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2 years ago

Find the value of the variables in the image above

Mathematics

1 answer:

enyata [817]2 years ago

5 0

Answer:

x = 8 $\sqrt{3}$ , y = 8

Step-by-step explanation:

Using the sine and cosine ratios in the right triangle and the exact values

sin60° = $\frac{\sqrt{3} }{2}$ , cos60° = $\frac{1}{2}$

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{x}{16}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2x = 16 $\sqrt{3}$ ( divide both sides by 2 )

x = 8 $\sqrt{3}$

----------------------------------------------------------

cos60° = $\frac{adjacent}{hypotenuse}$ = $\frac{y}{16}$ = $\frac{1}{2}$ ( cross- multiply )

2y = 16 ( divide both sides by 2 )

y = 8

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vaieri [72.5K]

Answer:

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Step-by-step explanation:

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2 years ago

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Step-by-step explanation:

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3 years ago

The lengths of nails produced in a factory are normally distributed with a mean of 4.84 centimeters and a standard deviation of

Helga [31]

Answer:

Top 3%: 4.934 cm

Bottom 3%: 4.746 cm

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

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