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Tanzania [10]
3 years ago
9

How to find the area of this figure

Mathematics
1 answer:
stiv31 [10]3 years ago
3 0

Answer:

45 square units.

Step-by-step explanation:

Applying the pythagoras theorem:

Base of the bigger triangle = \sqrt{15^2 - 9^2} = \sqrt{144} = 12 units

Area of a triangle is given by \frac{1}{2} × base × height

The area of the bigger triangle is  \frac{1}{2} × 12 × 9 = 54 square units.

The area of the smallest triangle is  \frac{1}{2} × (12 - 10) × 9 = 9 square units.

The area of the figure( required triangle) is 54 - 9 = 45 square units.

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A sample size of 345 is needed so that the confidence interval will have a margin of error of 0.07

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}}

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The margin of error of the interval is given by:

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

In this problem, we have that:

p = 0.69

99.5% confidence level

So \alpha = 0.005, z is the value of Z that has a pvalue of 1 - \frac{0.005}{2} = 0.9975, so Z = 2.81.

Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.07?

This is n when M = 0.07. So

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

0.07 = 2.81\sqrt{\frac{0.69*0.31}{n}}

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\sqrt{n} = \frac{1.2996}{0.07}

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(\sqrt{n})^{2} = (18.5658)^{2}

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A sample size of 345 is needed so that the confidence interval will have a margin of error of 0.07

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