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3 years ago

19 13 15 6 17 21 16 18 11 10 11 16 20 6 18 12 6 20 13 13 7 20 14 21 11 3 9 18

Mathematics

2 answers:

hoa [83]3 years ago

8 0

Answer:

13.08

Step-by-step explanation:

19 +13+ 15+ 6+ 17+ 21+ 16+ 18+ 11+ 10+ 11+ 16+ 20+ 6 +18 +12 +6 +20+ 13+ 13+ 7+ 20+ 14+ 21+ 11+ 3 +9 +18+12 +14+ 6 +11 +5 +18+ 8

485/35

13.08

Assoli18 [71]3 years ago

5 0

$19+13 +15 +6 +17 +21 +16 +18 +11+10+ 11 +16 +20+ 6 +18 +12 +6+ 20+ 13 +13+ 7+ 20+ 14 +21 11+3+9 +18+12+ 14+ 6 +11 +5 +18 +8=458\\458/35=13.08571429\\$

rounded to the nearest hundredth, it is 13.09

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If this is the sample data, the sample variance is 125.07 and the sample standard deviation is 11.18

If this is a population data, the population variance is 109.44 and the population standard deviation is 10.46

Step-by-step explanation:

We are given the following data-set:

70, 65, 71, 78, 89, 68, 50, 75

Deviations from the mean

–0.75, –5.75 , 0.25, 7.25, 18.25, –2.75, –20.75, 4.2

Sample size, n = 8

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$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

Sum of squares of differences =

0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5

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Population:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

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3 years ago

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Answer:

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There is no info in the problem/s text which one of the triangle's side is 21 cm. That is why we have to try all possible variants.

Let the triangle is ABC . Let the AK is the angle A bisector and BM is median.

Let O is AK and BM cross point.

Have a look to triangle ABM. AO is the bisector and AOB=AOM=90 degrees (means that AO is as bisector as altitude)

=> triangle ABM is isosceles => AB=AM (1)

1. Let AC=21 So AM=21/2=10.5 cm

So AB=10.5 cm as well. So BC= P-AB-AC=63-21-10.5=31.5 cm

Such triangle doesn' t exist ( is impossible), because the triangle's inequality doesn't fulfill. AB+AC>BC ( We have 21+10.5=31.5 => AB+AC=BC)

2. Let AB=21 So AM=21 and AC=42 .So BC= P-AB-AC=63-21-42=0 cm- such triangle doesn't exist.

3. Finally let BC=21 cm. So AB+AC= 63-21=42 cm

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Let check if this triangle exists ( if the triangle's inequality fulfills).

BC+AB>AC 21+14>28 - correct=> the triangle with the sides' length 21cm,14 cm, 28cm exists.

This variant is the only possible solution of the given problem.

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