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2 years ago

Please help me on this problem !

Mathematics

1 answer:

svp [43]2 years ago

4 0

Answer:

x = 8.66
y = 17.321

Step-by-step explanation:

Calculated based on 2 given angles and 1 given side.

∠C = 180° - A - B = 1.0472 rad = π/3 = 60°

a = c·sin(A)/sin(C) = 8.66025 = 5 $\sqrt{3}$

b = c·sin(B)/sin(C) = 17.32051 = 10 $\sqrt{3}$

Area = $\frac{ab·sin(C)}{2}$ = 64.95191

Perimeter p = a + b + c = 40.98076

Semiperimeter s = $\frac{a + b +c}{2}$ = 20.49038

Height ha = $\frac{2×Area}{a}$ = 15

Height hb = $\frac{2×Area}{b}$ = 7.5

Height hc = $\frac{2×Area}{c}$ = 8.66025

Median ma = $\sqrt{(a/2)^{2} + c2 - ac·cos(B)}$ = 15.61249

Median mb = $\sqrt{(b/2)^{2} + a2 - ab·cos(C)}$ = 8.66025

Median mc = $\sqrt{(c/2)^{2} + b2 - bc·cos(A)}$ = 11.45644

Inradius r = $\frac{Area}{s}$ = 3.16987

Circumradius R = $\frac{a}{2sin(A)}$ = 8.66025

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1) Notation and definitions

$X=1627$ number of permanent dwellings on the entire reservation that are traditional hogans.

$n=5120$ random sample taken

$\hat p=\frac{1627}{5120}=0.318$ estimated proportion of permanent dwellings on the entire reservation that are traditional hogans.

$p$ true population proportion of permanent dwellings on the entire reservation that are traditional hogans.

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".

The population proportion have the following distribution

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Part b

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by: