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masha68 [24]
3 years ago
11

What is AE? Enter your answer in the box.

Mathematics
1 answer:
ehidna [41]3 years ago
6 0

Answer:

AE=20\ units

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

Triangles AEB and DEC are similar by AA Similarity Theorem

so

\frac{AB}{DC}=\frac{AE}{DE}

substitute the given values and solve for x

\frac{10}{4}=\frac{2x+10}{x+3}

Multiply in cross

10x+30=8x+40\\10x-8x=40-30\\2x=10\\x=5

Find the length side AE

AE=2x+10

substitute the value of x

AE=2(5)+10=20\ units

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A random sample of 36 students at a community college showed an average age of 25 years. Assume the ages of all students at the
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Answer:

98% confidence interval for the average age of all students is [24.302 , 25.698]

Step-by-step explanation:

We are given that a random sample of 36 students at a community college showed an average age of 25 years.

Also, assuming that the ages of all students at the college are normally distributed with a standard deviation of 1.8 years.

So, the pivotal quantity for 98% confidence interval for the average age is given by;

             P.Q. = \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

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            n = sample of students = 36

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So, 98% confidence interval for the average age, \mu is ;

P(-2.3263 < N(0,1) < 2.3263) = 0.98

P(-2.3263 < \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } < 2.3263) = 0.98

P( -2.3263 \times {\frac{\sigma}{\sqrt{n} } < {\bar X - \mu} < 2.3263 \times {\frac{\sigma}{\sqrt{n} } ) = 0.98

P( \bar X - 2.3263 \times {\frac{\sigma}{\sqrt{n} } < \mu < \bar X +2.3263 \times {\frac{\sigma}{\sqrt{n} } ) = 0.98

98% confidence interval for \mu = [ \bar X - 2.3263 \times {\frac{\sigma}{\sqrt{n} } , \bar X +2.3263 \times {\frac{\sigma}{\sqrt{n} } ]

                                                  = [ 25 - 2.3263 \times {\frac{1.8}{\sqrt{36} } , 25 + 2.3263 \times {\frac{1.8}{\sqrt{36} } ]

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Therefore, 98% confidence interval for the average age of all students at this college is [24.302 , 25.698].

8 0
3 years ago
the forecast calls for a 30% chance of snow today and a 40% chance of snow tomorrow. what are the chances it will rain two days
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Answer:

The chances it will rain two days in a row is 12%

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So, chance of snowfall tomorrow= 40% = 0.4

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Since they are far apart from each other, Supplementary Angles, Adjacent Angles, Vertical Angles, and any other similar definitions can be ruled out.

Therefore, we are left with Alternate Interior Angles.

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