The interval of convergence of the power series is (-10/7, 10/7).
What does Interval of convergence tell you?
A group of x-values on which a power series converges is known as the interval of convergence. In order to create a convergent series, you can plug in this interval of x-values.
The interval of convergence of a power series is the set of values of x for which the series converges. To find the interval of convergence of the given power series, we can use the ratio test.
The ratio test states that if the series [tex]∑ a_nx^n[/tex] has a positive radius of convergence R, then the series converges for |x| < R and diverges for |x| > R. The radius of convergence is given by the formula
[tex]R = 1/limsup|a_n+1/a_n|.[/tex]
In the given power series, the coefficient [tex]a_n[/tex] is given by [tex]a_n = (7x)^n/(10n)!.[/tex]
We can rewrite this as [tex]a_n = x^n(7/10)^n/n!.[/tex]
Taking the limit of the ratio [tex]a_n+1/a_n[/tex] as n goes to infinity, we get:
[tex]limsup|a_n+1/a_n| \\\\= limsup|x^(n+1)(7/10)^(n+1)/(n+1)!/(x^n(7/10)^n/n!)|\\\\= limsup|x(7/10)/(n+1)|\\\\= |x(7/10)|[/tex]
Therefore, the radius of convergence R is [tex]1/|x(7/10)|[/tex].
This means that the interval of convergence is [tex]|x| < 1/|7x/10| = 10/7.[/tex]
We can check the endpoints of the interval to see if the series converges at these points. At x = 10/7, the series becomes [tex](7(10/7))^n/(10n)! = 1^n/(10n)!.[/tex]
This series is a geometric series with first term 1 and common ratio 1/10, and it converges because [tex]|1/10| < 1.[/tex]
At x = -10/7, the series becomes[tex](7(-10/7))^n/(10n)! = (-1)^n/(10n)![/tex]. This series is an alternating series with first term 1 and common ratio (-1/10), and it also converges because [tex]|-1/10| < 1.[/tex]
Therefore, The interval of convergence of the power series is (-10/7, 10/7).
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which graph correspond to the following-2x-3y
Answer:
Hi! The answer to your question is in the picture below
Step-by-step explanation:
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Hope this helps!!
- Brooklynn Deka
please do this thanks
Answer:
225 in²
Step-by-step explanation:
First you have to find the ∛3,375 since it is a cube you know that all the dimensions are the same so when 15 comes out all you have to do is multiply the height by the length to get the area of one of its sides to get the answer.
With double-digit annual percentage increases in the cost of health insurance, more and more workers are likely to lack health insurance coverage (USA Today, January 23, 2004). The following sample data provide a comparison of workers with and without health insurance coverage for small, medium, and large companies. For the purposes of this study, small companies are companies that have fewer than 100 employees. Medium companies have 100 to 999 employees, and large companies have 1000 or more employees. Sample data are reported for 50 employees of small companies, 75 employees of medium companies, and 100 employees of large companies.
Health Insurance
Size of Company Yes No Total
Small 33 17 50
Medium 68 7 75
Large 88 12 100
Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use = .05.
1. Compute the value of the 2 test statistic (to 2 decimals).
2. The p value is :_____.
a. less than .005
b. between .005 and .01
c. between .01 and .025
d. between .025 and .05
e. between .05 and .10
f. greater than .10
3. What is your conclusion?
a. health insurance coverage is not independent of the size of the company
b. Cannot reject the assumption that health insurance coverage and size of the company are independent
4. The USA Today article indicated employees of small companies are more likely to lack health insurance coverage. Calculate the percentages of employees without health insurance based on company size (to the nearest whole number).
Small %
Medium %
Large %
Answer:
1. χ² = 15.3902
2. The p value is :_____.a. less than .005
3. Conclusion
a. health insurance coverage is not independent of the size of the company
4. The percentages of employees
Small %= 33/50= 0.66
Medium %= 68/75 = 0.91
Large %= 88/100= 0.88
Step-by-step explanation:
1) We set up our null and alternative hypothesis as
H0: the employee health insurance coverage is independent of the size of the company
against the claim
Ha: the employee health insurance coverage is not independent of the size of the company
2) the significance level alpha is set at 0.05
3) the test statistic under H0 is
χ²= ∑ (O - E)²/ E where O is the observed and E is the expected frequency
which has an approximate chi square distribution with ( 3-1) (2-1)= 2 d.f
4) Computations:
Under H0 , the observed frequencies are :
Observed Expected E (O-E) (O-E)² (O-E)²/E
33 42 -9 81 1.928
68 63 5 25 0.3968
88 84 4 16 0.1904
17 8 9 81 10.125
7 12 -5 21 1.75
12 16 -4 16 1
15.3902
Expected Values are calculated using the formula :
Row Total * Column Total / sample size
E1= (33+17) (33+ 68+88)/ 50+75+100= 42
E4= (33+17) (17+ 7+ 12)/ 50+75+100=8
E2= (68+7) (33+ 68+88)/ 50+75+100= 63
E5= (68+7) (17+ 7+ 12)/ 50+75+100= 12
E3= (88+12) (33+ 68+88)/ 50+75+100= 84
E6= (88+12) (17+ 7+ 12)/ 50+75+100= 16
5) The critical region is χ² ≥ χ² (0.05)2 = 5.99
6) Conclusion:
The calculated χ² = 15.3902 falls in the critical region χ² ≥ 5.99 so we reject the null hypothesis that the employee health insurance coverage is NOT independent of the size of the company.
2. The p value is :_____.
a. less than .005
The p-value is .000385.
3. Conclusion
a. health insurance coverage is not independent of the size of the company
4. The percentages of employees
Small %= 33/50= 0.66
Medium %= 68/75 = 0.91
Large %= 88/100= 0.88
need help with math its a struggle
Answer:
(1,4)
(0,0)
Step-by-step explanation:
smarts
Answer:
1,4
0,0
Step-by-step explanation:
whatever is in the purple is valid and the closed line is inclusive so anything on it counts but the dotted line is exclusive
Luna's dining room is 19 feet wide and 22 feet long. Luna wants to install wooden trim
around the top of the room. The trim costs $0.06 per foot. How much will it cost Luna to buy
enough trim?
9514 1404 393
Answer:
$4.92
Step-by-step explanation:
The cost is found by multiplying the number of feet by the cost per foot. The number of feet is the perimeter of the dining room, the sum of the lengths of all the sides.
There are two sides of the rectangular room that are 19 feet, and two sides that are 22 feet, so the total length of trim is ...
P = 2(L +W) = 2(22 ft + 19 ft) = 2(41 ft) = 82 ft
The cost is then ...
cost = ($0.06/ft)(82 ft) = $4.92
It will cost Luna $4.92 to buy enough trim.
Pls help 10 ptsssssssssssss
NO LINKS
Answer:
the answer is 16
Step-by-step explanation:
8/2=4
4*4=16
Amiyah has two coupons from Macy's Department Store, one for $20 off
and another for 20% off. She wants to purchase a shirt for $64. Her
friend Emma told her to use the 20% off coupon because it is the best
deal and her other friend Jermaine told her to use the $20 off coupon
because it is the best deal. Which friend is correct and why?
Answer:Jermaine
Step-by-step explanation:
please anwser this thank you!!
Step-by-step explanation:
v>29 or 29,infinity sign i used an app called and this is what it showed
<3<3<3<3<3<3<3<3<3<3<<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
Answer:
v >_ 29
<3<3<3<3<3<3<3<3<3<3<<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
Please help!!!!!!!!!
Answer:
-1 is the remainder
hope it helps
Solve for q: 2q- 12 = -40
Answer:
q = -14
Step-by-step explanation:
2q - 12 = -40
Add 12 to both sides
2q - 12 + 12 = - 40 + 12
2q = - 28
Divide both sides by 2
2q/2 = -28/2
q = - 14
The mean height of women in a country (ages 20-29) is 63.9 inches. A random sample of 65 women in this age group is selected. What is the probability that the mean height for the sample is greater than 64 inches? Assume σ = 2.96.
Answer: The mean height of women in a country ages 20 29
The mean height of women in a country (ages 20-29) is 63.7 inches.
8 The circle graph below shows the number of votes each candidate received in a recent student
council election.
Student Council Election
Votes Received
Jacob
60
Elias
25
Jade
40
What percentage of the votes did Jacob receive?
F 36%
G 44%
H 48%
J 60%
Answer:
60%
Step-by-step explanation:
Use the box plots for 3 and 4. What are the two medians. Pls help me
Answer:
C
Step-by-step explanation:
Answer:
C. 40 and 50
Step-by-step explanation:
The median marks the mid-point of the data and is shown by the line that divides the box into two parts (sometimes known as the second quartile). Half the scores are greater than or equal to this value and half are less.
which expression is equivalent to 6^4x6^3
Answer:
C - (6x6x6x6)(6x6x6)
Step-by-step explanation:
What’s the volume of 9 cm 6 cm 4 cm
Answer:
bro tell me the shape
Step-by-step explanation:
13/4 + c = 3/4 what’s c,?
Answer:
c = -2.5
Step-by-step explanation:
13/4 + c =3/4
2.5 + c = 0
c=-2.5
Long division259560÷25
Answer:
21
Step-by-step explanation:
If 43x-2=4 x+1, then x
Answer:
Step-by-step explanation:
Picture has the answer, not a bad picture I promise.
Step-by-step explanation:
43x-4x=1+2
39x/39=3/39
x=0.076
I need some help! Will give brainliest!!!
Answer:
Positive 7 on the line pointing up (y axis) is where you start (where your first dot goes when graphing). Then down two and right one. (Your second dot will end up on (5,1))
Step-by-step explanation:
What is the missing length?
A. 15
B. 30
C. 8
D. 7
Answer:
red and blue are not a Selection!!!!!
4. What is the volume of the triangular pyramid?
10 in
6 in
8 in
Will Mark brainliest
Answer:
V=6240 in^3
Step-by-step explanation:
I am not sure what the base is but here is my guess:
V=13Ah
V=13(48)(10)
V=6240 in^3
A survey was conducted to investigate whether there is an association between a person's age and their thoughts on what a state senate should do about state parks. Participants selected from "leave state parks the way they are," "increase funding to state parks," or "completely overhaul state parks," and their age was categorized as under 30 years old, between 30 and 50 years old, and over 50 years old. The hypothesis test statistic was calculated to be 15.01. Which of the following is closest to the p- value of the test?
A. 0.0047
B. 0.0103
C. 0.0202
D. 09897
E. 0.9953
Answer:
E. 0.9953
Step-by-step explanation:
The computation of the p value is shown below:
According to the question
The participant choosen from 3 different state parks, r = 3
And there are 3 different age group, s = 3
So, degrees of freedom is
= (r-1) × (s-1)
= 2 × 2
= 4
And, the Test statistic is 15.01
Now
p-value = P(Chisq < 15.01 )
= 0.9953
In the chisquare table see the degree of freedom i.e. 4
Answer:
0.0047
Step-by-step explanation:
This is what college board says
The value 0.0047 is the probability that χ2 is greater than 15.01 in an χ2 distribution with (3−1)(3−1)=4 degrees of freedom.
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!
Answer:
angle 8 and 4
Step-by-step explanation:
it is shown by the picture I had just provided you
Answer:
A
Explination:
Hope this helps ^-^
Which expressions are equivalent to the one below? Check all that apply. 5^3 • 5^x
A. 5^3 + x
B. 125•5^3
C. (5 • x)^3
D. 25^3x
E. 53^3x
F. 53^3-x
Hi there, I'll help you out :)
The expression that is equivalent to 5^3 • 5^x is A. If you solve the expression given in the question, you get 5^3 + x, which is exactly the same as the first choice.
- B gives you 15625
- C gives you 125x^3
- D gives you 15625^x
- E gives you 148,877^x
- F can't really be solved
Because none of the other answer choices match up, that leaves A as your only answer.
Hope this helps!
The expressions which are equivalent to the one given below are 5³⁺ˣ and 125 (5ˣ).
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given expression is,
5³ . 5ˣ
We have the product rule of exponents that,
xᵃ . xᵇ = xᵃ⁺ᵇ
Using the same here,
5³ . 5ˣ = 5³⁺ˣ ------(1)
Now the value of 5³ = 5 × 5 × 5 = 125
So, 5³ . 5ˣ = 125 (5ˣ) --------(2)
Hence the equivalent expressions are 5³⁺ˣ and 125 (5ˣ).
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A child can choose one stuffed animal. She can choose from a dog or a bear. Each comes in brown, gray or white. You can also choose green eyes or blue eyes. How many possible stuffed animal choices does the child have?
Step-by-step explanation:
[tex]2 \times 3 = 6 \\ 6 \times 2 = 12[/tex]
Which of the following inequalities is correct
Select all numbers that have an absolute value of 4.
Find an equation in slope-intercept form of the line that has slope 2 and passes through point A(-3. - 1)
Answer:
Step-by-step explanation:
m = 2 ; x1 = -3 ; y1 = -1
Slope- point form: y - y1 = m(x -x1)
y - [-1] = 2(x - [-3])
y + 1 = 2(x + 3)
y + 1 = 2x + 3*2
y + 1 =2x + 6
y = 2x + 6 - 1
y = 2x + 5 This is slope intercept form : y = mx + b
What if the value of <5
Answer:
any number from -infinity to 4 is the value less then 5
David rode his bike a total of 214 miles from his house to the store. First he rode 34 mile from his house to his school. Then he rode 14 mile from his school to the library. Finally he rode from the library to the store. How many miles did David ride between the library and the store?
Answer:
166 miles
Step-by-step explanation:
Add the 34 miles he rode from home to school and the 14 miles he rode from school to the library.
34 + 14 = 48.
Subtract 48 from 214 to get 166
214 - 48 = 166
David rode 166 miles between the library and the store.
Hope this helps! Pls mark brainliest