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4 years ago

Use the Pythagorean theorem to find the length of x on the triangle below.

Mathematics

1 answer:

Elden [556K]4 years ago

5 0

$x^2+16^2=20^2\\
x^2=400-256\\
x^2=144
\\x=12$

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A school has 600 pupils. 1/5 are in the upper school, 1⁄4 in the middle school and

crimeas [40]

Step-by-step explanation:

the number of pupils are in the lower school

= (1- 1/5 - ¼) × 600

= (20/20 - 4/20 - 5/20)×600

= (11/20) ×600

= 330 pupils

4 0

3 years ago

Find c. Round to the nearest tenth

sergeinik [125]

Answer:

c = <u>0.5 cm</u>

Step-by-step explanation:

Using the Sine rule in the triangle, then

= ( cross- multiply )

c × sin105° = 2 × sin15° ( divide both sides by sin105°

c = ≈ 0.5 cm ( to the nearest tenth )

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3 years ago

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Nostrana [21]

Answer:

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3 years ago

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The dwarves of the Grey Mountains wish to conduct a survey of their pick-axes in order to construct a 99% confidence interval ab

Dmitry_Shevchenko [17]

Answer:

The minimum sample size needed is 125.

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 zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

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

For this problem, we have that:

$\pi = 0.25$

99% confidence level

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

What minimum sample size would be necessary in order ensure a margin of error of 10 percentage points (or less) if they use the prior estimate that 25 percent of the pick-axes are in need of repair?

This minimum sample size is n.

n is found when $M = 0.1$