<span>Real numbers can be either rational or irrational.
sqrt(13) ≈ 3.60555
sqrt(14) ≈ 3.74166
A simple nearby rational approximation is 3.7 = 37/10.
An example of an irrational number between them is sqrt(27/2).</span>
The midpoint of the line segment with endpoints (-6, -3) and (9, -7) is (1.5,-5).
Part A:
Considering the best possible outcome
The ideal case occurs if the two missing socks are from the same pair.
Consequently, there are 4 complete pairs remaining.
To choose 2 from the total of 10 socks (5 pairs), the number of combinations is given by 10C2 = 45.
Choosing 2 that are from the same pair means selecting one from 5 pairs, so the count is 5C1 = 5.
Thus, the probability for this best case is 5 / 45 = 1 / 9.
Part B:
Considering the worst-case outcome
This scenario occurs when the two missing socks are from different pairs.
As a result, we have 3 complete pairs left.
The total ways to select 2 socks from 10, again, is 10C2 = 45.
To select 2 that do not belong to the same pair, we calculate as follows: 10C2 - 5C1 = 45 - 5 = 40.
Therefore, the probability for the worst-case scenario is 40 / 45 = 8 / 9.
The formula to calculate the difference between two standard deviations of populations n1 and n2 is:
sigma (difference)=√(sigma1/n1 + sigma2/n2). For this scenario:
sigma(d)= √(49/100 + 36/50)
Thus, the calculated standard deviation of the difference equals 1.1.
