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In-s [12.5K]
3 years ago
14

Hays builds model sailboats as a hobby. The dimensions of the sailboats are given. What is the height, x, of the smaller sailboa

t's sail? Enter your answer, as a decimal, in the box. x = in. Two sailboats with sails that are right triangles. The top angle on the sails are marked congruent to each other. The smaller sail has a height of x and a base of 7 inches. The larger sail has a height of 12 inches and a base of 8 inches.
Mathematics
2 answers:
BabaBlast [244]3 years ago
4 0

Answer:

10.5

Step-by-step explanation:

I took the quiz

Vesnalui [34]3 years ago
3 0
The answer should be 10.5 
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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.

8 0
3 years ago
SOLVE PLEASE !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Aleks04 [339]

Answer:

-7

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Convert this franction into a percentage 9/12?
kolbaska11 [484]

<span>Hello, Yoloalanis. In order to solve this question that you have just posted, you only have to do a few simple steps. So, We can do this!</span>

<span />Let's start with your fraction. You will first have to change 9/12 into a decimal. In order to do this, you will have to divide the numerator by the denominator. A numerator is also known as the top part of the fraction. A denominator is the bottom part of the fraction. So, when you divide nine by twelve, you get 0.75 as a decimal. Now, you just have to multiply the decimal by 100 or to make it simpler, just move the decimal two places to the right. To sum it all up, you will get 75%.

Hope it helps :)

5 0
3 years ago
Read 2 more answers
Plz answer as fast possible
My name is Ann [436]
9. 500 5
6000 60
30000 300
10. 48 0.48
9.7 0.097
510.3 5.103
6 0
3 years ago
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Natalia lives in a house that is 2 meters below sea level. Natalia goes to school every day, which is 13 meters above sea level.
alisha [4.7K]

Answer: Natalia travels 15 meters to get from home to school

8 0
3 years ago
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