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nikdorinn [45]
3 years ago
15

If ABC ~ DEF and the scale factor from ABC to DEF is 1/5, what are the lengths of DE , EF and DF , respectively?​

Mathematics
1 answer:
crimeas [40]3 years ago
7 0

Answer:

option a (2,2,5)

Step-by-step explanation:

First we have to notice that it tells us that the scale is 1/5.

This means that the measures of the new triangle will be 5 times smaller than those of the other triangle.

Now we just have to take the measurements of the sides of the triangle and multiply them by 1/5 or divide them by 5

AB = 10      DE = 10/5 = 2

BC = 10      EF = 10/5 = 2

AC = 25     DF = 25/5 = 5

DE = 2

EF = 2

DF = 5

(2, 2, 5)

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Step-by-step explanation:

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2 years ago
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2 years ago
Read 2 more answers
We draw a random sample of size 36 from a population with standard deviation 3.5. If the sample mean is 27, what is a 95% confid
inessss [21]

Answer:

The 95% confidence interval for the population mean is between 25.86 and 28.14.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.95}{2} = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.025 = 0.975, so z = 1.96

Now, find the margin of error M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.96\frac{3.5}{\sqrt{36}} = 1.14

The lower end of the interval is the sample mean subtracted by M. So it is 27 - 1.14 = 25.86

The upper end of the interval is the sample mean added to M. So it is 27 + 1.14 = 28.14

The 95% confidence interval for the population mean is between 25.86 and 28.14.

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3 years ago
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