Answers
Answer:
R = 1
I = [-1, 1)
Step-by-step explanation:
Use the ratio test:
lim(n→∞)│aₙ₊₁ / aₙ│
lim(n→∞)│[xⁿ⁺¹ / (8(n+1) − 1)] / [xⁿ / (8n − 1)]│
lim(n→∞)│[xⁿ⁺¹ / (8n + 7)] × [(8n − 1) / xⁿ]│
lim(n→∞)│[x (8n − 1) / (8n + 7)]│
lim(n→∞)│[(8n − 1) / (8n + 7)]││x│
│x│
The series converges if the limit is less than 1.
│x│< 1
So the radius of convergence is 1.
Solving for x:
-1 < x < 1
Check the endpoints.
If x = -1, the series is ∑ (-1)ⁿ / (8n − 1), which converges.
If x = 1, the series is ∑ 1 / (8n − 1), which diverges.
So the interval of convergence is [-1, 1).
Related Questions
Marcus borrowed 13.45 on Thursday. He earned 45.32 on Friday and immediately
Answers
Answer: I'm not exactly sure what your asking, but throughout two days Marcus borrowed $13.45 and then made $45.32. If he immediately paid his owed money back then he would have a current amount of 31.87 in his possession. That is unless he had interest on that owed money for one day
Step-by-step explanation:
$45.32-$13.45 = $31.87
14. List the next nine multiples of each number. Find the common multiples.
1924
Multiples of 2:2,
Multiples of 8: 8,
Common multiples:
Answers
Answer:
2 if I am not mistaken I think it 2 4 6 8 10 12 14 16 18 20
Step-by-step explanation:
next 8 I believe it is 8 16 24 32 40 48 56 64 72 80
Answer:
2 4 6 8 10 12 14 16 18 20
8 16 24 32 40 48 56 64 72 80
Step-by-step explanation:
3.4. There are five learners in a class that have written a final year mathematics examination paper.
Aletta scored 55 % for this paper. Vera scored 36 % and Sibusiso scored 88 %. If Thoko scored 71 %
and the class average was 63 %, what was David's score (as a percentage)?
Answers
Answer:
average quiz mean = 85, exams =78, 81, 92, homework mean ... Infant Mortality 63.
Which percent problems will result in an answer that is smaller than the original number? Which will result in an
answer that is larger than the original number? Sort the tiles into the correct categories.
What is 9% of 998 pages?
Smaller
Larger
How many is 220% of 40 people?
Find 6% of $3,004
How many is 51% of 120 people?
Find 101% of 50
What is 1000% of $2?
Answers
Answer:
Step-by-step explanation:
Answer:
SMALLER
What is 9% of 998 pages?
Find 6% of 3004
how many is 51% of 120 people
LARGER
how many is 220% of 40 people
find 101% of 50
what is 1000% of 2
Step-by-step explanation:
Priya ran 10 meters in 2.4 seconds. At this rate, how long would it take her to run 50 meters? *
Answers
Complete the solution of the equation. Find
the value of y when x equals 12.
x + 3y = 21
Answers
Answer:
y=3
Step-by-step explanation:
12+3y=21
-12 -21 subtract 12 from both sides
------------------
3y=9
divide 3 from y and 9, so you can get y by itself
3y/3= y 9/3= 3
so y is equal to 3
y= 3 because
if you substitute 12 for x then you get
12+ 3y =21
you subtract 12 from each side and you get 3y =9 then you divide each side by 3 and you get y=3
What’s the distance between these two pair of points -3, -6 and -3, 1
Answers
Answer:
5
Step-by-step explanation:
r/6=-2 i need help TvT
Answers
Answer:
r=-12 (R equals negative 12)
Step-by-step explanation:
r/6=-2
r=-2*6
r=-12
At the potluck, there were 6 pecan pies, 7 lemon pies, 13 cherry pies, and 8 apple pies. Determine the ratio of apple pies to the total number of pies.
Answers
Makayla is reading a 400-page book for her book club. She reads 32 pages each hour.
Use the drop down menus below to construct a function that models the number of pages, P(t). Makayla has left to read after t hours of reading.
P(t) =
Answers
Answer: P(t)=400-32t
HELP PLEASE GOD I HAVE A DAY HELP!!!!) A daycare employee earns $10.90 per hour for the first 40 hours he works in 1 week. He is paid 1.5 times that rate for each additional hour that he works. How much money does he earn working for 43 hours in 1 week?
