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Sergeeva-Olga [200]
3 years ago
10

Please help!!! (Ignore the AD it’s actually supposed to be DC)

Mathematics
1 answer:
pashok25 [27]3 years ago
6 0

Answer:

BD = 22, DC = 11√3

Step-by-step explanation:

In triangle ABC, ∠B = 45°, ∠C = 90°. Hence:

∠A + ∠B + ∠C = 180° (sum of angles in a triangle)

∠A + 45 + 90 = 180

∠A + 135 = 180

∠A = 45°

Using sine rule to find BC:

\frac{BC}{sinA}=\frac{AB}{sinC}  \\\\\frac{BC}{sin45}=\frac{11\sqrt{2} }{sin90}  \\\\BC=\frac{11\sqrt{2}*sin45 }{sin90}  \\BC=11

In triangle BCD, ∠D = 30°, ∠C = 90°. Hence:

∠D + ∠B + ∠C = 180° (sum of angles in a triangle)

∠B + 30 + 90 = 180

∠B + 120 = 180

∠B = 60°

Using sine rule to find BD:

\frac{BD}{sinC}=\frac{BC}{sinD}  \\\\\frac{BD}{sin90} =\frac{11}{sin30} \\\\BD=\frac{11*sin90}{sin30}\\\\BD=22

Using sin rule to find DC:

\frac{DC}{sinB}=\frac{BC}{sinD}  \\\\\frac{DC}{sin60} =\frac{11}{sin30} \\\\DC=\frac{11*sin60}{sin30}\\\\DC=11\sqrt{3}

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Answer:

A sample of 16577 is required.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

The margin of error is of:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

99% confidence level

So \alpha = 0.01, z is the value of Z that has a p-value of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

She wants to estimate the proportion using a 99% confidence interval with a margin of error of at most 0.01. How large a sample size would be required?

We have no estimation for the proportion, and thus we use \pi = 0.5, which is when the largest sample size will be needed.

The sample size is n for which M = 0.01. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.01 = 2.575\sqrt{\frac{0.5*0.5}{n}}

0.01\sqrt{n} = 2.575*0.5

\sqrt{n} = \frac{2.575*0.5}{0.01}

(\sqrt{n})^2 = (\frac{2.575*0.5}{0.01})^2

n = 16576.6

Rounding up:

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8 0
3 years ago
The town of Hayward (CA) has about 50,000 registered voters. A political research firm takes a simple random sample of 500 of th
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Answer: (0.076, 0.140)

Step-by-step explanation:

Confidence interval for population proportion (p) is given by :-

\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

, where \hat{p} = sample proportion.

n= sample size.

\alpha = significance level .

z_{\alpha/2} = critical z-value (Two tailed)

As per given , we have

sample size : n= 500

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Sample proportion of Independents\hat{p}=\dfrac{x}{n}=\dfrac{54}{500}=0.108

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By using z-table , Critical value : z_{\alpha/2}=z_{0.01}=2.33

The 98% confidence interval for the true percentage of Independents among Haywards 50,000 registered voters will be :-

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8 0
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Answer:

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Step-by-step explanation:

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