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3 years ago

Find the missing length. The triangles in each pair are similar.

Mathematics

1 answer:

nikitadnepr [17]3 years ago

3 0

The answer is D.13
21/7=3
39/3=13

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g A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estim

kipiarov [429]

Answer:

a) n= 1045 computers

b) n= 442 computers

c) A. Yes, using the additional survey information from part (b) dramatically reduces the sample size.

Step-by-step explanation:

Hello!

The variable of interest is

X: Number of computers that use the new operating system.

You need to find the best sample size to take so that the proportion of computers that use the new operating system can be estimated with a 99% CI and a margin of error no greater than 4%.

The confidence interval for the population proportion is:

p' ± $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'(1-p')}{n} }$

$Z_{1-\alpha /2}= Z_{0.995}= 2.586$

a) In this item there is no known value for the sample proportion (p') when something like this happens, you have to assume the "worst-case scenario" that is, that the proportion of success and failure of the trial are the same, i.e. p'=q'=0.5

The margin of error of the interval is:

d= $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'(1-p')}{n} }$

$\frac{d}{Z_{1-\alpha /2}} = \sqrt{\frac{p'(1-p)}{n} }$

$(\frac{d}{Z_{1-\alpha /2}})^2 = \frac{p'(1-p')}{n}$

$n * (\frac{d}{Z_{1-\alpha /2}})^2 = p'(1-p')$

$n= [p'(1-p')]*(\frac{Z_{1-\alpha /2}}{d} )^2$

$n=[0.5(1-0.5)]*(\frac{2.586}{0.04} )^2= 1044.9056$

n= 1045 computers

b) This time there is a known value for the sample proportion: p'= 0.88, using the same confidence level and required margin of error:

$n= [p'(1-p')]*(\frac{Z_{1-\alpha /2}}{d} )^2$

$n= [0.88*0.12]*(\frac{{2.586}}{0.04})^2= 441.3681$

n= 442 computers

c) The additional information in part b affected the required sample size, it was drastically decreased in comparison with the sample size calculated in a).

I hope it helps!

4 0

4 years ago

Please help will Mark brainiest and please show your working out thanks

AlekseyPX

Step-by-step explanation:

$800ml \times \frac{1}{4} = 200ml \\ 200ml - - > 1800ml \\ 360ml - - - > x \\ \frac{200}{360} = \frac{1800}{x} \\ x = \frac{18}{2} \times 360 \\ \: \: = 9 \times 360 \\ = 3240ml \\ = 3.24l$

6 0

3 years ago

A clown has 54 purple balloons and 36 orange balloons. The clown arranges the balloons into groups that have the same ratio of p

ExtremeBDS [4]

I'd prefer 5/7 because both numbers would be in decimals and you dont need decimals

4 0

3 years ago

The diagram shows a cube of side length 2 cm.

Julli [10]

Dont mind this its just to ask a question

7 0

3 years ago

Read 2 more answers

A^3-b^3/a^3b^3+a^2b^4+ab^5

Len [333]

Hello,

If the question is to simplify then

$\dfrac{ a^{3}-b^{3}}{a^{3}b^{3}+a^{2}b^{4}+ab^{5}}$

$=\dfrac{ (a-b)(a^{2}+ab+b^{2})}{ab^{3}(a^{2}+ab+b^{2})}$

$=\dfrac{ a-b}{ab^{3}}$

8 0

3 years ago