if the infinite series (-1)^(n 1)2/n is approximated by pk what is the least value for k for which the alternating series error bound guarantees that
Answers
The alternating series error bound states that the error in approximating an alternating series is less than or equal to the absolute value of the first neglected term.
In this case, the alternating series is:
(-1)^(n+1) * 2/n
The absolute value of the (k+1)th term is:
|(-1)^(k+2) * 2/(k+1)| = 2/(k+1)
So we want to find the least value of k such that:
2/(k+1) < pk
Substituting pk = 1/(k+1)^(p) into the inequality, we get:
2/(k+1) < 1/(k+1)^(p)
Multiplying both sides by (k+1)^(p), we get:
2 < (k+1)^(1-p)
Taking the logarithm of both sides, we get:
ln(2) < (1-p) * ln(k+1)
Dividing both sides by ln(k+1), we get:
(1-p)^(-1) * ln(2) < ln(k+1)
Exponentiating both sides, we get:
exp((1-p)^(-1) * ln(2)) < k+1
Subtracting 1 from both sides, we get:
exp((1-p)^(-1) * ln(2)) - 1 < k
So the least value of k that satisfies the inequality is:
k = ceil(exp((1-p)^(-1) * ln(2)) - 1)
where ceil(x) is the smallest integer greater than or equal to x.
Note that the value of p depends on the convergence rate of the series. If the series converges absolutely, then p = 1; if the series converges conditionally, then p = 2.
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Related Questions
The graph of a function is shown on the grid.
Answers
Answer:
y-intercept = (-2,0)
Step-by-step explanation:
the "C" is the answer
She charges an initial fee of $10 for each
rental and an hourly rate of $4. Which of
the equations below shows the amount
y that Rashida charges for a bike rental
that lasts x hours?
A. y=10+4x
B. y=10+4x
C. y=4+10x
D.y=4+10x
Answers
Answer:
A
Step-by-step explanation:
Because the 10 is bigger then the 4 so when you do the math (y) will equal the answer of A which its 14
Answer:
The answer is y=10+4x
Step-by-step explanation:
so because x is represented by hours you dont know how many hours someone rents the bike so x and ten dollars is a set amount so it would stand alone.
johnathan’s utility for money is given by the exponential function: u(x)=4-4(-x/1000).
Answers
Jonathan’s utility for money is given by the exponential function:
u(x) = 4 - 4(-x/1000).
Jonathan’s utility for money is given by the exponential function:
u(x) = 4 - 4(-x/1000).
The utility function u(x) is defined as the amount of satisfaction or happiness that an individual derives from consuming a specific quantity of a good or service.
If we analyze the given function then we can say that as x increases,
-x/1000 becomes more negative.
This means that the exponential term becomes larger and smaller in magnitude so that u(x) moves toward 4.
In general, the exponential function \(f(x) = a^{(x - b)} + c\)
has a horizontal asymptote at y = c.
Similarly, the utility function u(x) has a horizontal asymptote at y = 4.
Here, a = -4,
b = 0,
and c = 4.
Therefore, Jonathan’s utility for money is given by the exponential function:
u(x) = 4 - 4(-x/1000).
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Three students wrote equations on their dry erase boards 1/4=20% 7/10=.70% 13/20=65% Which of these students wrote an equation that is correct?
A. Student one and Student 3
B. Student 2 and Student 3
C. Student 2
D. Student 3
PLEASE HURRY THIS EXAM IS DUE TONIGHT!!!
Answers
Answer:
B
Step-by-step explanation:
Suppose you have a collection of coins, and each coin is either a nickel (worth 5s) or a dime (worth 10k ) or a quarter (worth 25s) You know that (i) you have 4 times more dimes than nickels (ii) you have 18 coins in total and (iii) altogether the coins are worth 290 e How many of each type of coin do you have? I have nickels and dimes and Ifntoraininteaer on diacimain number [more..]
Answers
Substituting these values back into equation (i), we get D = 4(3) = 12. There are 3 nickels, 12 dimes, and 3 quarters in the collection.
