Use a half angle identity to find the exact value- sin(75 degrees)

Solution:

The line of a half angle identity is as follows:

If we plug in 75 degrees we get:

12 out of 1000 women at age forty who participate in routine screening have breast cancer. 880 out of 1000 women with breast cancer will get positive mammographies. 90 out of 1000 women without breast cancer will also let positive mammographies. If 100 women in this age group undergo a routine screening, about what fraction of women with positive mammographies will actually have breast cancer?

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:

What is law of motion?

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”)

What is the name of a 6-sided polygon?

Solution:

A six-sided polygon is known as a Hexagon:

What is the cardinality of the following set. P(S) stands for power set. Find p (p ((S) for S = {a, b}

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.

You are developing new bath soap, and you hire a public opinion survey group to do some market research for you. The group claims that in its survey of 450 consumers, the following were named as important factors in purchasing bath soap: Odor 425 Lathering Case 397 Natural Ingredients 340 Odor and lathering Case 284 Odor and Natural Ingredients 315 Lathering ease and natural ingredients 219 All three factors 147 should you have confidence in these results? Why or why not?

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:

Work out the grap y =x^-3

Solution: