find a power series representation for the function. (give your power series representation centered at x = 0.) f(x) = 8 3 − x
Answers
The power series representation for f(x) centered at x = 0 is:
f(x) = \(8 + (8/3) * x + (8/9) * x^2 + (8/27) * x^3 + ...\)
To find a power series representation for the function f(x) = 8/(3 - x) centered at x = 0, we can use the geometric series expansion.
First, we need to rewrite the function in a form that resembles a geometric series. We can rewrite f(x) as follows:
f(x) = 8/(3 - x) = 8 * 1/(1 - (x/3))
Now, we have a geometric series with a common ratio of x/3. We can use the formula for the sum of a geometric series to find the power series representation:
Sum = a / (1 - r)
In this case, the first term "a" is 8, and the common ratio "r" is x/3. Applying the formula, we get:
f(x) = 8 * (1/(1 - (x/3)))
f(x) = 8 *\((1 + (x/3) + (x/3)^2 + (x/3)^3 + ...)\)
Expanding the series, we have:
f(x) = 8 *\((1 + x/3 + (x^2/9) + (x^3/27) + ...)\)
Therefore, the power series representation for f(x) centered at x = 0 is:
f(x) = 8 +\((8/3) * x + (8/9) * x^2 + (8/27) * x^3 + ...\)
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Related Questions
The percent of pure gold in 14-karat gold is about 58.3%. A 14-karat gold ring weighs 5.6 grams. About how many grams of pure gold are in the ring?
Answers
Answer:
1.044 ounces
Step-by-step explanation:
Given : One ounce of 14 karat gold = 0.58 ounce of pure gold.
i.e. Weight of pure gold in 1 ounce of 14 karat gold = 0.58 ounce of pure gold.
Then, Weight of pure gold in 1.8 ounces of 14 karat gold = 1.8 x (Weight of pure gold in 1 ounce of 14 karat gold)
Weight of pure gold in 1.8 ounces of 14 karat gold = 1.8 x ( 0.58) ounces of pure gold.
It implies 1.8 ounces of 14 karat gold = 1.8 x ( 0.58) ounces of pure gold.
= 1.044 ounces of pure gold.
Therefore, If a 14 karat gold necklace weighs 1.8 ounces that means it contains 1.044 ounces of pure gold.
Find the value of x !!!!!
Answers
Answer:
91
Step-by-step explanation:
consecutive interior angles theorem states that the interior angles cut by a transversal are supplementary. That means they add up to 180. 180-89=91
The explicit formula for a sequence an = 5 – 7n . What is the value of a12?
Answers
Answer: its just 12 because a is just a variable
Step-by-step explanation: so like 5 - 7n its just 5 - 7 which in 2 so 12a is just 12
Answer:
-79
Step-by-step explanation:
an=5-7n This is the given equation
Now, we substitute 12 for n and do the equation
a(12)=5-7(12)
a(12)=5-84
a(12)=-79 This is our answer, negative 79
Which expression shows 7+21 written as a product of two factors?
(A)3(1+7)
(B)3(3+7)
(C)7(3+3)
(D)7(1+3)
Answers
Expressing or writing 7+21 as a product of two factors requires the application of Distributive Property
The expression that shows 7+21 written as a product of two factors is
7(1 + 3).
To solve the above question, we apply the Distributive property.This is expressed as:a (b + c) = ab + ac
Where
a is the common factor
We are given the expression:
7 + 21
Splitting this into two factors using the distributive property
7 + 21
The common factor for 7 and 21 is 7
Hence, by factorising we have:
7 + 21 = 7(1 + 3)
Therefore, the expression that shows 7+21 written as a product of two factors is :
7(1 + 3)
The correct option is D
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50 points!
Determine the degree measure of one angle of a 24-sided regular polygon.
a. 165°
b. 180°
c. 3,960°
d. 4,320°
Answers
Answer:
a. 165°Step-by-step explanation:
Sum of interior angles of n-sided polygon is:
Sₙ = 180°(n - 2)Substitute n with 24:
S₂₄ = 180°(24 - 2) = 180°(22) = 3960°Find measure of one interior angle:
3960°/24 = 165°Correct choice is a.
Answer: The answer is 165
Step-by-step explanation:
The number of triangles is 2 less than the number of sides.
The number of triangles multiplied by 180 equals the sum of the interior angles. This makes sense because each triangle has an angle sum of 180.
24-2 equals 22 times 180 equals 3,960 but were trying to find one angle so you would do 3,960 divided by 24 to get 165.
I also got it right on my test if you needed more conformation:)
if you answer right i’ll give you the brainliest
Answers
Answer: 3 and 4 are the answers
The parent of an underage client requests to see a sample of the questions on a standardized achievement test you are responsible for administering. Your best response would be to:
Answers
If a parent of an underage client requests to see a sample of the questions on a standardized achievement test that you are responsible for administering, your best response would be maintain professionalism, respect test policies, and address the parent's concerns.
If a parent of an underage client requests to see a sample of the questions on a standardized achievement test that you are responsible for administering, your best response would be to:
1. Explain the purpose of the test and how it is designed to assess the student's academic progress and achievement.
2. Inform the parent about test confidentiality policies and explain that sharing specific test questions may not be allowed to ensure test integrity and fairness.
3. Provide general information about the test format, content, and subject areas covered without disclosing actual questions.
4. Suggest resources, such as practice tests or sample questions that the test publisher might have released to the public, which can give the parent an idea of what the test might include.
5. Encourage the parent to discuss any concerns or questions they might have about the test and the testing process, and assure them that their child's well-being and success are of utmost importance.
By following these steps, you can maintain professionalism, respect test policies, and address the parent's concerns while also protecting the confidentiality and integrity of the standardized achievement test.
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I need help, pls answer.
Answers
Answer:
D the last one
Step-by-step explanation:
Answer:
I say D because new Orleans is closer to sea level than Salton Through
Step-by-step explanation:
Because ik it
find the value of 8 and 1/3
Answers
Answer:
(25/3) or 8.3333 . . . .
Step-by-step explanation:
We will assume this question want to know the sum of 8 and 1/3.
We could convert the (1/3) into a decimal format: 0.3333333 . . . and add the two:
8.3333333 . . . .
We could also kee the answer as a fraction:
6 = (24/3)
(24/3) + (1/3) = (25/3)
(25/3) is the same as 8.333333 . . .
A.If you deposit $10 into an empty bank account, and then withdraw $10 from the account, how much money is left in the account? B.. If you start at zero and add 7, then subtract 7, where do you end up?
Answers
Answer:
A. $0
B. 0
Step-by-step explanation:
A. If you deposit $10 in an empty bank account and you withdraw $10 from the account, the amount of money left in the account will be:
10 - 10 = $0
B. If you start at 0, add 7 and subtract 7, you'll end up at:
0 + 7 - 7 = 0
Rental of space = $68 per guest; Downpayment = 25% of total cost; Payment due one month before the reception includes a 7.4% interest payment on the balance.
Answers
This question is incomplete, the complete question is;
PROBLEM SOLVING WITH PERCENTS: You are planning a wedding reception for 75 guests that will take place in exactly 10 months. There are two different sites that you are contemplating using, with the stipulations on payments as described below. Determine the TOTAL cost of renting each location.
Rental of space = $68 per guest; Down payment = 25% of total cost; Payment due one month before the reception includes a 7.4% interest payment on the balance.
Answer: Total Cost of Renting = $5312.29
Step-by-step explanation:
Given that;
Rental space = $68 per guest, down payment = 25%, 7.4% interest payment on the balance.
