How many terms of the convergent series Sigma /n^1.1 should be used to estimate its value with error at most 0.00001? About 10^_____terms (Round up to the nearest whole number as needed.)
Answers
The answer is: \(10^5\) terms.
How the value of the series with error at most 0.00001?We know that the error bound for the nth partial sum of a series can be given by:
\(|E_n| < = S - S_n\)
where S is the sum of the infinite series, \(S_n\) is the sum of the first n terms, and \(E_n\) is the error in the approximation of S by \(S_n\).
For the given series, we have:
\(S = Σ(1/n^1.1)\)
We want to find the number of terms n such that the error\(|E_n|\) is at most 0.00001. In other words, we want to find the smallest value of n such that:
\(|E_n| < = 0.00001\)
Using the error bound formula, we have:
\(|E_n| < = S - S_n\)
Substituting the values, we get:
\(|Σ(1/n^1.1) - Σ(1/k^1.1)| < = 0.00001\)
where k is the number of terms we want to add.
We can simplify the left-hand side of this inequality using the reverse triangle inequality:
\(|Σ(1/n^1.1) - Σ(1/k^1.1)| < = |Σ(1/n^1.1)| + |Σ(1/k^1.1)|\)
Using the formula for the sum of a p-series, we have:
\(Σ(1/n^1.1) = Σ(1/n^(11/10)) = ∞\)
Therefore, we can ignore the second term on the right-hand side of the inequality, and focus on the first term. We want to find the smallest value of k such that:
\(|Σ(1/n^1.1)| < = 0.00001\)
We can approximate the sum of the series by an integral, using the integral test. Therefore, we have:
\(Σ(1/n^1.1) ≈ ∫[1,∞] dx/x^1.1 = [x^-0.1/-0.1]∞_1 = 10\)
Using this approximation, we get:
\(|Σ(1/n^1.1)| < = 10\)
Substituting this in the inequality, we have:
10 <= 0.00001
This is clearly not possible, so we need to increase the number of terms k. Let us try with k = 10000. Using a calculator or computer program, we can find that:
\(Σ(1/k^1.1) ≈ 9.986\)
Therefore, we have:
\(|Σ(1/n^1.1) - Σ(1/k^1.1)| ≈ |∞ - 9.986| ≈ 0.014\)
This is still greater than 0.00001, so we need to increase the value of k further. Let us try with k = 100000. Using a calculator or computer program, we can find that:
\(Σ(1/k^1.1) ≈ 9.9997\)
Therefore, we have:
\(|Σ(1/n^1.1) - Σ(1/k^1.1)| ≈ |∞ - 9.9997| ≈ 0.0003\)
This is less than 0.00001, so we can use k = 100000 terms to estimate the value of the series with error at most 0.00001.
Therefore, the answer is:
\(10^5\) terms.
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Related Questions
What is the sum of 4 + (-6)?
Answers
Answer:
-2
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
4+(-6)
4-6
-2
Help help help please !!
Answers
Answer:
\(\frac{40}{41}\)
Step-by-step explanation:
Sin = opposite / hypothenuse
Sin A = 40 / 41
Answer: \(\frac{40}{41}\)
Answer:
The answer is 40/41...............
Find the Area! Need help asap
Answers
Answer:
5.6ft squared
Step-by-step explanation:
4x7 = 28 divided by 5 which is 5.6
Connie collected 50 seashells during her 5 day vacation. Each day she collected 3 more than the previous day. How many seashells did she find each day?
Answers
Answer:
First day, N(1) = 4
Second day, N(2) = 4 + 3 = 7
Third day, N(3) = 4 + 6 = 10
Fourth day, N(4) = 4 + 9 = 13
Fifth day, N(5) = 4 + 12 = 16
Step-by-step explanation:
She spent 5 days on her vacation.
She collected 50 seashells in those days. Each day she collected 3 more than the previous day.
We can represent this with an arithmetic progression:
N(n) = x + 3(n - 1)
Where x is the amount of sea shells collected on the first day.
