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The standard deviation of a sample is proportional to 1/√N where N is the sample size. In this case we are decreasing N by half, so we can write:
1/√(N/2) = √2 / √N
If we say that our standard deviation is proportional to 1/√N, the difference that occurred from decreasing the sample size by half resulted in an increase in the standard deviation by a factor of √2.
Therefore, the standard deviation is multiplied by √2.
Answer:
D. alternate exterior angles
Step-by-step explanation:
Neither of the angles is between parallel lines a and b, so they are "exterior." They are on opposite sides of transversal c, so are "alternate".
∠2 and ∠7 are <em>alternate exterior</em> angles.
Answer:
x ≈ - 5.83 , x ≈ - 0.17
Step-by-step explanation:
x² + 6x + 1 = 0 ( subtract 1 from both sides )
x² + 6x = - 1
Using the method of completing the square
add ( half the coefficient of the x- term)² to both sides
x² + 2(3)x + 9 = - 1 + 9
(x + 3)² = 8 ( take square root of both sides )
x + 3 = ± 
( subtract 3 from both sides )
x = - 3 ±
Then
x = - 3 - ≈ - 5.83 ( to 2 dec. places )
x = - 3 + ≈ - 0.17 ( to 2 dec. places )
As, order is important so we use permutation,
total no. of students= n=8
selected students= r=3
nPr= n!/(n-r)! = 8!/(8-3)! =336 different ways
