Summarize the source of the calculations for the Richter scale. – Compare the Richter scale and Mercalli scale. In your opinion, explain which is more meaningful in the use of reporting earthquake destruction. – Describe how math and science has made reporting earthquakes more accurate.

## -Provide one example to show how you can use the Expected Value computation to assess the fairness of a situation

-Provide one example to show how you can use the Expected Value computation to assess the fairness of a situation (probability experiment). Provide the detailed steps and calculations. -Develop a tree diagram for tossing two, eight-sided gaming dice to figure out how many possibilities there are. -Discuss the purpose of using such a visual in working out probability.

## Let a, b, c, d positive real numbers, such that a/b < c/d.

Let a, b, c, d positive real numbers, such that a/b < c/d. Show that a/b < (a+c)/(b+d) < c/d.

## Use Euler’s Criterion to determine whether a is a quadratic residue modulo p in each of the following instances:

Use Euler’s Criterion to determine whether a is a quadratic residue modulo p in each of the following instances: (a) a = 2, p = 5; (b) a = 4, p = 7; (c) a = 3, p = 11; (d) a = 6, p = 13

## Prove that if c is odd , then

Prove that if c is odd , then :::: (ab/c) = (a/c)(b/c) The problem is also in the attached file.

## Radioactive radium has a half-life of approximately 1599 years. What percent of a given amount remains after 100 years?

Radioactive radium has a half-life of approximately 1599 years. What percent of a given amount remains after 100 years?