n = the particular day
So, for the five days day:
N(1) = x + 3(1 - 1) = x + 3(0) = x
N(2) = x + 3(2 - 1) = x + 3(1) = x + 3
N(3) = x + 3(3 - 1) = x + 3(2) = x + 6
N(4) = x + 3(4 - 1) = x + 3(3) = x + 9
N(5) = x + 3(5 - 1) = x + 3(4) = x + 12
The sum of all the sea shells is 50:
N(1) + N(2) + N(3) + N(4) + N(5) = 50
=> x + x + 3 + x + 6 + x + 9 + x + 12 = 50
5x + 30 = 50
5x = 50 - 30 = 20
x = 20 / 5
x = 4
Therefore:
First day, N(1) = 4
Second day, N(2) = 4 + 3 = 7
Third day, N(3) = 4 + 6 = 10
Fourth day, N(4) = 4 + 9 = 13
Fifth day, N(5) = 4 + 12 = 16
Simplifying Complex Fractions
x+2
+27 -3
Y+2
x-X
Simplify
1
+3x
X
X +3
x +3
O
x² + 3x
Answers
Answer:
ubub
Step-by-step explanation:
In a recent election, 2/3 of the citizens in a town voted. Of those voting, 60% voted in favor of a school bond. What fraction of the citizens voted for the school bond?
Answers
Answer:
2/5 of the citizens who voted , 4/15 of all citizens
Step-by-step explanation:
We have,
2/3 citizens voted
In those who votes, 60% voted in favor of a school bond
Therefore,
People who voted in favor of the school bond= 60% of 2/3
=60/100*2/3=2/5
Therefore, 2/5 of the citizens who voted had voted in favor of the school bond.
For all citizens,
x% of 1 = 2/5 of 2/3
x/100*1=2/5/100*2/3
x=4/15/100*100
x=4/15
\(▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)
The fraction of citizen who voted in election :
\( \dfrac{2}{3} \)now, 60% of them in favor of a school bond, so the fraction of citizens who voted for school bond :
\(60 \% \: \: \: \: of \: \: \: \: \dfrac{2}{3} \)\( \dfrac{60}{100} \times \dfrac{2}{3} \)\( \dfrac{20}{50} \)\( \dfrac{2}{5} \)hence, 2/5 th of the citizens voted for school bond.
almost 40% of the citizens
Pls someone help idk
Answers
Answer:
first one c and the second on b
Step-by-step explanation:
Kristina made rectangular place mats for her dining room table, as shown below. The area of each place mat is 135 square Inches. The width of each place mat is 9 inches. How many inches long are all the sides of the place mat? Figure not drawn to scale. in 9 in in in
Answers
Answer:
The length of all sides of place mat is 48 inches.
Step-by-step explanation:
Given that:
Area of place mat = 135 square inches
Width of place mat = 9 inches
Length of place mat = x
Area = Length * Width
135 = 9x
\(\frac{9x}{9}=\frac{135}{9}\\x = 15\)
For length of all sides, we will find the perimeter.
Perimeter = 2(Length + Width)
Perimeter = 2(15+9)
Perimeter = 2(24) = 48 inches
Hence,
The length of all sides of place mat is 48 inches.
Answer:
45
tbh i don't really know. I've seen people say that it's 45, others have said 48. I don't see how either of them make sense. Maybe i'm doing the math wrong I don't know. I think it's 45
Name 1 and 2 another name
Answers
Answer:
triangle, square, circle, pentagon, and horcux.
jk whats the question
Step-by-step explanation:
Hey there!
Answer:
One, two, three, delta, pi, hexagon, octagon, pentagram....
Step-by-step explanation:
Name another name of what??
Your question doesn't make a lot of sense but I thought that maybe I could share a few really cool shape and number names that maybe you didn't know!
Hope you enjoy!
:D
how many three-letter initials with none of the letters repeated can people have?
Answers
To find the number of three-letter initials with none of the letters repeated, we need to consider the number of choices for each position in the initials.
To determine the number of three-letter initials with none of the letters repeated, we can analyze each position in the initials. For the first letter, we have 26 choices since there are 26 letters in the English alphabet.
After selecting the first letter, for the second letter, we have 25 choices remaining since we cannot repeat the letter used in the first position. Similarly, for the third letter, we have 24 choices remaining since we cannot repeat either of the previous letters.
Therefore, the total number of three-letter initials with none of the letters repeated can be found by multiplying the number of choices for each position: 26 * 25 * 24 = 15,600. Hence, there are 15,600 different three-letter initials that people can have if none of the letters are repeated.
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
1. is 24
2. is 18
Step-by-step explanation:
Assume that the farmer and the rancher can switch between producing pork and producing tomatoes at a constant rate. Labor Hours Needed to Make 1 Pound of Pounds Produced in 24 Hours Pork Tomatoes Pork Tomatoes Farmer 8 Rancher 4 4 6 Refer to Table 3-23. The opportunity cost of 1 pound of pork for the rancher is O a. 1 pound of tomatoes. B. 1 hour of labor. C. 1. 5 pounds of tomatoes. O d. 1. 5 hours of labor
Answers
The opportunity cost of 1 pound of pork for the rancher is 1 pound of tomatoes (option A).