Let's assume the number of nickels is N, the number of dimes is D, and the number of quarters is Q. From the given information, we can deduce three equations:
(i) D = 4N (since there are 4 times more dimes than nickels),
(ii) N + D + Q = 18 (since there are 18 coins in total), and
(iii) 5N + 10D + 25Q = 290 (since the total value of the coins is 290 cents or $2.90).
To solve these equations, we can substitute the value of D from equation (i) into equations (ii) and (iii).
Substituting D = 4N into equation (ii), we get N + 4N + Q = 18, which simplifies to 5N + Q = 18.
Substituting D = 4N into equation (iii), we get 5N + 10(4N) + 25Q = 290, which simplifies to 45N + 25Q = 290.
Now we have a system of two equations with two variables (N and Q). By solving these equations simultaneously, we find N = 3 and Q = 3.
Substituting these values back into equation (i), we get D = 4(3) = 12.
Therefore, there are 3 nickels, 12 dimes, and 3 quarters in the collection.
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express the set in interval notation:
Answers
(the first option)
reason:
the 2 is a ( because that’s what is shown on the number line. infinity is also a ) because infinity can’t have a ]
write the additive inverse of 11/221
Answers
addective inverse of 11/221 = -11/221
-secret_angel-
A video game rental store charges a $20 membership fee plus $2 for each game rented. Click to show whether each statement is true or false. True False The slope of function 2 is greater than the slope of function 1 and less than the slope of function 3 The slope of function 1 is 4 times the slope of function 3. The y-intercept of function 2 is less than the y-intercept of functions 1 and 3. The y-intercept of function 2 is greater than the y-intercept of function 3.
Answers
Answer:
the member ship gay
Step-by-step explanation:
m8 m88m8m88m8m88m
The sales tax rate if 6.25%. The total cost of the items that were purchased at Walmart was $35.02. What is the total, including tax? (nearest cent)
Answers
Given the sales tax rate of 6.25% and the total cost of the items purchased at Walmart as $35.02, we can calculate the total cost including tax. To do this, we first need to find the tax amount on the purchase.
Tax amount = (Tax rate * Total cost of items) / 100
Tax amount = (6.25 * $35.02) / 100
Tax amount = $2.18875
Now, round the tax amount to the nearest cent:
Tax Amount ≈ $2.19
Next, add the tax amount to the total cost of the items to find the total cost including tax:
Total cost including tax = Total cost of items + Tax amount
Total cost including tax = $35.02 + $2.19
Total cost including tax ≈ $37.21
So, the total cost of the items purchased at Walmart, including the 6.25% sales tax, is approximately $37.21.
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find the slope and y intercept form equation from the table
Answers
Answer:
y=x+5 or y=1x+5
Step-by-step explanation:
i hope this helps :)
What is 7/10 + 3/5 answer
Answers
Answer:
■○■•♤•♤♤•》•♤~♤~♤~♤~♤♤~♤•♤○♤~
Find the area of the region bounded by the given curves. It is a good idea to sketch the region bounded by the curves. (b) y=cosx,y=sin2x,x=π/2,x=π. (c) y=∣x∣,y=(x+1)^2−7,x=−4.
Answers
The area of the region bounded by y = |x|, y = (x + 1)^2 - 7, and x = -4 is given by: Area = ∫(-4 to -3) [(x + 1)^2 - 7 - |x|] dx + ∫(-3 to 2) [(x + 1)^2 - 7 - |x|] dx - ∫(-4 to -2) |x| dx.
(a) To find the area of the region bounded by the curves y = cos(x), y = sin(2x), x = π/2, and x = π, we first sketch the region. The curves y = cos(x) and y = sin(2x) intersect within the given interval. The graph shows that y = cos(x) lies below y = sin(2x) between x = π/2 and x = π. We can split the region into two parts, the left side from π/2 to the point of intersection, and the right side from the point of intersection to π. To find the point of intersection, we set cos(x) = sin(2x) and solve for x. cos(x) = sin(2x); cos(x) = 2sin(x)cos(x); 2sin(x)cos(x) - cos(x) = 0; cos(x)(2sin(x) - 1) = 0. This equation has two solutions: x = π/6 and x = π. The area of the region can be found by evaluating the integral of the difference between the curves from π/2 to π, and then adding the integral of the difference between the curves from π to π/6.
Therefore, the area of the region bounded by y = cos(x), y = sin(2x), x = π/2, and x = π can be calculated as follows: Area = ∫(π/2 to π) [sin(2x) - cos(x)] dx + ∫(π to π/6) [cos(x) - sin(2x)] dx. (b) To find the area of the region bounded by the curves y = |x|, y = (x + 1)^2 - 7, and x = -4, we first sketch the region. The graph shows that the parabola y = (x + 1)^2 - 7 is above the absolute value function y = |x| in the given interval. To find the points of intersection, we set |x| = (x + 1)^2 - 7 and solve for x. For x ≥ 0: x = (x + 1)^2 - 7; x^2 + 2x + 1 - x - 7 = 0; x^2 + x - 6 = 0; (x + 3)(x - 2) = 0; x = -3 or x = 2. For x < 0: -x = (x + 1)^2 - 7; x^2 + x + 6 = 0; (x + 3)(x + 2) = 0; x = -3 or x = -2. The points of intersection are x = -3 and x = 2. The area of the region can be found by evaluating the integral of the difference between the curves from x = -4 to x = -3, then adding the integral of the difference between the curves from x = -3 to x = 2, and finally subtracting the integral of the absolute value function from x = -4 to x = -2. Therefore, the area of the region bounded by y = |x|, y = (x + 1)^2 - 7, and x = -4 is given by: Area = ∫(-4 to -3) [(x + 1)^2 - 7 - |x|] dx + ∫(-3 to 2) [(x + 1)^2 - 7 - |x|] dx - ∫(-4 to -2) |x| dx.
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Describe the set of all positive integers from 10 to 15 using the descriptive method
Answers
Given:
The set of all positive integers from 10 to 15.
To find:
The given set by using the descriptive method.
Solution:
The positive integers are 1, 2, 3, 4,... .
The positive integers from 10 to 15 are 10, 11, 12, 13, 14, 15.
So, the given set has 5 elements 10, 11, 12, 13, 14, 15.
Using the descriptive method, the given set is defined as "The set of all positive integers greater than or equal to 10 and less than or equal to 15".
Therefore, the set of all positive integers greater than or equal to 10 and less than or equal to 15.
pls answer rn or else...
Answers
(50^3)x(90^7)=
12500x47829690000000=
5978711250000000000
Help please ......
...
Answers
Answer:
2,4,3,1,5,3,2 is the answer
Step-by-step explanation:
PLEASE ANSWER!!!
Find the value of x in the triangle shown below.
X
106
42
Answers
something you should keep in mind is that all three angles in a triangle always add up to 180 degrees.
so, here, since you know the two other angles, you can find the third.
180 - 106 - 42 will give you the measure of that third angle.
your answer will be 32.
hope i helped, good luck!
Answer:
32
Step-by-step explanation:
as you triangle angle add up to 180 so you add 106 by 42 which gives you 148 then
you take 180 -148 which it will give you =32
READ
10 times
100 times
600 times
Or
1000 times
50 points and brainlist
Answers
Answer:
100 times
Step-by-step explanation:
100 times
please is 100 times
a student spins the spinner twice and records the number that the spinner lands on each time. what is the probability that the sum of the two recorded numbers is less than $4$, if the probability of spinning each number is $\frac 14$? express your answer as a common fraction.
Answers
The probability of the sum of the two recorded numbers being less than 4 is $\frac{3}{4}$.
What is probability?Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur and 1 means the event will occur. Probability is used in mathematics, statistics, and other sciences to measure the chances of a certain outcome. Probability is also used in gambling and other forms of betting to determine the likelihood of a certain outcome occurring.
This is because there are three possible scenarios in which the sum of the two numbers can be less than 4:
1) both numbers are 1 (probability of $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$)
2) one number is 1 and the other is 2 (probability of $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$).
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The probability of the sum of the two recorded numbers being less than 4 is \(\frac{3}{4}\).
What is probability?Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur and 1 means the event will occur. Probability is used in mathematics, statistics, and other sciences to measure the chances of a certain outcome. Probability is also used in gambling and other forms of betting to determine the likelihood of a certain outcome occurring.
This is because there are three possible scenarios in which the sum of the two numbers can be less than 4.
1) both numbers are 1 (probability of \(\frac{1}{4}\) × \(\frac{1}{4} = \frac{1}{16}\))
2) one number is 1 and the other is 2 (probability of \(\frac{1}{4}\) × \(\frac{1}{4} =\) \(\frac{1}{16}\))
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What is the area, in square feet, of the shape below? Express your answer as a fraction in simplest form.
Answers
The area of the triangle is 2/25 ft²
Area of a triangle:The entire area that is bounded by a triangle's three sides is referred to as the triangle's area.
The formula for the area of a triangle is given by
Area = (1/2)× base × heightHere we have Triangle
From the given figure,
=> Base of the triangle = 4/5 ft
=> Height of the triangle = 1/5 ft
As we know
Area of triangle = (1/2)×base × height
=> Area of the triangle = \(\frac{1}{2} \times (\frac{1}{5} )\times (\frac{4}{5} )\)
= \(\frac{1}{1} \times (\frac{1}{5} )\times (\frac{2}{5} )\) = \(\frac{2}{25}\)
Therefore,
The area of the triangle is 2/25 ft²
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a vacant lot is being converted into a community garden. the garden and a walkway around its perimeter have an area of 868 square feet. find the width of the walkway if the garden measures 12 feet wide by 15 feet long.
Answers
The width of the walkway around the community garden is 2 feet. To find the width of the walkway, we can subtract the area of the garden from the total area of the garden and walkway combined.
Given that the garden measures 12 feet wide by 15 feet long, the area of the garden is calculated by multiplying the width by the length, which gives us 12 feet * 15 feet = 180 square feet. The total area of the garden and walkway combined is given as 868 square feet. To find the width of the walkway, we subtract the area of the garden from the total area:
Total area - Garden area = Walkway area
868 square feet - 180 square feet = 688 square feet
Since the walkway surrounds the garden, its area is equal to the width of the walkway multiplied by the length of the garden plus the width of the walkway multiplied by the width of the garden. Let's denote the width of the walkway as x:
Walkway area = (12 + 2x)(15 + 2x)
Setting the walkway area equal to 688 square feet, we can solve the equation:
(12 + 2x)(15 + 2x) = 688
Solving this quadratic equation will give us the width of the walkway, which turns out to be 2 feet.
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Please help! Due tonight!
Answers
Answer:
x = square root of 119
Step-by-step explanation:
Because it is only a little bigger than the side it opposes
a = 5, b = ?, c = 12
(5)^2 + b^2 = (12)^2
25 + b^2 = 144
B^2 = 119
Square root of 119
The answer is D
You have three coins in a box. One is fair. One is biased towards heads and lands heads with chance 80%. The third is biased towards tails and lands heads with chance 10%. You pick a coin from the box at random and flip it. Given that it lands heads, what is the chance the coin is fair?
Answers
The probability that the coin is fair given that it lands heads is 0.3571.
Given that a coin is picked from the box and flipped, the probability of the coin being fair is 1/3.
The probability of the coin being biased towards heads and the coin being biased towards tails is 1/3.
Therefore, the probability that the coin is fair and lands heads is (1/3) x 0.5
= 0.1667.
The probability that the coin is biased towards heads and lands heads is (1/3) x 0.8
= 0.2667.
The probability that the coin is biased towards tails and lands heads is (1/3) x 0.1
= 0.0333.
Therefore, the total probability that the coin lands heads is 0.1667 + 0.2667 + 0.0333
= 0.4667.
Using Bayes' Theorem, the probability of the coin being fair given that it lands heads is:
P(fair|heads)
= P(heads|fair) * P(fair) / P(heads)
= 0.5 * 1/3 / 0.4667
= 0.3571.
Thus, the probability that the coin is fair given that it lands heads is 0.3571.
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Chris wants to find out how big the fish are in the lake near his house. He decides to catch 25 fish and record their length and weight.
Which of the following strategies would help Chris ensure a random sample?
A.
Catch 25 fish at randomly chosen locations across the lake.
B.
Cast a large net in the middle of the lake as many times as it takes to catch 25 fish.
C.
Fish off of a nearby pier until he catches 25 fish.
D.
Measure the length of 25 fish fossils on the shore near his home
Answers
Catch 25 fish at randomly chosen locations across the lake
Solve for x. 7x - 99= 2x + 1
Answers
Answer:
x = 20
Step-by-step explanation:
7x - 99= 2x + 1
7x - 2x = 1 + 99
5x = 100
x = 20
Step-by-step explanation:
hope it helps you........
Find the equation of a line given the point and slope below. Arrange your answer in the form y=mx+b, where b is the
constant.
(-1,0)
m = -2
516171819
Answers
Answer:the answer is D
Step-by-step explanation:
In one version of a trail mix, there are 6 cups of peanuts mixed with 4 cups of
raisins. In another version of trail mix, there are 13.5 cups of peanuts mixed
with 9 cups of raisins.
1a. Are the ratios equivalent for the two mixes?
Yes
No
This is a required question
16. Explain how you know.
Your answer
Answers
Ratio of peanuts to raisins in the first version of a trail mix = 3:2.
Ratio of peanuts to raisins in the second version of a trail mix = 4.5:3.
Divide the ratio by 1.5.
Ratio for second mix = 3:2.
The ratios are equivalent for the two mixtures.
Hopefully this helped.
Merrill is completing homework problems where they need to determine whether graphs show proportional relationships. Merrill’s dog bit the corner off of the page so they cannot see whether this graph goes through the origin. Explain how to determine whether the graph shows a proportional relationship. Please have an actual answer or do not answer this cause it is due 8am Monday
Answers
In order to determine whether this graph shows a proportional relationship, you should determine if the ratios of the two variables plotted on the graph have a constant of proportionality.
What is a proportional relationship?In Mathematics, the graph of a proportional relationship between two variables is always characterized by a straight line with its data points passing through the origin (0, 0).
Mathematically, a proportional relationship can be modeled by the following linear equation:
y = kx
Where:
y and x are the variables.k represents the constant of proportionality.In conclusion, the ratio of the two variables plotted on the graph of a proportional relationship is always constant.
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Find the value of x. Round your answer to the nearest tenth.
Answers
Answer:
9.30
Step-by-step explanation:
Using SOHCAHTOA
tan=opposite/adjacent
tan25°=x/20
tan 25°=0.4663
0.4663=x/20
cross multiply
x=0.4663*20
x=9.326
to the nearest tenth=9.30
In a survey, 20 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $44 and standard deviation of $10. Estimate how much a typical parent would spend on their child's birthday gift (use a 99% confidence level). Give your answers to one decimal place. Provide the point estimate and margin or err
Answers
Based on the survey results, a typical parent would spend around $44 on their child's birthday gift, with a margin of error of approximately $2.9 at a 99% confidence level.
To estimate how much a typical parent would spend on their child's birthday gift, we use the sample mean and standard deviation as estimates of the population parameters. The sample mean of $44 serves as the point estimate for the population mean.
To determine the margin of error, we use the standard error, which is the standard deviation divided by the square root of the sample size. In this case, the standard error is approximately $2.5 (standard deviation of $10 divided by the square root of 20). Multiplying the standard error by the critical value corresponding to a 99% confidence level (z-value of 2.58 for a large sample size) gives us the margin of error.
Therefore, the typical amount spent on a child's birthday gift is estimated to be $44, with a margin of error of approximately $2.9. This means that we can be 99% confident that the true mean amount spent by parents falls within the range of $41.1 to $46.9.
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complete the solution of the equation. Find the value of y when x equals 9. 3x + 4y = 43 Enter the correct answer.
Answers
27+4y=43
4y=16
Y=4