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n200080 [17]
3 years ago
11

Solve the equation 1.87 = x + 11.04

Mathematics
2 answers:
Alina [70]3 years ago
7 0

Answer:

-9.17 = x

Step-by-step explanation:

1.87 = x + 11.04

Subtract 11.04 from each side

1.87-11.04 = x + 11.04-11.04

-9.17 = x

OverLord2011 [107]3 years ago
3 0

Answer:

x =  - 1.97

Step-by-step explanation:

1.87 = x + 11.04 \\ 1.87 - 11.04 = x \\ x =  - 9.17

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leva [86]

Answer:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2 (2)  

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025,0,1)", and we got z_{\alpha/2}=1.96, replacing into formula (2) we got:  

n=(\frac{1.96(0.25)}{0.1})^2 =24.01  

So the answer for this case would be n=25 rounded up to the nearest integer  

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=0.25 represent the population standard deviation

n represent the sample size (variable of interest)  

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}}  

The margin of error is given by this formula:  

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}} (1)  

And on this case we have that ME =0.1 and we are interested in order to find the value of n, if we solve n from equation (1) we got:  

n=(\frac{z_{\alpha/2} \sigma}{ME})^2 (2)  

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025,0,1)", and we got z_{\alpha/2}=1.96, replacing into formula (2) we got:  

n=(\frac{1.96(0.25)}{0.1})^2 =24.01  

So the answer for this case would be n=25 rounded up to the nearest integer  

8 0
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____________________

6(3+a)=18+6a


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