What does the opportunity cost mean?The opportunity cost can be defined as the cost of choosing an alternative over another. In the case of farmers for example the opportunity cost includes not growing a different crop.
What is the opportunity cost for the rancher?Based on the chart, the rancher can produce 4 pounds of pork or 4 pounds of tomato every day. This means that if he chooses to produce pork for each pound of pork he misses the opportunity of producing one pound of tomato.
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can someone help with this im confused
A. Find x. The figure is not drawn to scale.
b. Is the triangle equilateral, isosceles, or scalene? Explain.
Answers
Answer:
6.43, scalene.
Step-by-step explanation:
assuming that those are meant to represent the angles in the triangle,
6x + 30 + 7x + 15 + 8x = 180
21x + 45 = 180
21x = 135
x = 6.43
The triangle is not equalateral because the angles would all be the same, it isn't isosceles since 2 aren't the same, it must be scalene since all 3 angles are different
Using R, construct and store a 4 x 2 matrix that is filled row-wise with the following values: 4.3, 3.1, 8.2, 9.2, 3.2, 0.9, 1.6, and 6.5, in that order. Using R, overwrite the second column of the matrix you have created in Q6 with the following numbers: 8, 9, 11, and 17 in that order. Save your updated matrix to an object named BruceLee.
Answers
To construct and store a 4 x 2 matrix filled row-wise with the given values in R, you can use the following code:
# Create the matrix
myMatrix <- matrix(c(4.3, 3.1, 8.2, 9.2, 3.2, 0.9, 1.6, 6.5), nrow = 4, ncol = 2, byrow = TRUE)
This code creates a matrix called "myMatrix" with 4 rows and 2 columns, filled row-wise with the provided values.
To overwrite the second column of the matrix with the numbers 8, 9, 11, and 17 in that order, you can use the following code:
# Overwrite the second column
myMatrix[, 2] <- c(8, 9, 11, 17)
This code selects the second column of the matrix using the indexing notation [, 2] and assigns the new values using the c() function. The second column is replaced with the numbers 8, 9, 11, and 17.
Finally, to save the updated matrix to an object named "BruceLee", you can use the following code:
# Save the updated matrix
BruceLee <- myMatrix
Now the updated matrix with the overwritten second column is stored in the object "BruceLee" for further use.
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I need helppp what’s the answerrr?!!?
Answers
Answer:
3,240
Step-by-step explanation:
if there are more than 10 children at the party, the balloon artist charges an additional supply fee of $55. there will be 16 children at the abara party. how much will the balloon artist charge mrs. abara for a party that is 4.5 hours long?
Answers
The balloon artist will charge Mrs. Abara $55 as an additional supply fee since there are more than 10 children at the party, and the party duration is irrelevant to the fee calculation.
1. Given that there will be 16 children at the party, which is more than 10, the balloon artist will charge an additional supply fee.
2. The additional supply fee is $55, as stated in the question.
3. The duration of the party, which is 4.5 hours, is not mentioned as a factor affecting the fee calculation.
4. Therefore, regardless of the party's duration, the balloon artist will charge Mrs. Abara $55 as the additional supply fee due to the number of children exceeding 10.
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1. Statistics from Cornell’s Northeast Regional Climate Center indicate that Ithaca, NY, gets an average of 35.4" of rain each year, with a standard deviation of 4.2". Assume that a Normal model applies. (Problem from Intro Stats by De Veaux, Velleman, Bock – 3rd Edition)
a. During what percentage of years does Ithaca get more than 40" of rain?
b. Less than how much rain falls in the driest 20% of all years?
c. A Cornell University student is in Ithaca for 4 years. Let represent the mean amount of rain for those 4 years. Describe the sampling distribution model of this sample mean, Be sure to check assumptions and conditions.
d. What’s the probability that those 4 years average less than 30" of rain?
Answers
Probability is a measure of the likelihood or chance of an event occurring.
a. To find the percentage of years where Ithaca gets more than 40" of rain, we need to calculate the z-score for this value and then use a standard normal table to find the percentage. The z-score is:
z = (40 - 35.4) / 4.2 = 1.33
From a standard normal table, we find that the percentage of values above z = 1.33 is approximately 9.87%. Therefore, during about 9.87% of years, Ithaca gets more than 40" of rain.
b. To find the value of rainfall corresponding to the driest 20% of years, we need to calculate the z-score for the 20th percentile and then convert it back to rainfall units. The z-score is:
z = invNorm(0.20) = -0.84
where invNorm is the inverse normal function. Therefore,
-0.84 = (x - 35.4) / 4.2
Solving for x, we get:
x = 32.2"
So less than 32.2" of rain falls in the driest 20% of all years.
c. Since the sample size n = 4 is small and the population standard deviation is unknown, we need to use the t-distribution to describe the sampling distribution model of the sample mean. However, since the sample size is small, we also need to assume that the population follows a normal distribution.
