The radius of convergence of the power series representation of 10x f(x)= = 11 x+9 11 is R= Flo 9 Select one: True O False The interval of convergence of the power series Σ xn+1 n=o n24" is (-4,4].
Answers
The radius of convergence R for the power series representation of f(x) is R = 1.
The radius of convergence of a power series can be determined using the ratio test. For the power series representation of f(x) = Σ(10x^n)/(11^n+9), we need to apply the ratio test to find the radius of convergence.
Using the ratio test, we compute the limit as n approaches infinity of the absolute value of the ratio of consecutive terms:
lim(n→∞) |(10x^(n+1))/(11^(n+1)+9)| / |(10x^n)/(11^n+9)|
Simplifying the expression, we have:
lim(n→∞) |10x^(n+1)(11^n+9)| / |10x^n(11^(n+1)+9)|
Canceling out the common terms, we get:
lim(n→∞) |x(11^n+9)| / |(11^(n+1)+9)|
Taking the absolute value of x outside the limit, we have:
|x| * lim(n→∞) |(11^n+9)| / |(11^(n+1)+9)|
Now, as n approaches infinity, the terms (11^n+9) and (11^(n+1)+9) both grow exponentially, and their ratio approaches 11/11 = 1.
Thus, the limit simplifies to:
|x| * 1 = |x|
Therefore, the radius of convergence R for the power series representation of f(x) is R = 1.
Regarding the statement "The interval of convergence of the power series Σ xn+1 n=0 n^2/4 is (-4,4]," it is false. The interval of convergence cannot be determined solely based on the given series. Further information or calculations are needed to determine the actual interval of convergence.
Learn more about radius of convergence here:
https://brainly.com/question/32087701
#SPJ11
Related Questions
what is the confidence coefficient when the level of significance is 0.03? A. 0.0376
B. 0.7924
C. 0.9700
D. 0.7776
Answers
In thsi question, the confidence coefficient when the level of significance is 0.03 is C. 0.9700.
In statistics, the confidence coefficient is the complement of the level of significance (α) used in hypothesis testing. The confidence coefficient represents the confidence level or the degree of certainty associated with a confidence interval.
The level of significance, denoted by α, is the probability of rejecting the null hypothesis when it is true. It is typically chosen before conducting a statistical test and determines the critical value or the cutoff point for decision-making.
To find the confidence coefficient, we subtract the level of significance from 1. In this case, the level of significance is 0.03. Subtracting 0.03 from 1 gives us a confidence coefficient of 0.97, which can be written as 0.9700 when rounded to four decimal places.
Therefore, the correct answer is C. 0.9700, which represents the confidence coefficient when the level of significance is 0.03.
Learn more about confidence coefficient here:
brainly.com/question/28545662
#SPJ11
The perimeter of a square is 28 cm.
a) Write an equation you can solve to find
the side length of the square.
b) Solve the equation.
Answers
28/4. all sides of a square are equal. there are four sides of a square…
If
(
m
2
−
1
)
2
−
9
is expressed as
(
m
2
+
2
)
(
n
+
p
)
(
n
−
p
)
, what are the values of
n
and
p
?
Answers
Answer:
you need to repost your question bcos it's not understandable
Magnetism: So I need help on this question but please explain how you got the answer so I can learn and better provide evidence :) If you are able to answer this I also am putting a few questions on here for this similar subject for my test and pls explain them all ty!
Answers
Step-by-step explanation:
A) as you can see there is no current flowing in a bar magnet so (incorrect)
B) Lines of magnetic field is going in A-->B direction so it have starting and ending points.(incorrect)
C) Yes whenever a magnetic object is placed near the another magnetic object they either attract or repell so they have a force in a form of push and pull [correct]
D)No because magnetic field lines goes from North--> South so A is the South pole [ incorrect]
E) Yes it will point always towards North pole of the magnet [correct]
F) yes it depends upon the density of field lines[correct]
G)No the near the magnet is it becomes more stronger as compared to magnet kept far.(incorrect)
So option C E F are correct
Hope this helps
Have a great day
What is a acute triangle and what do a acute triangle look like?
Answers
Answer:
An acute triangle is a triangle with three acute angles. An obtuse triangle is a triangle with one obtuse angle and two acute angles. Since a triangle's angles must sum to 180° in Euclidean geometry
the waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 8 minutes. find the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.
Answers
The probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is 0.5278
The uniform distributed between a and b minutes.
The probability of finding a value above x is:
P(X > x) = \(\frac{b-x}{b-a}\)
The time is evenly distributed between 0 and 9 minutes.
