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Colt1911 [192]
3 years ago
13

The area of a mirror is 225 square inches,and it’s width is 13 3/4 inches.Will the mirror fit in a space that is 15 inches by 16

inches?
Mathematics
2 answers:
In-s [12.5K]3 years ago
6 0

Answer: No


Step-by-step explanation:

225/13.75= about 16.36

But 16.36 is more than both 15 and 16

Andru [333]3 years ago
6 0

Answer:

No

Step-by-step explanation:

It will be close.

Formula

Area = L * W

Givens

Area = 225 square inches

W = 13 3/4 = 13.75

Solution

  • Area = L * W
  • 225 = L * 13.75                    Divide both sides by 13.75
  • 225/13.75 = L*13.75/13.75  
  • 16.36 = L

Answer

No it won't fit in the given space. The mirror is too large.

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Answer:

10.08-1.64\frac{0.1}{\sqrt{6}}=10.013    

10.08+1.64\frac{0.1}{\sqrt{6}}=10.147    

So on this case the 90% confidence interval would be given by (10.013;10.147)    

Step-by-step explanation:

Previous concepts

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)

\sigma =0.1 represent the population standard deviation

n represent the sample size  

Solution to the problem

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

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

In order to calculate the mean and the sample deviation we can use the following formulas:  

\bar X= \sum_{i=1}^n \frac{x_i}{n} (2)  

s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}} (3)  

The mean calculated for this case is \bar X=10.08

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that z_{\alpha/2}=1.64

Now we have everything in order to replace into formula (1):

10.08-1.64\frac{0.1}{\sqrt{6}}=10.013    

10.08+1.64\frac{0.1}{\sqrt{6}}=10.147    

So on this case the 90% confidence interval would be given by (10.013;10.147)    

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Answer:

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