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Rina8888 [55]
3 years ago
10

(HELP NEEDED RIGHT NOW)Marisol is making lemonade to sell at her lemonade stand. Her recipe calls for 5 cups of sugar for every

9 cups of water. Which ratio of cups of sugar to cups of water will make the same flavor? *
30 : 54

6 : 10

10 : 45

27 : 15
Mathematics
2 answers:
zvonat [6]3 years ago
4 0
I think it’s the first one. 30:54 because 5 times 6 is 30 and 9 times 6 is 54.
Yakvenalex [24]3 years ago
3 0

My answer would have to be:

30 : 54

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V = - 3

Step-by-step explanation:

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How could Brent use a rectangle to model the factors of x2 – 7x + 6?
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An archaeologist uses an accelerator mass spectrometer to find the age of a buried branch. At the 68\%68%68, percent confidence
Komok [63]

Answer:

B. 10000 years old, with a margin of error of 400 years

Step-by-step explanation:

Assuming this complete problem: "12. An archaeologist uses an accelerator mass spectrometer to find the age of a buried branch. At the 68% confidence level, the spectrometer estimates that the branch was 10,000 years old with a following could the spectrometer estimate as the age of the branch at the 95% confidence level?"

The possible options are:

A. 9500 years old, with a margin of error of 500 years

B. 10000 years old, with a margin of error of 400 years

C. 9500 years olds, with a margin of error of 50 years

D. 10000 years old, with a margin of error of 40 year

Solution to the problem

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".

\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

The margin of error for this case is given by this formula:

ME= z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

For the first case the confidence was 68% so then \alpha =1-0.68 =0.32 and \alpha/2 =0.16 we can find a critical value on the normal standard distribution that accumulates 0.16 of the area on each tail and this value is z=\pm 0.994, because P(z<-0.944) = 0.16 and P(Z>.944) = 0.16

The margin of error can be expressed like this:

ME = z_{\alpha/2} SE

We can solve for the standard error on this case and we got:

SE = \frac{ME}{z_{\alpha/2}} =\frac{200}{0.994}=201.207

And then for the new confidence interval we need to calculate the new z_{\alpha}. For the first case the confidence was 95% so then \alpha =1-0.95 =0.05 and \alpha/2 =0.025 we can find a critical value on the normal standard distribution that accumulates 0.025 of the area on each tail and this value is z=\pm 1.96, because P(z<-1.96) = 0.025 and P(Z>1.96) = 0.025. So then the new margin of error would be:

ME = z_{\alpha/2} SE = 1.96*201.207=394.366

The estimation for the mean not changes and from the before and new case is 1000 years. So then the best option for this case would be:

B. 10000 years old, with a margin of error of 400 years

And makes sense since a larger confidence interval means a wider interval.

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Answer:

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Step-by-step explanation:

f(x) = 9+3x

Let x=-2

f(-2) = 9+3(-2)

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