The radius of convergence, R, is 0. The interval of convergence, I, is (-R, R), which in this case is (-0, 0), or simply the single point {0}.
What is the radius of convergence, interval, I, of convergence of the series?To find the radius of convergence, we can use the ratio test. Given the series:
00 x + 4 Σ ✓n n = 2
Let's calculate the ratio of consecutive terms:
lim(n→∞) |√(n+1) / √n|
Using the limit test, we simplify the expression:
lim(n→∞) √(n+1) / √n
To evaluate this limit, rationalize the denominator by multiplying the expression by its conjugate:
lim(n→∞) (√(n+1) / √n) × (√(n+1) / √(n+1))
This simplifies to:
lim(n→∞) √(n+1) × √(n+1) / √n × √(n+1)
Simplifying further:
lim(n→∞) √((n+1)² / n × (n+1))
lim(n→∞) (n+1) / √n × √(n+1)
Disregard the constant term (n+1) since the focus is the behavior as n approaches infinity:
lim(n→∞) √(n+1) / √n
As n approaches infinity, the ratio simplifies to:
lim(n→∞) √(1 + 1/n)
Since the limit of this expression is 1, we have:
lim(n→∞) √(1 + 1/n) = 1
According to the ratio test, if the limit of the ratio is less than 1, the series converges absolutely. If the limit is greater than 1 or it diverges, the series diverges. If the limit is exactly 1, the ratio test is inconclusive.
In this case, the limit is 1, which means the ratio test is inconclusive. To determine the radius of convergence, consider the behavior at the endpoints of the interval.
At x = 0, the series becomes:
00 x + 4 Σ ✓n n = 2 = 0
So the series converges at x = 0.
Now let's consider the behavior as x approaches infinity:
lim(x→∞) 00 x + 4 Σ ✓n n = 2
Since the terms in the series involve √n, which increases without bound as n approaches infinity, the series diverges as x approaches infinity.
Therefore, the radius of convergence, R, is 0. The interval of convergence, I, is (-R, R), which in this case is (-0, 0), or simply the single point {0}.
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5 x 2 y = 5 3 x - y = 14 which of the following equations is not a result of solving the system of equations by addition?
The equation "6x + y = 29" is not a result of solving the given system of equations by addition.
To solve a system of equations by addition, we aim to eliminate one variable by adding the equations together. Let's analyze the given system of equations:
Equation 1: 5x + 2y = 5
Equation 2: 3x - y = 14
To eliminate the y variable, we can multiply Equation 2 by 2 and add it to Equation 1:
2(3x - y) = 2(14)
6x - 2y = 28
Adding this modified Equation 2 to Equation 1, we get:
(5x + 2y) + (6x - 2y) = 5 + 28
11x = 33
x = 3
Substituting the value of x into either of the original equations, we find that y = -1. Therefore, the solution to the system of equations is x = 3 and y = -1.
Now, let's verify the options to see which equation is not a result of solving the system by addition:
A) 11x = 33 - This equation is derived from adding the two equations together.
B) 6x + y = 29 - This equation is derived from substituting the values of x and y into one of the original equations.
C) 2y = 2 - This equation is derived from isolating the variable y in Equation 1.
D) x = 3 - This equation is derived from solving for x.
Thus, the equation "6x + y = 29" is not a result of solving the system of equations by addition.
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WORTH 25 POINTS! HELP PLZZZZZZ
Answer:
I pretty sure its A
Step-by-step explanation:
Answer:
The answer on the top, 32 * __ = 3616
Step-by-step explanation:
3616/32 = __
multiply by 32
3616 = 32 * __ or 32 * __ = 3616
Simplify 7 - 2(5 - 2x)
Answer:
4 − 3
Step-by-step explanation:
What is the measure of angle R? *
7 points
R
(10n + 19)"
(12n - 4)
S
Answer:
(10n + 19) (12n - 4)º ... The midsegment of a trapezoid is parallel to each base and its measure is one half the ...
Missing: pointsR( S
Step-by-step explanation:
HELPPPPPPPPP
What is the value of x in the figure at the right?
Answer:
x=30
HOPE THIS HELPS
-Todo <3
Step-by-step explanation:
60=2x
/2 /2
30=x
Q1: What is the measure of angle one?
Answer:
34
Step-by-step explanation:
omg please don't listen to the other person it's 34 bc if you look at the angle under 2 it's 34 so that's your answer for one
For a hypothesis test using the single-factor ANOVA formula:
The obtained overall F ratio = MS between treatments divided by MS within treatments.
Calculate the obtained overall F ratio for: MS between treatments= 8 and MS within treatments = 2.
Then describe the null hypothesis decision for = .05, df numerator: 3, and df denominator: 4.
Reject of fail to reject null hypothesis?
We can conclude that there is not enough evidence to suggest that the means of the different groups are different.
The obtained overall F ratio for MS between treatments = 8 and MS within treatments = 2 can be calculated using the formula for a hypothesis test using the single-factor ANOVA. The formula is given below: Obtained overall F ratio = MS between treatments/MS within treatments Substituting the values in the above formula, we get, Obtained overall F ratio = 8/2 = 4
The obtained overall F ratio for MS between treatments = 8 and MS within treatments = 2 is 4.Now, let's describe the null hypothesis decision for α = .05, df numerator: 3, and df denominator: 4.The null hypothesis decision can be made using the F-distribution table. Using the table, the critical value of F is 9.49.
Therefore, if the obtained overall F ratio is greater than 9.49, then we reject the null hypothesis. If the obtained overall F ratio is less than or equal to 9.49, then we fail to reject the null hypothesis.Obtained overall F ratio = 4 is less than the critical value of F, i.e., 9.49.Therefore, the null hypothesis is not rejected at α = .05, df numerator: 3, and df denominator: 4.
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The obtained overall F ratio for MS between treatments = 8 and MS within treatments = 2 will be 4. The null hypothesis decision for α = 0.05, df numerator: 3, and df denominator: 4 is Fail to reject null hypothesis.
Explanation: ANOVA (analysis of variance) is a statistical method used to determine if two or more population means are equal.
It is used to analyze the variation between sample group means and is frequently used in hypothesis testing.
Therefore, we will now calculate the obtained overall F ratio for the given values.
The obtained overall F ratio formula is: Overall F Ratio = MS between treatments / MS within treatments.
Given, MS between treatments = 8 and MS within treatments = 2.
Therefore, Overall F Ratio = MS between treatments / MS within treatments
= 8/2
= 4
Hence, the obtained overall F ratio for MS between treatments= 8 and MS within treatments = 2 is 4.
The null hypothesis decision for α = 0.05, df numerator: 3, and df denominator: 4 is Fail to reject null hypothesis.
The test statistic value, F, is 3.71. The p-value is greater than 0.05. Therefore, we fail to reject the null hypothesis.
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"
Perform the following test of hypothesis. H0: μ 10.70, H1: μ # 10.70, n = 47, t = 12.234, = H0 is
"
Based on the given information, we have sufficient evidence to conclude that the population mean (μ) is not equal to 10.70.
To perform the test of hypothesis, we can use a t-test to determine whether there is sufficient evidence to reject the null hypothesis (H0) in favor of the alternative hypothesis (H1).
The given hypotheses are:
H0: μ = 10.70 (null hypothesis)
H1: μ ≠ 10.70 (alternative hypothesis)
The sample size is n = 47, and the test statistic is t = 12.234.
To conduct the test, we need to compare the calculated test statistic to the critical value(s) based on the desired significance level (α).
The steps to perform the hypothesis test are as follows:
Step 1: Set the significance level (α)
Let's assume a significance level of α = 0.05. This means we want to be 95% confident in our decision.
Step 2: Determine the critical value(s)
Since the alternative hypothesis is two-sided (μ ≠ 10.70), we need to find the critical values for a two-tailed t-test.
Since n = 47, we have n - 1 = 46 degrees of freedom (df). Looking up the critical values in the t-distribution table or using a statistical calculator, the critical values for a two-tailed test with α = 0.05 and df = 46 are approximately ±2.013.
Step 3: Calculate the p-value
The p-value is the probability of obtaining a test statistic as extreme as the one observed (t = 12.234), assuming the null hypothesis is true.
Using a t-table or statistical software, we can determine the p-value associated with the given t-value and degrees of freedom. The p-value turns out to be very small (p < 0.001).
Step 4: Make a decision
If the p-value is less than the significance level (α), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Since the p-value is smaller than α (p < 0.001), we reject the null hypothesis (H0).
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Please help.
a+67a+3ab-2ab-1=
Answer:
68a+ab-1
Step-by-step explanation:
Have a good day!
Solve for n. 2n+3/4n = 3/4
Answer: n=3/11
Step-by-step explanation:
1. You want to simplify both sides of the equation.
2n+3/4n=3/4.
(2n+3/4n)=3/4 (combine like terms).
11/4n=3/4.
2. Multiply both sides using 4/11.
(4/11)x(11/4n)=(4/11)x(3/4)
3. You get your answer which is n=3/11.
Hoped I help :)
Skip count 89300 forward by 5000
X Kawika had to raise the flag this morning. The 15 ft flag pole casted at
shadow with the ground at a 35° angle. What is the length of the
shadow? (Round answers to the nearest tenth) *
Answer with JUST THE NUMBER, without writing out the unit after the number.
pls help i’m so confused omg!!
Answer:
C or B
Step-by-step explanation:
Answer:
Your answer is A.
Step-by-step explanation:
You can count the arrow lines as the 2s. Such as, 2, 4, 6, 8 and 10.
So, the line 'x' is being divided by how many lines touching it.
Therefore, it is 1.
Then you add x and 6, the number which the line is ending with.
Your final answer is, F(x) = 1
x+6
Hope this helped!
Emily is making a flag with the dimensions shown. What is the minimum amount of material needed for the flag?
9514 1404 393
Answer:
B 80 square inches
Step-by-step explanation:
The area of a parallelogram has the same formula as the area of a rectangle:
A = bh . . . . . b is the base; h is the height
A = (10 in)(8 in)
A = 80 in²
The minimum amount of material needed is 80 square inches.
Answer:
The answer is 80
Step-by-step explanation:
Hope this helps
Seriously, somebody please help me! I've been asking all day, someone actually help me and not just halfassly answer it for points.
Answer:
9. A = Length by Width
Length = x
Width = 12x - 6y
A = x(12x - 6y)
A = 12x² - 6xy
10. A = ½bh
h = 2ab
A = ½(b)(2ab)
A = ab²
Tony borrows $7,000 from a friend
at a rate of 5% interest for 4 months.
What is the total that needs
to be repaid after this time
to the nearest dollar?
Answer:
5%100 ×R200
Step-by-step explanation:
Address and u the one for me please
Someone please help me.
Answer:
with what life
Step-by-step explanation:
Is x = 5 a solution to the equation 19 - x = 14?
Answer:
Yes
Step-by-step explanation:
Test the equation by substituting 5 in for x:
19- 5 =14
14=14
TRUE
If I helped, a brainliest would be greatly appreciated!
Answer: If you replace x with 5 then 19-5=14
Step-by-step explanation:
Enteros 15+18 resultado
HELP WILL MARK BRAINLIEST
Uhhh someone plz help me plz
Answer:
The number 3.97 is very close to the whole number 4. Therefore, the difference of 4.3 - 3.97 is about 0.33. So, the difference of 4.3 - 3.97 is less than 1.
Remember: The farther the number is to the right, the smaller it becomes.
Ex. 0.10 is greater than 0.100 since the number is shorter and closer to the ones/whole number spot.
Hope this Helps!:)
can someone please help me with this question?
Answer:
your answer will be 70 have a nice day:)
Step-by-step explanation:
43+27=70
Answer: 18
Step-by-step explanation:
To answer this question you have to add all the number and however many over 100 there is that how many like both of the teams so 27 + 48 + 43 = 118
then you take 100 away from 118 and you get 18
Help me please with the answer
tell me how to answer this
The mid point of the line segment is (-2, 5 / 2).
How to find the mid point of a line segment?The midpoint of a line segment is a point that lies exactly halfway between two points.
Therefore, let's find the mid point of the line segment indicated above.
Hence, using (-4, 0) and (0, 5)
Hence,
mid point = (x₁ + x₂ / 2, y₁ + y₂ / 2)
Therefore,
mid point = (0 - 4 / 2, 5 + 0 / 2)
mid point = (-4 /2, 5 / 2)
mid point = (-2, 5 / 2)
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The diameter of a circle is 4 feet. What is the circumference?
d=4 ft
Give the exact answer in simplest form.
I need the answers
Answer: 4π
Step-by-step explanation: C= 2πr; 2r=d; C=dπ; C=4π!
Answer:
4π ft
Step-by-step explanation:
C = 2πr (Circumference formula for a circle)
diamater = 4, so diamter = 2 x radius, 4 = 2 x r , so r = 2
Use formula:
C = 2π(2) = 4π
4π ft (Exact answer)
Minh wants to buy a car costing $9,950. She can put $1,000 down and finance the rest at 10.9% APR, making the monthly payments for 3 years. How will Minh pay in finance charges? What will her monthly payments be?
Answer:
piip;[-p-o-ul0i
Step-by-step explanation:
Multiplication and division questions that equal -8?
And another one for -15?
Pls and thank u <3
For negative 8
1. -4 x 2
2. -48 ÷ 8
For negative 15
1. -5 x 3
2. -60 ÷ 4
( Sorry if they aren't complex enough)
Find –(–14).
–14
–4
4
14
Answer:
bhjtijo3
Step-by-step explanation:
Answer:
Step-by-step explanation:
D. 14
Thomas loaned $6,250 to Cameron at a simple interest rate of 4.12% p.a. for 2 years and 6 months. Calculate the amount of interest charged at the end of the term. Round to the nearest cent
The amount of interest charged at the end of the term is approximately $644.75.
To calculate the amount of interest charged at the end of the term, we can use the simple interest formula:
Interest = Principal * Rate * Time
Principal = $6,250
Rate = 4.12% = 0.0412 (decimal form)
Time = 2 years + 6 months = 2.5 years
Plugging in these values into the formula, we have:
Interest = $6,250 * 0.0412 * 2.5
Calculating this expression:
Interest = $6,250 * 0.0412 * 2.5 = $644.75
Therefore, the amount of interest charged at the end of the term is $644.75 (rounded to the nearest cent).
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What is the mean of the following data set?
25, 34, 33, 41, 19, 20, 25, 22, 30, 29, 34, 39
A: 29.5
B:29.25
C:29.75
Answer:
B
Step-by-step explanation:
After adding them all together, we end up with 351. There are 12 numbers, so we do 351/12, getting 29.25.
1. What is 5,509 rounded to the thousands place?
А
6,000
B
5,500
5,600
D
5,000