Total Cost of Renting = Down Payment + Remaining payment
Total Cost of Renting = $68 × Guests × 25% + ($68 × Guest - Down payment) × (1 + Interest *9/12)
Total Cost of Renting = $68 × 75 × 25% + ($68 × 75 - Down payment) × (1 + 7.40% × 9/12)
Total Cost of Renting = $1275 + ($5100 - 1273) × (1.0555)
Total Cost of Renting = $1275 + 4037.29
Total Cost of Renting = $5312.29
m2 +14m+40
m+10
pls help
Answers
Answer:
m + 4
Step-by-step explanation:
I think you mean divide. Is that correct? If it is not leave me a note in your comments.
m^2 + 14m + 40
=============
m + 10
(m + 4)(m + 10)
============
m + 10
Cancel m + 10 on both the top and bottom
m + 4 is your answer.
1) Prepare in good form and in the correct order, a classified Statement of marks) 2) Prepare the required closing entries. No explanations needed. Show all necessary calculations. (26 marks)
Answers
To fulfill the request, two tasks need to be completed. First, a classified statement of marks must be prepared, displaying the marks in the correct order and format. Second, the required closing entries should be prepared, including all necessary calculations.
1) To prepare a classified statement of marks, the marks should be organized in the correct order, such as by subject or category. The statement should clearly display the marks achieved by each student, enabling easy comparison and analysis.
2) Closing entries are necessary to transfer temporary account balances to permanent accounts at the end of an accounting period. These entries help ensure that the temporary accounts are reset to zero for the next accounting period. The required closing entries typically involve transferring revenues, expenses, and dividends to the appropriate accounts. Calculations may be required to determine the closing entries, such as calculating net income or determining the dividend amount. These calculations will depend on the specific financial data and accounts involved in the accounting system being used.
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the 5th grade is having a picnic this Friday. There will be 182 students and 274 adults. Each table seats 12 people. How many tables are needed??
PLS I need the help
Answers
Then to see how many tables are needed, divide the total amount of people by the number of people 1 table can seat, so 456 / 12, which is 38.
So you need 38 tables.
Solve the compound inequality. Express the solution using interval notation. 4x-4<=16 and 3-x<-3
Answers
To express the solution in interval notation, we can write it as:
(-∞, 5] ∪ (6, ∞)
Let's solve the compound inequality step by step:
4x - 4 ≤ 16
To isolate x, we add 4 to both sides of the inequality:
4x - 4 + 4 ≤ 16 + 4
4x ≤ 20
Next, divide both sides of the inequality by 4:
(4x) / 4 ≤ 20 / 4
x ≤ 5
3 - x < -3
To isolate x, we subtract 3 from both sides of the inequality (note that the inequality sign flips when we multiply or divide by a negative number):
3 - x - 3 < -3 - 3
-x < -6
Multiplying both sides of the inequality by -1 (and flipping the inequality sign):
x > 6
So we have the solutions:
x ≤ 5 and x > 6
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A large school district is considering moving up the start date for the school year by two weeks. In order to determine if families would support this, surveys were mailed out to 1000 parents/guardians in the district. The survey said, "We believe that starting school two weeks earlier will be beneficial to the students in our District. Would you support moving up the start date for the school year by two weeks?" The School Board received 492 responses from the survey, 72% of which supported the proposal. -Describe a potential source of bias in the wording of the question. -Due to the bias described in part (a), is the sample proportion of 72% likely greater than or less than the actual proportion of families who support the proposal? Explain. -What type of sample was taken? -Less than half of those sent the letter returned a response. What type of bias is this?
Answers
Answer:
(a) Confirmation bias
(b) Likely less than actual proportion of families who support the proposal
(c) Random sample
(d) Nonresponse bias
Step-by-step explanation:
In confirmation bias, the researcher already has and intends to prove an assumption about the effect the of a treatment before carrying out the survey, such that the survey or research is tries to dictate to the participants in the survey about the desired outcome
In the question, the belief of the researcher is expressed to the participants in a form of brief at the start of the survey which is attempting to influence the responses to the survey, such that the actual result should be less than what was observed.
a sample of 50 drills had a mean lifetime of 12.68 holes drilled when drilling a low-carbon steel. assume the population standard deviation is 6.83. what sample size (i.e., how many) would you need to have so that a 95% confidence interval will have a margin of error of 1.0?
Answers
Using the z-distribution, it is found that the 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).
We are given the standard deviation for the population, hence, the z-distribution is used. The parameters for the interval is:
Sample mean of \(x = 12.7\)
Population standard deviation of \(\sigma = 6.37\)
Sample size of .n = 50
The margin of error is:
\(M = z \frac{\sigma }{\sqrt{n} }\)
In which z is the critical value.
We have to find the critical value, which is z with a p-value of \(\frac{1+\alpha }{2}\) , in which \(\alpha\) is the confidence level.
In this problem, , thus, z with a p-value of , which means that it is z = 1.96.
Then:
\(M= 1.96\frac{6.37}{\sqrt{50} } = 1.77\)
The confidence interval is the sample mean plus/minutes the margin of error, hence:
x- M = 12.17 - 1.77 =10.4
x+M = 12.17 + 1.77 = 13.94
The 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).
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exercise 5.3.1. recall from exercise 4.4.9 that a function f : a → r is lipschitz on a if there exists an m > 0 such that ∣∣∣∣ f(x) − f(y) x − y ∣∣∣∣ ≤ m for all x ?
Answers
If f is differentiable on a closed interval [a,b] and if f' is continuous on the interval [a,b], Then f is Lipschitz on [a,b].
What is a Lipschitz function?
If a neighborhood U of x exists for any x in X such that f restricted to U is Lipschitz continuous, then the function is said to be locally Lipschitz continuous. Alternatively, f is locally Lipschitz if and only if it is Lipschitz continuous on each compact subset of X if X is a locally compact metric space.
Now,
Assume that f can be differentiated and that f' is continuous on [a,b]. Therefore, f' is bounded since [a,b] is compact. In other words, for all x [a,b] there exists M > 0 such that: |f'(x)| ≤ M.The Mean Value Theorem therefore ensures that there exists c between x and y such that: \(|\frac{f(x)-f(y)}{x-y}|=|f'(c)|\leq M\), for each x,y ∈[a,b].Given that x and y were chosen at random, we can infer that f is Lipschitz on [a,b] since the inequality: \(|\frac{f(x)-f(y)}{x-y}|\leq M\), holds for all x,y ∈ [a,b].Hence, If f is differentiable on a closed interval [a,b] and if f' is continuous on the interval [a,b], Then f is Lipschitz on [a,b].
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An experiment must have a placebo group in order to be valid. (T/F)
Answers
The statement is false.
Hotel P offer two type of room for it cutomer: a Deluxe room and a Suite room. The price per night for the uite room for check-in on Sunday until Thurday i 70% higher than the price per night for a Deluxe room for the exact check-in period. The price per night for the Deluxe room for check-in on Friday and Saturday i 25% higher than for price per night for the Deluxe room for check-in on Sunday until Thurday. If the hotel management want to maintain the price difference between the two type of pace, and the price per night for a Suite room for check-in on Sunday until Thurday i $223, what hould be the price per night for a Suite room for check-in on Friday and Saturday?
Answers
The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50 .
The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50.
1. Calculate the price of a Deluxe room for check-in on Sunday until Thursday:
$223 / 1.70 = $131.18
2. Calculate the price of a Deluxe room for check-in on Friday and Saturday:
$131.18 x 1.25 = $163.98
3. Calculate the price of a Suite room for check-in on Friday and Saturday:
$163.98 x 1.70 = $278.50
The price per night for a Suite room for check-in on Friday and Saturday would be $278.50.
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a car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time it takes the truck to travel the same distance. what is the speed of the car? how about the truck?
Answers
A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time. The speed of the car is 50 km/h. The speed of truck is 70 km/h.
Define speed.You can determine an object's speed if you know how far it moves in a given amount of time. For instance, an automobile is moving at a pace of 70 miles per hour if it covers 70 miles in an hour (miles per hour).
Given,
A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time.
