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4 years ago

1)

Mathematics

1 answer:

MrRissso [65]4 years ago

7 0

Answer:

Step-by-step explanation:

The diagram of the triangles are shown in the attached photo.

1) Looking at ∆AOL, to determine AL, we would apply the sine rule

a/SinA = b/SinB = c/SinC

21/Sin25 = AL/Sin 105

21Sin105 = ALSin25

21 × 0.9659 = 0.4226AL

AL = 20.2839/0.4226

AL = 50

Looking at ∆KAL,

AL/Sin55 = KL/Sin100

50/0.8192 = KL/0.9848

50 × 0.9848 = KL × 0.8192

KL = 49.24/0.8192

KL = 60

AK/Sin25 = AL/Sin 55

AKSin55 = ALSin25

AK × 0.8192 = 0.4226 × 50

AK = 21.13/0.8192

AK = 25.8

2) looking at ∆AOC,

Sin 18 = AD/AC = 18/AC

AC = 18/Sin18 = 18/0.3090

AC = 58.25

Sin 85 = AD/AB = 18/AB

AB = 18/Sin85 = 18/0.9962

AB = 18.1

To determine BC, we would apply Sine rule.

BC/Sin77 = 58.25/Sin85

BCSin85 = 58.25Sin77

BC = 58.25Sin77/Sin85

BC = 58.25 × 0.9744/0.9962

BC = 56.98

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$29.4+1.96\frac{7}{\sqrt{10}}=33.74$

So on this case the 95% confidence interval would be given by (25.06;33.74)

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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 table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

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

$29.4-1.96\frac{7}{\sqrt{10}}=25.06$

$29.4+1.96\frac{7}{\sqrt{10}}=33.74$

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The statistic for this case is given by:

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We can replace in formula (1) the info given like this:

$z=\frac{29,4-25}{\frac{7}{\sqrt{10}}}=1.988$

Give the appropriate conclusion for the test

Since is a one side right tailed test the p value would be:

$p_v =P(z>1.988)=0.0234$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

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