Answers
Answer:
$485.05 per week of 43 hours labor
Step-by-step explanation:
First of all, we already know that he works the first 40 hours, so:
$10.90*40= $436
Now it says the next three hours are 1.5* the original pay;
$10.90*1.5= $16.32 (x 3 because thats the extra hours)
$16.32*3 = $49.05
Now, we add the numbers:
$436+$49.05= $485.05
All done!
Solve. Give the solutions for "m"
100m² =100,000
Answers
Answer:
I think m= +or- 31.623
Step-by-step explanation:
divide 100k by 100 then square root. its a quadratic so 2 answers
Section 3 - Topic 1 What is a Function? 1. A group of students were discussing whether the relationship on the graph is o function Ed: The relotionship is not a function because if I craw a horizontal line at y= 2, the horizon al line crosses the graph ot two points. Debra: The relationship is a function because it is a graph of two different Alejandro: The relationship is not a function because x = 1 has two different y-values. Antoine: The relationship is a function because I can write an equation for diline. Which students are not correct and whot is the flow in their argument:
Answers
9514 1404 393
Answer:
Not correct: Ed, Debra, Antoine
Step-by-step explanation:
Ed is incorrect because he is using a horizontal line test instead of the appropriate vertical line test.
Debra is incorrect because the fact it is two different lines is irrelevant. A piecewise linear function may be two or more different lines.
Antoine is incorrect because the existence of an equation for the curve has nothing to do with whether or not it is a function. (Here, Antoine would need two equations with overlapping domains. The overlap of the domains is what tells you it is not a function.)
__
Alejandro is correct. The relation fails the vertical line test
A frequency distribution for the response time for EMTs after a 911 call is shown below.
Response Time for EMTS
Frequency
Response Time
(in minutes)
7-7.9
19
8-8.9
23
9-9.9
38
47
10 - 10.9
11 - 11.9
12 - 12.9
43
29
13-13.9
21
Step 2 of 2: Calculate the population variance for the response time. Round any intermediate calculations, if needed, to no less than four decimal places, and round
your final answer to two decimal places.
Answers
Answer: σ² = 2.90
Step-by-step explanation: For a frequency table, population variance is calculated by:
[tex]\sigma^{2}=\frac{\Sigma f(x-\mu)^{2}}{\Sigma f}[/tex]
where
f is frequency
μ is expected value or mean of the distribution
In this case, mean of the distribution for a grouped frequency table is calculated by:
[tex]\mu=\Sigma x.f(x)[/tex]
where
x is (as the data is grouped) the mid value of the response time
So, the table is
x | f
6.45 | 18
7.45 | 21
8.45 | 34
9.45 | 46
10.45 | 46
11.45 | 25
12.45 | 21
And mean will be:
[tex]\mu=6.45(18)+7.45(21)+8.45(34)+9.45(46)+10.45(46)+11.45(25)+12.45(21)[/tex]
μ = 9.5874
To calculate the variance, the formula above is transformed into
[tex]\sigma^{2}=\frac{\Sigma f.x^{2}-\frac{(\Sigma f.x)^{2}}{\Sigma f} }{\Sigma f}[/tex]
So, to facilitate the calculations, divide each term in a table:
f | x | f.x | f.x²
18 | 6.45 | 116.1 | 748.845
21 | 7.45 | 156.45 | 1165.5525
34 | 8.45 | 287.3 | 2427.685
46 | 9.45 | 434.7 | 4107.915
46 | 10.45 | 480.7 | 5023.315
25 | 11.45 | 286.25 | 3277.5625
21 | 12.45 | 261.45 | 3255.0525
∑ 211 | | 2022.95 | 20005.9275
Population variance will be:
[tex]\frac{(\Sigma f.x)^{2}}{\Sigma f} =[/tex] [tex]\frac{(2022.95)^{2}}{211}[/tex] = 19394.9133
[tex]\sigma^{2}=\frac{\Sigma f.x^{2}-\frac{(\Sigma f.x)^{2}}{\Sigma f} }{\Sigma f}[/tex]
[tex]\sigma^{2}=\frac{20005.9275-19394.9133}{211}[/tex]
σ² = 2.90
The population variance for the response time for EMTs is 2.90.
A man and a woman start from the same point. The man walks S60°E at 1.3 m/sec. The woman
walks south at 1.6 m/sec. At what rate is the distance between the man and woman changing
after 35 minutes?
Answers
Answer:
The distance between the man and woman is changing at the rate of 1.5 m/sec.