Let s represent the truck's speed and (s+20) represent the car's speed.
to determine each vehicle's time
Time = Speed / Distance
truck time = 350/s
Time in an automobile is 350/(s+20)
Truck time - car time = 2 hours
So,
(350/s) - [350/(s+20)] = 2
LCM is s(s+20)
[350(s+20) - 350s]/s(s+20) = 2
Cross multiplying,
350(s+20) - 350s = 2s(s+20)
Simplifying the equation,
350s + 7000 - 350s = 2s² + 40s
Now, we have quadratic equation to simplify,
2s² + 40s - 7000 = 0
Dividing the equation by 2
s² + 20s - 3500 = 0
Factorizing,
s= 50
s= -70 (impossible because of the sign)
Hence the truck's speed is s = 50 km/h.
The speed of the car is s + 20 = 70 km/h.
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Jemma gave 0.30 of her candy to her sister and 0.25 of her candy to her brother. How much of her candy to her brother. How much of her candy did she give away.
Answers
So, Jemma gave away 0.30 percent and also gave 0.25 away all we have to do is add these two percents and we have our answer!
0.30% + 0.25% =
0.30 plus 0.25 equals to 0.0055 so you get your answer 0.0055!
A proportional relationship must form a straight line, but it does not have to go through the origin. True or False?
Answers
Answer:
False
Step-by-step explanation:
A graph of a proportional relationship is a straight line that passes through the origin. The constant of a proportionality in a graph of a proportional relationship is the constant ratio of y to x (the slope of the line).
marie likes to jump up steps. she can jump up one step at a time, two steps at a time, or a combination of both. how many different ways can she jump up a set of five steps?
Answers
The different ways in which she can jump up a set of five steps is: 4 + 3 + 1 = 8 ways.
What is permutation and combination?By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.
Here, the differences between permutation and combination are described in detail.
The given steps are 5.
Thus, we have the following possibilities:
For 1 double step and 3 single steps:
4! / 3! = 4
For 2 double steps and 1 single step:
3! / 2! (1!) = 3
For 5 single steps: 1 way
Thus, the different ways in which she can jump up a set of five steps is:
4 + 3 + 1 = 8 ways.
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Tree A is 5 feet tall and grows at a rate of 1.5 feet per year. The table shows the height h (in feet) of Tree B after x years. a. Does the table represent a linear or nonlinear function? Explain. b. Which tree is taller after 10 years? Explain.
Answers
Answer:
where is the table ? I can't answer
the mass of an adult north pacific right whale is about 70,000 kg, or 7 x 10 4 kg. the mass of a male polar bear is about 700 kg, or 7 x 10 2 kg. about how many times more massive is the right whale than the polar bear?
Answers
Pls mark brainliest
Solve the system of equations:
y = 2x
3x + 3y = −18
Answers
Answer:
x = -2, y = -4
Step-by-step explanation:
Substitution:
y = 2x
3x + 3y = -18
3x + 3(2x) = -18
3x + 6x = -18
9x = -18
x = -2
y = 2(-2)
y = -4
May I please have brainliest? Thank you!
What's Part of a 1 minute and 5 seconds?
Answers
Round to the nearest cent 6 divided by 2.29
Answers
Answer: $0.38
Step-by-step explanation:
2.29/8=
0.38167=
0.38167=$0.38
Select the values that are solutions to the inequality x2 + 3x – 4 > 0. –6 –2 0 5
Answers
The values that are solutions to inequality are -6 and 5.
Options A and D are the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
x² + 3x - 4 > 0
Now,
Substituting x = -6, -2, 0, 5
(-6)² + 3(-6) - 4 > 0
36 - 18 - 4 > 0
36 - 22 > 0
14 > 0
True.
x² + 3x - 4 > 0
(-2)² + 3 x (-2) - 4 > 0
4 - 6 - 4 > 0
-6 > 0
This is not true.
x² + 3x - 4 > 0
0 + 3 x 0 - 4 > 0
0 + 0 - 4 > 0
-4 > 0
This is not true.
x² + 3x - 4 > 0
5² + 3 x 5 - 4 > 0
25 + 15 - 4 > 0
40 - 4 > 0
36 > 0
This is true.
Thus,
-6 and 5 are the solutions to inequality.
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