This implies that a=0 , b=9
Determine the likelihood that a randomly selected passenger will have to wait longer than 4.25 minutes.
p(X > 4.25) = \(\frac{9-4.25}{9-0}\)
= 0.5278
There is a 52.78% chance that a randomly selected passenger will have to wait longer than 4.25 minutes.
To learn more about Probability:
https://brainly.com/question/11234923
#SPJ4
what percentage of the variation in productivity is explained by the quadratic regression model?
Answers
Depends on the specific data and coefficients of the quadratic regression model used.
The coefficient of determination, denoted as R-squared (R2), is used to calculate the percentage of variation in productivity explained by the quadratic regression model. R-squared is a statistical measure that represents the proportion of the variance explained by an independent variable or variables in a regression model for a dependent variable.
R-squared is calculated by comparing the total sum of squares (TSS) and the residual sum of squares (RSS):
TSS = Σ(y - ȳ)^2
RSS = (y - - x - b*x2)2.
where y is the actual productivity value, is the mean of the productivity values, x is the independent variable, and b are the quadratic regression model coefficients.
R-squared can be calculated using the formula:
R2 = 1 minus (RSS/TSS)
We can then convert R-squared to a percentage to get the percentage of variation in productivity explained by the quadratic regression model.
As a result, the answer to this question is dependent on the specific data and quadratic regression model coefficients used.
To know more about Quadrilateral visit:
brainly.com/question/12131358
#SPJ1
i need help on this assignment
Answers
u will provide best content on the brainly app
suppose f € c([a, b]) and p1,..., pn € (a,b) are given. prove that there exists a point
Answers
There exist points c1, c2, ..., cn in [a, b] such that f(c1) = f(p1), f(c2) = f(p2), ..., f(cn) = f(pn). f is continuous on [a, b], g is continuous on [a, b] as well.
To prove the statement, we will use the intermediate value theorem. Consider the function g(x) = f(x) - f(p1). Since f is continuous on [a, b], g is continuous on [a, b] as well.
Now, we have g(p1) = f(p1) - f(p1) = 0. Also, g(a) = f(a) - f(p1) and g(b) = f(b) - f(p1). Without loss of generality, assume that g(a) ≤ 0 and g(b) ≥ 0. (If not, swap a and b.)
Since g is continuous on [a, b] and g(a) ≤ 0 ≤ g(b), there exists a point c in [a, b] such that g(c) = 0. That is, f(c) - f(p1) = 0, or f(c) = f(p1). Therefore, we have found a point c in [a, b] such that f(c) = f(p1).
Repeating this argument for p2, p3, ..., pn, we can find points c2, c3, ..., cn in [a, b] such that f(c2) = f(p2), f(c3) = f(p3), ..., f(cn) = f(pn).
Therefore, we have proved that there exist points c1, c2, ..., cn in [a, b] such that f(c1) = f(p1), f(c2) = f(p2), ..., f(cn) = f(pn).
Learn more about continuous here
https://brainly.com/question/17141874
#SPJ11
Rewrite the expression using the division symbol and as a fraction. The quotient of m and 11
Answers
M÷11 M/11
Step-by-step explanation:
when you find the quotient you divide so when you divide with a fraction you take what number you were given first and out it on top of the number you were given second
Goaladinho recorded the scorers of the 60 goals scored
by his team during an entire season.
He then started to draw a pie chart to show the results.
Rotaldo
Goaladinho
Sheaver
a) How many goals did Goaladinho score?
54
(0)
Roofy
Bectam
b) The table below shows the other players who scored goals for the team.
Name of scorer Number of goals Angle
Roofey
22
132
(i) Complete the table. (3)
Bectam
3
Sheaver
54
(1) Complete the pie chart.
121
Rotaldo
Active
MathWatch L.
Terms & Conditions Privacy Policy
Develo
Type here to search
Answers
Answer:
See attached image:
Step-by-step explanation:
I believe this is the question, you are looking for.
Hope this helps.
Wich ratio is equivalent to 4:5
A 10/15
B 4/10
C 16/20
D 15/8
Answers
Answer:
16/20
Step-by-step explanation:
4:5
Multiply each side by 4
4*4: 5*4
16:20
16/20
Answer:
The answer is C. 16/20.