Step-by-step explanation:
Speed = [tex]\frac{distance}{time}[/tex]
⇒ distance = speed x time
After 35 minutes (2100 seconds) ,
the man has walked a distance = 1.3 x 2100
= 2730 m
After 35 minutes, the woman has walked a distance = 1.6 x 2100
= 3360 m
The sketch of the displacement of the man and woman forms a triangle with an included angle. Applying the cosine rule, we have:
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2abCos θ
= [tex]3360^{2}[/tex] + [tex]2730^{2}[/tex] - 2 x 3360 x 2730 x Cos [tex]60^{o}[/tex]
= 11289600 + 7452900 - 18345600(0.5)
= 18742500 - 9172800
= 9569700
c = [tex]\sqrt{9569700}[/tex]
= 3093.5 m
The distance between the man and woman at 35 minutes is 3093.5 m.
The distance between the man and woman is changing at the rate = [tex]\frac{3093.5}{2100}[/tex]
= 1.4731
= 1.5 m/sec
The distance between the man and woman is changing at the rate of 1.5 m/sec.
A football team lost 9 yards during a play. The team had a combined gain or loss of 0 yards after the next A football team lost 9 yards during a play. The team had a combined gain or loss of 0 yards after the night bye play. What integer represents The yards gained or lost on the next play? Show this on the number line
Answers
Find the radius c=63 ft
Answers
The winner of a 200 mile race drove his car to victory at a rate of 108.4493 mph. What was his time to the nearest thousandth of an hour)?
Answers
Answer:
The answer is 1.844 sStep-by-step explanation:
From the question the time taken can be found by using the formula
[tex]t = \frac{d}{v} \\ [/tex]
where
d is the distance
v is the velocity
From the question we have
[tex]t = \frac{200}{108.4493} \\ = 1.844179...[/tex]
We have the final answer as
1.844 s to hr the nearest thousandthHope this helps you
Answer:
108.449
Step-by-step explanation:
The ratio of boys to girls in Ms. Fullbright's class is 2 to 3. There are 18 girls in the class. What is the total number of students in Ms. Fullbright's class?
Answers
Mark and a friend went out for dinner. The bill was $23.40. They will leave a 20% tip. How much of a tip will they leave
Answers
Answer: $4.68
Step-by-step explanation: $23.40 % 20% = $4.68.
if i add 456 plus 789 then subtract it by 656 then multiply it by 1000 what is the answer?
Answers
Answer:
I got -654,755
Step-by-step explanation:
456+789-656×1000
help idk how to do this whats the answer plz
Answers
Answer:
79 degrees i think
Step-by-step explanation:
Lines that are horizontal and straight are always 180 degrees so i just subtracted 180 degrees from 101 and i got 79 degrees
Answer:
x = 79
Step-by-step explanation:
A straghit line is equal to 180 degrees.
If 101 of it is taken, you have to find out what the other side is equal to.
The equation would look like: 101 + x = 180 or 180 - 101 = x
I hope you understand now! :D
ASAP NO ROCKY RN
What is an equation of the line that passes through the point (-5,7) and is parallel
to the line 3 - 5y = 15?
Answers
Answer
y=0x+7
Step-by-step explanation:
Parallel lines share the same slope, to solve, you need to find the slope of the line it is parallel to.
3-5y=15, since this equation has no x value, that basically means that the slope is 0.
Since the slope is 0 and you have an ordered pair, you can now substitute the ordered pair and the slope into slope intercept form to solve for 'b' or the y intercept.
y=mx+b
(-5,7)
7=0(-5)+b
b=7
y=0x+7
name the order of operations
Answers
Answer:
PEMDAS
Step-by-step explanation:
Parentheses, Exponents, Division and Multiplication, Addition and Subtraction. When I put an and I mean do them in order of left to right.
Answer:
PENDMAS
Step-by-step explanation:
Parenthesis, Exponent, Multiplication, Addition, Subtraction.
|10-4x|-2=9
Please help
Answers
Answer:
x=-0.25,5.25 The values in their fraction form are -1/4 21/4
Help please and thank you
Answers
a restaurant found that 6 people out of 20 wanted cheese on their sandwich. what percent of the people wanted cheese
Answers
Answer:
30%
Step-by-step explanation:
did it
What is the probability that the spinner will land on a heart
Answers
Answer:
There isnt any image to answer this question, sorry
How is 24,902 written in expanded form?
2,000 + 400 + 90 + 2
24,000 + 900 + 2
20,000 + 4,000 + 90 + 2
20,000 + 4,000 + 900 + 0 + 2
Answers
Answer:
D
Step-by-step explanation:
Because 24000 + 900 = 24900 then 0, and 2 added is 24902
In a group of 42 tourists, everyone speaks English or French; there are 35 English speakers and 18 French speakers. How many speak both English and French?
Answers
Answer:
7
Step-by-step explanation:
35 speak english
18 speak french
42-35 = 7
Answer:
7
Step-by-step explanation:
