1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anni [7]
3 years ago
6

Show that the series is convergent by the alternating series test, and find the number of terms necessary to estimate the sum of

the series with an error of less than 0.05.

Mathematics
1 answer:
Murljashka [212]3 years ago
7 0

Answer:

6 terms

Step-by-step explanation:

2 − 2/4 + 2/9 − 2/16 + ...

∑ (-1)ⁿ⁺¹ 2 / n²

Applying alternating series test:

lim(n→∞) 2/n² = 0

2/(n+1)² < 2/n², so the series is decreasing.

Therefore, the series converges.

2/(n+1)² < 0.05

(n+1)²/2 > 20

(n+1)² > 40

n+1 > 6.32

n > 5.32

n = 6

You might be interested in
The dolphins are feed 64 buckets of fish each day. The penguins are feed 1/8 as many buckets of fish as the dolphins. How many b
Sav [38]

Answer:

8

Step-by-step explanation:

You just gotta divide 64 by 8

4 0
3 years ago
Let f(x) = Ax + B and g(x) = Cx + D where A, B, C, and D are non-zero constants. Use upper case letters for A, B, C, D and lower
Elodia [21]

Answer:

Let f(x) = Ax + B and g(x) = Cx + D where A, B, C, and D are non-zero constants. Use upper case letters for A, B, C, D and lower case letter for x in your answers below. (a) Find f(g(x)). f(g(x)) = A(Cx + D) + B (b) Find the slope of the function you found in part (a). slope = (c) Find the vertical intercept of the function you found in part (a). Do not write your answer as a point

6 0
3 years ago
A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associ
andrew11 [14]

Answer:

there were 2 partners and 4 associates

Step-by-step explanation:

at 1300 per partner if you hire 2 thats 1300 x 2 = 2600

thrn 4 associates at 400 each 400 x 4 = 1600

now add 2600 + 1600 = 4200

6 0
3 years ago
Which number is between 3.22 and 3.36? <br> A. 3.2<br> B. 3.93<br> C. 3.37
siniylev [52]

Answer:

a?

Step-by-step explanation:

5 0
3 years ago
A Pew Internet poll asked cell phone owners about how they used their cell phones. One question asked whether or not during the
EastWind [94]

Answer:

a) \hat p=\frac{471}{1024}=0.460

The standard error is given by:

SE= \sqrt{\frac{\hat p(1-\hat p)}{n}}=\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0156

And the margin of error is given by:

ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}=1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0305

b) The 99% confidence interval would be given by (0.429;0.491)

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Data given and notation  

n=1024 represent the random sample taken    

X=471 represent the people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

\hat p=\frac{471}{1024}=0.460 estimated proportion of people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering    

p= population proportion of people responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering

Part a

The confidence interval would be given by this formula

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

For the 95% confidence interval the value of \alpha=1-0.95=0.05 and \alpha/2=0.025, with that value we can find the quantile required for the interval in the normal standard distribution.

z_{\alpha/2}=1.96

The standard error is given by:

SE= \sqrt{\frac{\hat p(1-\hat p)}{n}}=\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0156

And the margin of error is given by:

ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}=1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.0305

Part b

If we replace the values obtained we got:

0.460-1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.429

0.460+1.96\sqrt{\frac{0.460(1-0.460)}{1024}}=0.491

The 99% confidence interval would be given by (0.429;0.491)

8 0
3 years ago
Other questions:
  • Heather is saving for retirement and has been doing a lot of research on how much she should put aside each month. The newest ar
    12·2 answers
  • A local gym offers a trial membership for 3 months. It discounts the regular monthly fee x by $25. If the total cost of the tria
    14·2 answers
  • A total of
    15·1 answer
  • A burglar alarm system has six fail-safe components. the probability of each failing is 0.05. find the probability that exactly
    6·1 answer
  • A line passes through (2,8) and (4,12) which equation best represents the line
    13·2 answers
  • Bailey brought a rectangular prism shaped fish tank the tanks length is 20 inches width is 12 inches and the height is 18 inches
    12·1 answer
  • The energy saving from recycling one glass bottle will power the oven Adam uses to cook the turkey for 7.5 minutes.
    8·1 answer
  • Describe a sequence ​
    10·1 answer
  • Holly spends
    8·1 answer
  • Can someone help me with this?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!