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navik [9.2K]
3 years ago
15

web based software company is interested in estimating the proportion of individuals who use the Firefox browser. In a sample of

200 of individuals, 30 users stated that they used Firefox. Using this data, construct a 99% confidence interval for the proportion of all individuals that use Firefox. What is the lower limit on the 99% confidence interval? Give your answer to three decimal places.
Mathematics
1 answer:
nata0808 [166]3 years ago
6 0
<h2>Answer with explanation:</h2>

Let \hat{p} denotes the sample proportion.

As per given , we have

n= 200

\hat{p}=\dfrac{30}{200}=0.15

Critical value for 99% confidence : z_{\alpha/2}=2.576

Confidence interval for population proportion :-

\hat{p}\pm z_{\alpha/2} \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.15\pm (2.576)(\sqrt{\dfrac{0.15(1-0.15)}{200}})\\\\\approx0.15\pm0.065\\\\=(0.15-0.065,\ 0.15+0.065)\\\\=(0.085,\ 0.215)

Hence, a 99% confidence interval for the proportion of all individuals that use Firefox: (0.085,\ 0.215)

The lower limit on the 99% confidence interval = 0.085

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Find the 9th term of the geometric sequence 6,-24,96... <br><br>​
spin [16.1K]

Answer:

A9 = 393216

Step-by-step explanation:

the first thing that will help you solve this question is finding the common ratio between each terms

the first thing that I like to do that usually helps is to take the second term (-24) and divide it by the first term (6) --> this will usually help you spot the common ratio fairly quickly

in your case, the common ratio is -4

- you can also check this by following my note above and then multiplying the second term by the common ratio to see if it matches the third term, which it does!

so now you can go about this two different ways

1. solve directly for the 9th term

2. use the nth term formula for geometric sequences

METHOD 1:

if you continue to multiply by -4 to solve for each term you would end up with:

6, -24, 96, -384, 1536, -6144, 24576, -98304, 393216

and you will recieve 393216 as your answer

METHOD 2:

the nth term formula is An = A1*r^(n-1)

where An = the nth term of the sequence

A1 = first term of the sequence (6)

and r = common ratio

using this formula, you would get:

A9 = 6(-4)^8

A9 = 393216

I hope this helped :)

 

5 0
2 years ago
Which shows another way to write 64?
Taya2010 [7]

None of those show another way to 64

6*6*6*6=1296

4*4*4*4*4*4=4096

6+6+6+6=24

6*4=24

Another way to show 64 is 8*8 or 4^3

4 0
3 years ago
Write the quotient as a mixed number.<br> 63 divided by 5 = 12 R3
Whitepunk [10]
12 1/4 because the original answer is 12 3/12 but you should simplify it to 12 1/4.
6 0
3 years ago
Simplify foundation of alegebra
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1.) -8 + 10(6 + 4r)

First multiply the 10 into (6 + 4r)

-8 + 60 + 40r

52 + 40r


2.) (8m² - 8m + 8) - (2m - 7m² - 6)

Distribute the - into (2m - 7m² - 6)

8m² - 8m + 8 - 2m + 7m² + 6

Combine like terms

15m² - 10m + 14

(idk if you need to factor this or if you can leave it as is)

3 0
3 years ago
A painter mix 98.7 gallons of blue paint with 67.05 gallons of red paint in a paint mixing machine how much total paint is in th
Nat2105 [25]
67.05 plus 9807 equals 165.75
There is 165.75 gallons of paint in the machein 
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