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tatuchka [14]
3 years ago
7

Two cars leave from the same point (A) and travel along a straight road, which are at angle of 78° to each other. If their speed

s are 120 km/h (truck) and 90 km/h (car) respectively, how far apart will they be after one half hour?
Mathematics
1 answer:
densk [106]3 years ago
7 0
T=(60cos78, 60sin78)

T=(12.47, 58.69)

C=45

d=√((45-12.47)^2+58.69^2)

d≈67.1km
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Answer:

39-1.96\frac{1}{\sqrt{25}}=38.608    

39+1.96\frac{1}{\sqrt{25}}=39.392    

So on this case the 95% confidence interval would be given by (38.608;39.392)    

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.

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\bar X=39 represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma=1 represent the population standard deviation

n=25 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)

The margin of error is given by:

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

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that z_{\alpha/2}=1.96

And replacing we got:

ME= 1.96 *\frac{1}{\sqrt{25}}= 0.392

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

39-1.96\frac{1}{\sqrt{25}}=38.608    

39+1.96\frac{1}{\sqrt{25}}=39.392    

So on this case the 95% confidence interval would be given by (38.608;39.392)    

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