AG=1 => BG=3 => CG=sqrt3 => CD = 2sqrt3 => perimeter = 3*CD= 6sqrt3
Answer:
Social Darwinism provided an ideological justification for the social inequalities that capitalism had brought with it: these would result from the hereditary inferiority of the poor and the hereditary excellence of the richer classes, which are best enjoyed under a laissez-faire system. Applied to peoples and races, it became a justification for racism and imperialism.
As can be seen, social Darwinism is a retrograde political and philosophical stance, which considered different ethnic or national groups as different in terms of capacity or development possibilities. Therefore, since this position has been regarded as false, social Darwinism has no justification in our time.
The answer would be 16
11 + (8-3)^2 - 20 = 16
Let's call our estimate x. It will be the average of n IQ scores. Our average won't usually exactly equal the mean 97. But if we repeated averages over different sets of tests, the mean of our estimate the average would be the same as the mean of a single test,
μ = 97
Variances add, so the standard deviations add in quadrature, like the Pythagorean Theorem in n dimensions. This means the standard deviation of the average x is
σ = 17/√n
We want to be 95% certain
97 - 5 ≤ x ≤ 97 + 5
By the 68-95-99.7 rule, 95% certain means within two standard deviations. That means we're 95% sure that
μ - 2σ ≤ x ≤ μ + 2σ
Comparing to what we want, that's means we have to solve
2σ = 5
2 (17/√n) = 5
√n = 2 (17/5)
n = (34/5)² = 46.24
We better round up.
Answer: We need a sample size of 47 to be 95% certain of being within 5 points of the mean