Let's figure this out as though we have no idea what the answer would be.
Step One
Find the new five numbers.
3*3, 8*3, 12*3, 17*3, 25*3
9 , 24 , 36, 51, 75
Step 2
Find the average
(9 + 24 + 36 + 51 + 75)/5 = 195/5 = 39
Step 3
Subtract the individual numbers from the average
(39 - 9) = 30
(39 -24) = 15
(39 - 36) = 3
(39 - 51) = - 12
(39 - 75) = -36
Step 4
Square the results from Step 3
30^2 = 900
15^2 = 225
3^2 = 9
(-12)^2 = 144
(-36)^2 = 1296
Step 5
Take the average of the results from step 4
(900 + 225 + 9 + 144 + 1296)/5
2574 / 5 = 514.8
Step 6
Take the square root of the result from step 5
deviation = sqrt(514.8)
deviation = 22.689
Step seven
Compare the two standard deviations.
s2/s1 = 22.689 / 7.563 = 3
Conclusion
If you are given 1 set of numbers to find a population standard deviation and you multiply each member by a, then the result will be a * the standard population deviation of the first set of numbers.
Note
Your calculator will do this as well, but you have to know how to enter the data into your calculator. That requires that you follow the directions carefully.
If we discuss this as if it is a triangle then the "rise" is the vertical side and the "run" is the adjacent side.
So the ratio of the rise to the run is 8 / 15 which equals
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0.5333333333
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To find the angle of this roof pitch we look up the arc tangent of
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0.5333333333
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and we find that is 28.072 Degrees
Trigonometry Calculator:
http://www.1728.org/trigcalc.htm
The integers are -8 and -6.
To find these, first assume that the first integer is x. Then, because it is an even integer, assume the next is x + 2. Now we can write an equation to solve.
Tripling the greater = subtracting 10 from the lesser
3(x + 2) = x - 10 ----> Distribute the 3
3x + 6 = x - 10 ----> Subtract x from both sides
2x + 6 = -10 ----> Subtract 6 from both sides
2x = -16 ----> Divide both sides by 2
x = -8
Which is the first integer. We then can determine that the second one, which is two higher than the first, would be -6.