Step by step explanation:
This is because if you were to multiply 4 and 5 by 4, you would get 16/20. That means that both ratios are the same. Hope this helps! :)
a circle has a circumference of 15 pi. what is the area of pi
Answers
Answer:
= 112.5π sq. units is the area of pi
Step-by-step explanation:
In your case it's 15π
So that becomes:
2πr=15π
Now dividing the equation on both sides by π,the result is:
2r=15
That means 2 times radius(r) is 15
r=15/2
r computes out to be 7.5
Now r=7.5
So the area of circle(AoC) i.e. πr^2
AoC=3.14*(7.5)^2
AoC=3.14*(7.5)*(7.5)
AoC=176.625
Note: Don't forget to multiply the result to respective unit square for e.g. if the circumference was 15π in cm then the Area would compute out as 176.625 cm^2
may be helpful to your discussion.
7. Here's how Mo solved the subtraction problem
635 - 813:
635
- 813
- 222
Mo did this by working from right to left, saying
5 – 3 = 2
3 - 1 = 2
6 - 8 = -2
a. Is Mo's answer right?
b. Solve
6(100) + 3(10) + 5(1)
- [8(100) + 1(10) + 3(1)]
by working with expanded forms. Discuss how
Mo's work compares with your work in expanded
forms.
Answers
Answer:
Mo's answer is wrong.
635 - 813
= -178
Step-by-step explanation:
a. Is Mo's answer right?
No, Mo's answer is incorrect
Mo did this by working from right to left, Just like Subtraction
• 3 - 5 =
We that 1 from the number in tens , add that to 3, making it 13
13 - 5 = 8
• 1 - 3 = 7
The one above becomes 0, because 1 was taken from it. We add 1 to 0, making it 10
10 - 3 = 7
• 8 - 6 = 1
The 8 above reduces to 7 because 1 has been taken from 8.
Hence: 7 - 6 = 1
635 - 813
= -178
The answer is minus 178 because, we are subtracting the bigger number form the smaller number.
b. Solve
6(100) + 3(10) + 5(1)
- [8(100) + 1(10) + 3(1)]
by working with expanded forms. Discuss how Mo's work compares with your work in expanded forms.
= -1(100) + 7(10) + 8(1)
Match a recursive formula for the graph and identify the sequence as arithmetic or geometric.
Graph of a sequence
Arithmetic, t0=15
and tn=2.8+tn−1
where n≥1
.
Geometric, t0=15
and tn=2.8⋅tn−1
where n≥1
.
Arithmetic, t0=15
and tn=2.8⋅tn−1
where n≥1
.
Geometric, t0=15
and tn=2.8+tn−1
where n≥1
.
Answers
The recursive formula in this case is;
Arithmetic, t0=15
and tn=2.8+tn−1
where n≥1
Option A
What is a recursive formula?A recursive formula is a formula that defines a sequence of values in terms of its previous values. It provides a way of defining a sequence in a compact form, with each term of the sequence depending on one or more preceding terms.
In mathematics, recursive formulas are often used to define sequences. We can see that in this sequence, the first term is 15 and the common difference is obtained by simple subtraction .
Learn more about recursive formula:https://brainly.com/question/8972906
#SPJ1
Parrel lines and angles how do I do this one
Answers
Answer:
Step-by-step explanation:
if two lines are parallel and a transversal cuts it,then corresponding angles are equal.
?=130°(corresponding angles)
Find the rate of change of y with respect to x if dy dx x²y-5+2 ln y = x³
Answers
The rate of change of y with respect to x is given by dy/dx = xy - (3/2)x²y.
To find the rate of change of y with respect to x, we need to differentiate the given equation. The rate of change can be determined by taking the derivative of both sides of the equation with respect to x.
First, let's differentiate each term separately using the rules of differentiation.
Differentiating x²y with respect to x gives us 2xy using the product rule.
To differentiate 5, we know that a constant has a derivative of 0.
Differentiating 2ln(y) with respect to x requires the chain rule. The derivative of ln(y) with respect to y is 1/y, and then we multiply by dy/dx. So, the derivative of 2ln(y) is 2/y * dy/dx.
Differentiating x³ gives us 3x² using the power rule.
Now, we can rewrite the equation with its derivatives:
2xy - 2/y * dy/dx = 3x²
To solve for dy/dx, we can isolate it on one side of the equation. Rearranging the equation, we get:
2xy = 2/y * dy/dx + 3x²
To isolate dy/dx, we move the term 2/y * dy/dx to the other side:
2xy - 2/y * dy/dx = 3x²
2xy = 2/y * dy/dx + 3x²
2/y * dy/dx = 2xy - 3x²
Now, we can solve for dy/dx by multiplying both sides by y/2:
dy/dx = (2xy - 3x²) * (y/2)
Simplifying further, we have:
dy/dx = xy - (3/2)x²y
To know more about rate of change, refer here:
https://brainly.com/question/29181688#
#SPJ11
343^2x-5=49^x/2 solve for x
Answers
Answer:
Step-by-step explanation:
We can start by simplifying the expression using the laws of exponents:
343^(2x) * 49^(-x/2) = 49^(x/2)
We can then simplify further by expressing everything in terms of 7 (since 7 is the common factor of both 343 and 49):
(7^3)^(2x) * (7^2)^(-x/2) = (7^2)^(x/2)
Applying the laws of exponents again, we get:
7^(6x) * 7^(-x) = 7^x
7^(6x - x) = 7^x
7^(5x) = 7^x
Now we can solve for x by equating the exponents on both sides:
5x = x
4x = 0
x = 0
Therefore, the solution to the equation is x = 0.
