Math 170 Project #9 Scarlitte Ponce Starlitte Ponce Cristina Hernandez

4.6 #22 Consider the statement “For all real numbers r, if r^2 is irrational the r is irrational” (a) Write what you would suppose and what you would need to show to prove this statement by contradiction. In this case you would suppose that r^2 is irrational and you would want to show some contradiction, probably that r^2 is both rational and irrational. (b) Write what you would suppose and what you would need to show to prove this statement by contraposition. In this case you would suppose that r were rational and you would want to show that r^2 is rational.

9.2 #33 Six people attend the theater together and sit in a row with exactly six seats. A. How many ways can they be seated together in the row? th six people can be seated in 6!, or 720 ways B. Suppose on of the six is a doctor who must sit on the aisle in case she is paged. How many ways can the people be seated together in the row with the doctor in an aisle seat? if one sit is out of the equation then it will be 5!1!, or 120 seating arrangements C. Suppose the six people consist of three married couples and each couple wants to sit toegther with the husband on the left. How many ways can the six be seated together in the row? Since their couples that will sit next to each with treat them like as idividuals as a couple with the equation would be 3! or 6 seating possibilites

9.5 #10 Two new drugs are to be tested using a group of 60 laboratory mice, each tagged with a number for identication purposes. Drug A is to be given to 22 mice, drug B is to be given to another 22 mice, and the remaining 16 mice are to be used as controls. A single assignment involves specifying the treatment for each mouse-whether drug A, drug B, or no drug. How many ways can the assignment of treatments to mice be made? = x = ≈ ×

Biography: Pierre-Simon Laplace Pierre-Simon Laplace was a French mathematician and astronomer. He was born in Beaumont- en-Auge, Normandy, France on the 23rd of March 1749 and died the 5th of March He became a math teacher and at the age of eighteen was in hope of finding a career in Paris through letters of recommendation and by approaching Jean le Rond d’Alembert. He was turned away but that did not stop him. He wrote to the great geometer a letter on the principles of mechanics which did not go unoticed. His work translated to one based on calculus that opened a broader range of problems. His early work started with differential equations and finite differences but he had already started to think about probability and statistics. He was elected to the Academie in 1773 but prior to that he wrote two drafted papers that upheld his reputation. His second paper elaborated his statistical thinking and began his work on celestial mechanics and stability of the solar system.

Bibliography Epp, Susanna S. Discrete Mathematics with Applications. 4. Boston, MA: Brooks/Cole, Print. Ball, W. W. Rouse. "Pierre Simon Laplace ( ).". N.p.. Web. 24 Nov