So what we can assume from the things given,
m∠A = x
<span>
</span>m∠B = 2x
m∠C = 3x
m∠C + m∠B + <span>m∠A = 180º
x = 30º
Because 30º + 60º + 90º = 180º
</span>
Write 8 and 512 as powers of 2:
![8=2^3](https://tex.z-dn.net/?f=8%3D2%5E3)
![512=2^9=(2^3)^3](https://tex.z-dn.net/?f=512%3D2%5E9%3D%282%5E3%29%5E3)
So we have
![\log_8512=\log_{2^3}(2^3)^3=3\log_{2^3}2^3=3](https://tex.z-dn.net/?f=%5Clog_8512%3D%5Clog_%7B2%5E3%7D%282%5E3%29%5E3%3D3%5Clog_%7B2%5E3%7D2%5E3%3D3)
To get the variance, start with finding the mean of your data points:
(23 + 19 + 22 + 30 + 28) / 5 = 24.4
Now take each data point and subtract the mean from it, then square that value:
23 - 24.4 = -1.4 * -1.4 = 1.96
19 - 24.4 = -5.4 * -5.4 = 29.16
22 - 24.4 = -2.4 * -2.4 = 5.76
30 - 24.4 = 5.6 * 5.6 = 31.36
28 - 24.4 = 3.6 * 3.6 = 12.96
Now get the average of those new numbers. That is your variance:
(1.96 + 29.16 + 5.76 + 31.36 + 12.96) / 5 = 16.24
The standard deviation will be the square root of the variance:
√(16.24) = 4.0299 (rounded to 4DP)
Using it's concept, it is found that the surface area of the figure given in this problem is of 710.6 mm².
<h3>What is the surface area of a prism?</h3>
It is the sum of the areas of all faces of the prism.
In this problem, the prism is composed by:
- Two squares of sides 13 mm.
- Four rectangles of sides 5 mm and 13 mm.
- One triangle with measures in mm of
.
Hence, the areas in square millimeters are given by:
.
.
Adding them, the surface area of the figure is given by:
S = 338 + 260 + 112.6 = 710.6 mm².
More can be learned about surface areas at brainly.com/question/26702574
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