'm assuming everything is in standard form. Just plug in the values.

1(x)^2+(0)x+(-100)=0

0 times x is 0, so it simplifies to

x^2-100=0

PLSSSSSSSSSSSSS HELp VERY URGENT The graph of F(x), shown below, resembles the graph of G(x) = x^2, but it has been stretched somewhat and shifted. Which of the following could be the equation of F(x)?

Answers

Answer:

Option B

Step-by-step explanation:

Function 'g' is,

g(x) = x²

Since, leading coefficient of this function is positive, parabola is opening upwards.

From the graph attached,

Function 'f' is opening upwards leading coefficient of the function will be positive.

Since, the graph of function 'f' is vertically stretched, equation will be in the form of f(x) = kx²

Here, k > 1

Since, function 'f' is formed by shifting the graph of function 'g' by 1 unit upwards,

f(x) = g(x) + 1

Combining all these properties, equation of the function 'f' should be,

f(x) = 4x² + 1

Option B will be the correct option.

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