Under these assumptions, the sampling distribution of the sample mean is approximately normal with a mean of μ = 35.4" and a standard error of σ/√n = 4.2/√4 = 2.1". Therefore, the sampling distribution of the sample mean is:
t(3, 35.4, 2.1)
where t denotes the t-distribution, 3 is the degrees of freedom (n - 1), 35.4 is the mean, and 2.1 is the standard error.
d. To find the probability that the 4-year average is less than 30", we need to calculate the z-score for this value and then use the t-distribution with 3 degrees of freedom to find the probability. The z-score is:
z = (30 - 35.4) / (4.2 / √4) = -2.57
Using a t-table or calculator with 3 degrees of freedom, we find that the probability of a t-value less than -2.57 is approximately 0.041. Therefore, the probability that those 4 years average less than 30" of rain is approximately 0.041 or 4.1%.
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Use the following scenario to answer the question below:
When the new book units of fire was released, Johnathan decided to read it in one sitting for his book report. He started at 11:00 a.m. on Saturday morning and read until 8:00 p.m. that night, for a total of 9 hours. For school, however, he needed to record the exact number of minutes he spent reading.
To figure out how many minutes he read, what is a conversion ratio he should use?
\(A. \frac{9.30 minutes}{1 hour}\)
\(B. \frac{1 hour}{60 minutes}\)
\(C. \frac{60 minutes}{1 hour}\)
\(D. \frac{60 hours}{1 minute}\)
Answers
Answer:
9 hr * 60 min/hr = 540 min. 540 min * 60 sec/min = 32,400 sec. Use the method described by panic mode: round the number down until there is only one non-zero digit left. Here, 32,400 rounds down to 30,000. Now count the number of zeroes; the result is the order of magnitude: 4. (You see this in scientific notation also: 30,000 = 3 × 10^4.)
lisa, aldo, and miguel have a total of in their wallets. miguel has times what aldo has. lisa has more than aldo. how much does each have?
Answers
Amounts that have with Lisa, Aldo, and Miguel in their wallets are $35, $25, and $100 respectively.
Lisa, Aldo, and Miguel have a total of $160 in their wallets.
Miguel has 4 times what Aldo has.
Lisa has $10 more than Aldo.
Let the amount that the Aldo has to be $x
Then according to the given question.
The amount that the Lisa has $(x+10)
The amount that the Miguel has $(4x)
So the total amount can be resulted as the sum of the amounts of the three each individual.
x + x + 10 + 4x = 160
6x + 10 = 160
6x = 160 - 10
6x = 150
x = 25
Therefore the amount in the Aldo wallet is $25
Hence, the amount in the Lisa's wallet is:
x + 10 = 25 + 10 = $35
Hence, the amount in the Miguel's wallet is:
4x = 4(25) = $100
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Lisa, Aldo, and Miguel have a total of $160 in their wallets. Miguel has 4 times what Aldo has. Lisa has $10 more than Aldo. how much does each have?
to amend the u.s constitution,3/4 of the 50 states amendment, if 35 states approve an amendment, will the constitution be ameded
Answers
Therefore, if 35 states approve an amendment, the Constitution would not be amended, as it falls short of the required three-fourths majority fraction of 37 states.
When determining the number of states required to ratify a constitutional amendment, we round up or down to the nearest whole number. In the case of three-fourths of 50 states, calculating (3/4) * 50 gives us 37.5 states. Since we cannot have a fraction of a state, we must round either up or down.
In this context, the general practice is to round down to the nearest whole number. Therefore, three-fourths of 50 states would be considered as 37 states. Hence, if 35 states were to approve an amendment, it would not meet the requirement for three-fourths majority (37 states) needed to amend the U.S. Constitution.
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how many operations are required to find the number 3, located at the 1st position in the same list, {3, 37, 45, 57, 93, 120}? operation
Answers
This means that we can find the number 3 in either 2 or 3 operations, depending on the steps taken during the binary search.
To find the number 3 located at the 1st position in the list {3, 37, 45, 57, 93, 120}, we can use binary search algorithm. In each step, we divide the list in half and check if the middle element is equal to 3. If not, we continue searching in the appropriate half until we find the number.
In this case, since the list has 6 elements, we can find the number 3 in at most log2(6) = 2.585 operations. This means that we can find the number 3 in either 2 or 3 operations, depending on the steps taken during the binary search.
