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2 years ago

Please answer this question now

Mathematics

1 answer:

Alex787 [66]2 years ago

8 0

Answer:

541.7 (m2)

Step-by-step explanation:

Applying the sine theorem:

WV/sin(X) = XV/sin(W)

=> WV = XV*sin(X)/sin(W) = 37*sin(50)/sin(63) = 31.81

Angle V = 180 - X - W = 180 - 50 - 63 = 67

Denote WH is a height of the triangle VWX, H lies on XV

=> WH = WV*sin(V) = 31.81*sin(67) = 29.28

=> Area of triangle VWX is calculated by:

S = side*height/2 = XV*WH/2 = 37*29.28/2 = 541.7 (m2)

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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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$\bar X=54$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=21$ represent the sample standard deviation

n=16 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)

Since the Confidence is 0.90 or 90%, the value of $\alpha=1-0.9=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table 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):

$54-1.64\frac{21}{\sqrt{16}}=45.39$

$54 +1.64\frac{21}{\sqrt{16}}=62.61$

So on this case the 90% confidence interval would be given by (45.39;62.61)

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