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harkovskaia [24]
3 years ago
8

Which equation represents the value of x? x=100−y2−−−−−−−√ x=10+y2 x=10−y x=y2+100−−−−−−−√ Right triangle A B C with angle B as

the right angle. A C is equal to 10. B C is equal to y. A B is equal to x.

Mathematics
1 answer:
Nostrana [21]3 years ago
8 0

Answer:

Therefore the required value of x,

x=\sqrt{(100-y^{2})}

Step-by-step explanation:

Given:

ΔBC is a Right Angle Triangle at ∠ B = 90°

As ∠ B = 90° , AC will be the Hypotenuse

AC = 10 = Hypotenuse

BC = y = Longer leg ( say )

AB = x = Shorter leg ( say )

To Find :

x = ?

Solution:

In Right Angle Triangle Δ ABC , By Pythagoras Theorem we get

(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}

Substituting the given values we get

10^{2}= x^{2}+y^{2} \\\\x^{2}=100-y^{2} \\\\\textrm{square rooting on both the side we get}\\\\x=\sqrt{(100-y^{2})}\\\therefore x=\sqrt{(100-y^{2})}\ \textrm{ which is the required value of x}

Therefore the required value of x,

x=\sqrt{(100-y^{2})}

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A population has mean 187 and standard deviation 32. If a random sample of 64 observations is selected at random from this popul
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Answer:

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Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

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

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The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 187, \sigma = 32, n = 64, s = \frac{32}{\sqrt{64}} = 4

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