Solution:

The line of a half angle identity is as follows:

If we plug in 75 degrees we get:

Solution:

1.    Out of 100 women, we expect 1.2 to actually have breast cancer (12 out of 1000)
2.    However, only 88% (880 out of 1000) of these will be detected, so 1.056 (i.e. 88% of 1.2) will be detected
3.    In addition, of the 98.8 women who don’t have breast cancer 9% (90 out of 1000) will trigger a false positive” (9% of 98.8 = 8.892)
4.    So out of 100 women, 9.948 will have positive mammography readings (1.056+9.892)
5.    Of these 9.948, only 1.056 will actually have breast cancer
6.    10.6% = (1.056/1.056+9.892) This ratio is essentially an application of Bayes Theorem

Please click on http://www.thegodofreason.com/bayesintro.pdf to download a PDF that explains how Bayes Theorem works. Page 3 gives an example that is very similar to your problem:

Solution:

1. http://en.wikipedia.org/wiki/Laws_of_motion (Newton, Kepler, etc.)
2. http://www.schooltrainer.com/study-material.html (look at the left column under the heading Physics”)

Solution:

A six-sided polygon is known as a Hexagon:

Solution:

1.    The cardinality of a set is a measure of the “number of elements of the set”. For example, the set A = {2, 4, 6} contains = elements, and therefore A has a cardinality of 3.
2.    Given a set S, the power set of S, written , P(S), is the set of all subsets of S, including the empty set and S itself.
3.    If S={a, b}, then P(S) ={{},{a},{b},{a,b}} and the Cardinality of P(S) is 4.

Solution:

First, take a look at this link to understand the Principle of Inclusion and Exclusion:

http://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle

Next, make a list of all the subsets:

Solution: