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Veronika [31]
3 years ago
15

Congruent Triangles ?

Mathematics
1 answer:
mel-nik [20]3 years ago
4 0

Check the picture below.

well, it's noteworthy to say that when dropping a perpendicular line from a right angle in a right triangleto the hypotenuse, we'd end up with 3 similar triangles, a Large a Medium and a Small one, all three similar.

3a)

is the Small similar to the Large one? well, let's notice, they both have a 90° angle and also they share the purple one, similar triangles by AA.

3b)

are the Medium and the Large one similar?  well, let's notice, just like before, they both have a 90° and they also share the green one, similarity by AA.

3c)

are the Small and Medium similar?

if Large ~ Medium

and

Large ~ Small

then

Medium ~ Small.

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a = 9b

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3 years ago
Bottles filled by a certain machine are supposed to contain 12 oz of liquid. In fact the fill volume is random with mean 12.01 o
Irina-Kira [14]

Answer:

a

 P(X <  12)  = 0.3660

b

  P(X <  12) = 0.1521

Step-by-step explanation:

Considering question a

From the question we are told that

   The mean is  \mu = 12.01 \ oz

    The standard deviation is  \sigma = 0.35 \  oz

 The standard error of mean is mathematically represented as

      \sigma_{x} =  \frac{\sigma}{\sqrt{n} }

=>   \sigma_{x} =  \frac{0.35}{\sqrt{144} }              

=>   \sigma_{x} =  0.02917

Generally the  probability that the mean volume of a random sample of 144 bottles is less than 12 oz is mathematically represented as

           P(X <  12) = P(\frac{X - \mu }{\sigma_{x}} < \frac{12 - 12.01 }{0.02917 }  )

\frac{X -\mu}{\sigma_{x} }  =  Z (The  \ standardized \  value\  of  \ X )

      P(X <  12) = P(Z < -0.3425  )

From the z table  the area under the normal curve to the left corresponding to   -0.3425  is

      P(X <  12) = P(Z < -0.3425  ) = 0.3660

=>  P(X <  12)  = 0.3660

Considering question a

From the question we are told that

   The mean is  \mu = 12.03 \ oz

Generally the  probability that the mean volume of a random sample of 144 bottles is less than 12 oz is mathematically represented as

           P(X <  12) = P(\frac{X - \mu }{\sigma_{x}} < \frac{12 - 12.03 }{0.02917 }  )

          P(X <  12) = P(Z < -1.0274  )

From the z table  the area under the normal curve to the left corresponding to   -1.0274   is

      P(X <  12) = P(Z < -1.0274  ) =0.1521

=>   P(X <  12) = 0.1521

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3 years ago
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