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Let m = x^2 - 5
Which equation is equivalent to (x^2-5)^2 - 3x^2 + 15= -2 in terms of m ?
A m^2+3m+2=0
B m^2-3m+17=0
C m^2-3m+2=0
D m^2+3m+17=0
Thanks!
Answers
The equivalent equation to the (x² - 5)² - 3x² + 15 = -2 in form of 'm' is given by option c. m² -3m + 2 = 0.
The equation is equal to,
(x² - 5)² - 3x² + 15 = -2
let the value of m be equals to x² - 5.
Simplify the equation we have,
⇒ ( x² - 5 )² - 3x² + 15 = -2
Take '3' common factor from the 3x² + 15 so that it get convert into x² - 5 we get,
⇒ ( x² - 5 )² - 3 (x² - 5 ) = -2
Now replace x² - 5 by m to get the equivalent equation,
⇒ ( m )² - 3 (m ) = -2
⇒ m² -3m + 2 = 0
Therefore, the equivalent equation to the given equation is written as option c. m² -3m + 2 = 0.
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decimals equivalent to 8.1
Answers
Answer:
8.10 & 8.100
Hope this helps ^^
Have a good day <3!
The cost to make each T-shirt is $10. You estimate that you will
sell 50 shirts. If you want to make a profit of at least $250, what
price will you charge for these T-shirts? Show your solution in two
different ways.
Answers
The price per T-shirt should be at least $15 to achieve a profit of $250.
To calculate the price per T-shirt that will yield a profit of at least $250, we need to consider the cost of production, the desired profit, and the number of shirts to be sold.
Given that the cost to make each T-shirt is $10, and we want to sell 50 shirts, the total cost of production would be 10 * 50 = $500.
Now, let's calculate the minimum revenue needed to achieve a profit of $250. We add the desired profit to the total cost of production: $500 + $250 = $750.
Finally, to determine the price per T-shirt, we divide the total revenue by the number of shirts: $750 ÷ 50 = $15.
Therefore, to make a profit of at least $250, the price per T-shirt should be set at $15.
By selling each T-shirt for $15, the total revenue would be $15 * 50 = $750. From this revenue, we subtract the total production cost of $500 to calculate the profit, which amounts to $750 - $500 = $250. Thus, by charging $15 per T-shirt, the desired profit of $250 is achieved.
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Choose the set of equations that best represent the following information:
The sum of two numbers, a and b, is 12. The first number, a, is 8 more than the second number.
a+b= 12, a = b+8
a+ a = 12, b-8 = a
a+b = 8, a>b+12
ab = 12, a+8>b
Answers
Answer:
a+b= 12, a = b+8
Step-by-step explanation:
We know that a plus b equals 12 a+b=12
The only other thing we know is that a is 8 more than b so a=b+8
Simplify 2¾+(3⅜-1½) please I need your help now, and I want you to explain it accordently ,am waiting
Answers
Answer:
1⁷/15
Step-by-step explanation:
2¾(3⅜-1½)
using the rule of BODMAS
change the fractions in the bracket into improper fraction
2¾(27/8-3/2)
find LCM of the fractions in the bracket
2¾(27-12)/8
2¾(15/8)
convert the other mixed fraction to an improper fraction
11/8(15/8)= 5.15625~ 5.2
Please help I don't understand!
Answers
\(\large{\underline{\underline{\pmb{\sf {\color {blue}{Solution:}}}}}}\)
\(\pink\star\)a reduction.
\( \sf \green{Explanation}\)
As we can see that, the figure given in the above picture is compressed or reduced. Thus, this is an example of reduction.
\( \boxed{ \frak \red{brainlysamurai}}\)
3/2(4x – 1) – 3x = 5/4 – (x + 2)
Answers
Hope it helps!
Brainliest would be nice but you don’t have to :)
(Simple)......Classify the transformation pls
Answers
The classification of the transformation is c. translation.
What is transformation?Transformation is a process by which the orientation or dimension of a given object is changed so as to produce expected image. Some types of transformation are: translation, dilation, rotation and reflection.
i. Translation: This process implies shifting a given object a number of units in a particular direction.
ii. Dilation: This requires resizing a given object.
iii. Rotation: When a given object is turned about a reference point at a certain angle, then the process is called rotation.
iv. Reflection: This requires turning an object over a line or point to produce the desired image.
Considering the shapes given in the question, it can be deduced that the transformation to classify the process is translation.
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Please Helpppppppppp!!!!!!!!!!!!!!!
Answers
Answer:
122/3435.35/67
Step-by-step explanation: