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.
The angle between two vectors is:
CosФ = u - v / Magnitude(u) x magnitude(v)
Magnitude of u = SQRT(7^2 + -2^2) = SQRT(49 +4) = SQRT(53)
Magnitude of v = SQRT(-1^2 +2^2) = SQRT(1 +4) = SQRT(5)
u x v = (7 x -1) + (-2 x 2) = -7 + -4 = -11
cosФ = -11 / sqrt(53) x sqrt(5)
cosФ = -11sqrt265) / 265
Ф =cos^-1(-11sqrt265) / 265)
Ф=132.51 degrees.
Since you don't want any leftover items, you have to find the greatest common factor (GCF) of both the crayons and bubbles. Since the highest common factor for both 28 and 12 is 4, the greatest number of gift bags you can make without any leftover items would be 4 gift bags.
Hope I could help.
Answer:
Step-by-step explanation:
D. 18 1/5 +22 2/5 +40 1/5
-(-22 2/5) and -(-40 1/5) -----> -*- will become +
Answer:
A the first one ( the rotation of 90 degree)
Step-by-step explanation:
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