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user100 [1]
2 years ago
9

Given: m∠A = m∠C = 90° AB ║ DC Prove: ∆ABD ≅ ∆CBD

Mathematics
1 answer:
Genrish500 [490]2 years ago
4 0

Answer:

Angle-Angle-Side (AAS)

Step-by-step explanation:

Given triangles; ΔABD and ΔCBD

  <A = <C = 90^{0} (right angle property)

   AB ║ DC (given)

Then,

    DA ║ CB

   <B ≅ <D (congruent property)

    DB ≅ BD (similarity property)

    <D + <B = <B + <D (complementary angles, and property of triangles)

Therefore by Angle-Angle-Side (AAS),

                 ∆ABD ≅ ∆CBD

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Answer:

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Since the distribution for X is normal then the distribution for the sample mean  is also normal and given by:

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So then is appropiate use the normal distribution to find the probabilities for \bar X

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

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Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

X \sim N(61,14)  

Where \mu=61 and \sigma=14

Since the distribution for X is normal then the distribution for the sample mean \bar X is also normal and given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

\mu_{\bar X} = 61

\sigma_{\bar X}= \frac{14}{\sqrt{6}}= 5.715

So then is appropiate use the normal distribution to find the probabilities for \bar X

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3 years ago
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