Answer:
x = 0
Step-by-step explanation:
343^(2x) * 49^(-x/2) = 49^(x/2)
(7^3)^(2x) * (7^2)^(-x/2) = (7^2)^(x/2)
7^(6x) * 7^(-x) = 7^(x)
Now, we can simplify the equation further by combining the like terms on both sides:
7^(6x - x) = 7^(x)
7^(5x) = 7^(x)
We can solve for x by equating the exponents on both sides of the equation:
5x = x
4x = 0
x = 0
Therefore, the solution to the equation is x = 0.
What is the image of ( 3 , − 2 ) after a reflection over the line y = x?
Answers
Answer:
(2,-3)
Step-by-step explanation:
When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and the signs are changed.
(-2, 3)
Solution:Remember, when you reflect a point over the line y=x, the x- and y-coordinates switch places.So if we had a point with the following coordinates: (4, 5) and we reflected it over the line y=x, then the coordinates of the point are (5, 4)Therefore, if we take a point (3,-2) and reflect it over the line y=x, then the coordinates of the point are now (-2, 3)Hope it helps.
Do comment if you have any query.
Question 2
Help
Meeeeeeeeeeeeeee
Answers
Answer:
black screen
Step-by-step explanation:
this is a black screen
40 is 50% of what number?
A. 20
B. 40
C. 60
D. 80
Answers
Answer:
D. 80
Step-by-step explanation:
multiply 40 by 2 cause its 50 percent
Answer:
80
Step-by-step explanation
50% is half
So 40+40=80
80/2=40
the value of the is used to estimate the value of the population parameter. a. population statistic b. population estimate c. sample statistic d. sample parameter
Answers
The value that is used to estimate the value of the population parameter is the sample statistic. Hence, option (c) is the correct answer.
A sample statistic is a piece of statistical information that is obtained from a fraction of the population. Just as its name suggests, it is computed from our sample data to help provide us insight into the population parameters.
A sample is a fraction of a given population. Once one has a sample, one can calculate various statistics about the sample, like median, average, or deviation. This can help one draw inferences about large populations using small samples.
A sample statistic is a random variable. Thus, it has an associated probability distribution, called the sampling distribution. The nature of the sampling distribution is essential in determining the properties of the sample statistic.
Learn more about sample statistics:
brainly.com/question/28165409
#SPJ4
Consider the graph of the function f(x)=logx.
Match each transformation of function f with a feature of the transformed function.
Answers
Transformation of function f with a feature of the transformed function.
g(x)=-f(x-3) is vertical asymptote of x=3j(x)= f(x+3) is x-intercept of (-2,0)h(x)=3f(x)-3 is domain of (0, ∞)What is asymptote?An asymptote is a line that the graph of a function approaches as either x or y go to positive or negative infinity. There are three types of asymptotes: vertical, horizontal and oblique
Given function is : f(x)= log x
g(x)= -f(x+3)= - log(x+3)g(x)=-f(x-3) is vertical asymptote of x=3
j(x)= f(x+3) = log (x+3) thenj(x)= f(x+3) is x-intercept of (-2,0)
Domain: As (0,∞),{x | x>0}h(x)=3f(x)-3 is domain of (0, ∞)
Learn more about asymptote here:
https://brainly.com/question/4084552
#SPJ2
Answer:
Step-by-step explanation:
Find an equation of the line that passes through the point (2, -8) and is perpendicular to the line 2x-6y=10
Answers
9514 1404 393
Answer:
3x +y = -2
Step-by-step explanation:
First of all, it is helpful to put the given equation in standard form. We can do that by dividing it by 2 to eliminate the common factor from the numbers.
x -3y = 5
Next, since you want the perpendicular line, you can swap the coefficients of x and y, and negate one of them. This can give you ...
3x +y = (some constant)
The constant will be found using the given point.
3x +y = 3(2) +(-8) = -2 . . . the perpendicular line
An equation is ...
3x +y = -2
9. At a clothing store, a pair of jeans costs $40. Using a coupon, Shanice is
able to pay $10 less than the original price.
Determine the percentage off the original price the coupon represents.
Show your work in the space provided. Then, complete the statement.
Work
The coupon gives Shanice
off of the original price.
_%
Answers
The coupon give Shanice 75 percent off the original price of the pair of jeans.
How to find the percentage of the original price of a goods?At a clothing store, a pair of jeans costs $40. Using a coupon, Shanice is
able to pay $10 less than the original price. Therefore, the percentage off the original price the coupon represents can be calculated as follows:
Therefore,
Price Shanice bought the jeans = 40 - 10 = 30 dollars
Hence,
let
x = percentage off the original price
Therefore,
x / 100 × 40 = 30
40x / 100 = 30
cross multiply
3000 = 40x
divide both sides by 40
x = 3000 / 40
x = 75%
Therefore, the coupon gives Shanice 75% off of the original price.
learn more on percentage here: https://brainly.com/question/29992861
#SPJ1
Last year, there were “x” students in the Math Club, but this year, there was a 40% increase in membership. Represent this year’s membership in terms of “x”.
Answers
Answer:
(x)1.4=Y
Step-by-step explanation:
40% increase of memeber so ita 140% of X
computer time. it take a computer 8 days to print all of the personalized letters for a national sweepstakes. a new computer is purchased that can do the same job in 5 days. how long would it take to do the job with both computers working on it
Answers
Work is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.
To determine the number of days it would take two computers to print personalized letters, the formula to use is given as follows:
1/Total Work = 1/Work of Computer A + 1/Work of Computer B
= 1/TimeTaken
In this question, Computer A takes 8 days to do the job, and Computer B takes 5 days to do the job.
Therefore, 1/Total Work = 1/8 + 1/5 = 0.25
Therefore, the total work would be equal to 1/0.25, which is equal to 4 days.
Therefore, it would take four days to complete the job with both computers working on it.
To learn more about “total work” refer to the https://brainly.com/question/24900258
#SPJ11
a bacteria culture doubles in size every 8 hours. the culture starts with 150 cells. what function models this situation?
Answers
The function model for a bacteria culture that doubles in size every 8 hours is A(t) = 150*2^(t/8)
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
Information about the problem:
A(0) = 150 cellsDoubles in size = 2Hours = 8The function that models the situation is the following:
A(t) = A(0)*2^(t/8)
A(t) = 150*2^(t/8)
Where A(0) is the culture start and t is the time passed.
Learn more about equation at: brainly.com/question/2972832 and brainly.com/question/27815607
#SPJ4
What kind of triangle is this please help me find the relationship and value please.
Answers
Answer: x=14°
Step-by-step explanation:
All angles of a triangle added together is 180°. So we can add the angles together.
7x-11+5x-2+2x-3=180 [combine like terms]
14x-16=180 [add both sides by 16]
14x=196 [divide both sides by 14]
x=14
Therefore, x=14°.
A bolt manufacturer is very concerned about the consistency with which his machines produce bolts. The bolts should be 0.2 centimeters in diameter. The variance of the bolts should be 0.025. A random sample of 15 bolts has an average diameter of 0.21 cm with a standard deviation of 0.1587. Can the manufacturer conclude that the bolts vary by more than the required variance at α=0.01 level? Step 1 of 5: State the hypotheses in terms of the standard deviation. Round the standard deviation to four decimal places when necessary. A bolt manufacturer is very concerned about the consistency with which his machines produce bolts. The bolts should be 0.2 centimeters in diameter. The variance of the bolts should be 0.025. A random sample of 15 bolts has an average diameter of 0.21 cm with a standard deviation of 0.1587. Can the manufacturer conclude that the bolts vary by more than the required variance at α=0.01 level? Step 2 of 5: Determine the critical value(s) of the test statistic. If the test is twotailed, separate the values with a comma. Round your answer to three decimal places. A bolt manufacturer is very concerned about the consistency with which his machines produce boits. The bolts should be 0.2 centimeters in diameter. The variance of the boits should be 0.025. A random sample of 15 bolts has an average diameter of 0.21 cm with a standard deviation of 0.1587. Can the manufacturer conclude that the bolts vary by more than the required variance at α=0.01 level?
Answers
To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).
Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.
Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).
If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.
To learn more about Hypothesis test - brainly.com/question/29996729
#SPJ11
To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).
Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.
Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).
If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.
To learn more about Hypothesis test - brainly.com/question/29996729
#SPJ11