Mat 113 1st EditionExam # 1 Study Guide Lectures: 1 - 10Lecture 1 1. Scientific Notation a. Scientific Notation can be referred to as a way of writing numbers that are too big or too small to be conveniently written in decimal form. 2. Examplesa. 6 x 10^4 = 60,000b. 7 x 10^-6= .000007c. 3.48 x 10^11= 348,000,000,000d. 8.9 x 10^-9 = .00000000193. Calculator Usea. If you were going to divide 2 by 4.1 + 5.3, you would put it in your calculator as 2/(4.1+5.3), which is 2/ (9.4) and it equals 8^(3x4)4. Conversions a. 1 Yard = 3 Feetb. 1 Foot = 12 Inchesc. 1 Inch = 2.54 Centimeters d. 1 Kilometer = 1000 Meterse. 1 Meter = 1000 Millimetersf. 1 Meter = 100 Centimeters Lecture 2 How to do conversions of different units Say we want to convert meters per second to miles per hour; we have two things going on. We simply handle them separately. The order we do that in does not matter at all. We need to convert meters to miles, which is the distance part of what is going on. And we need to convert seconds to hours. That is the time portion. It looks like this: meters -> centimeters -> inches -> feet -> miles and seconds -> minutes -> hours. (That will help you keep the process in mind.)A. Example Problem1. Convert 55 mph to feet per second. (Round to the nearest whole number and give the units as fps.)- First you would set up a proportion: 55mph/1 hour x 1 hour/60 seconds x 1 foot/12 inches- You divide the mph by how much time is in an hour, to get from mph to miles per second and then divide that by feet to get feet per second- Next, you would multiply across the top and bottom of the proportion: 55x1x1/1x60x12, which equals 81 fpsVI. Geometry FormulasIn this section, we learn the basic formulas for geometric shapes. (The formulas are in the chartat the bottom of the study guide). You can also use Pythagorean theorem to find the side lengths for right triangles, that formula isa2 +b2 =c2 (everything is squared). Lecture 31. Heron’s FormulaHeron’s Formula is used to fins the area of a square when you have the length of all 3 sides. There are two parts to this formula:S= ½ (a+b+c) (A,B,C are the side lengths)A= √s(s-a)(s-b)(s-c) ( you have to find the square root of the whole thing)2. ExampleLet’s say you were given a triangle with the side lengths 5 in, 6 in and 7 in. 1st- S=1/2 (5+6+9), which = 102nd- A= √10(10-5)(10-6)(10-9), which = 14.4The area of your triangle would be 14.4 inLecture 41. What is a fallacy?a. A fallacy is a flaw of logic. Logic is the study if the methods and principles of reasoning.b. An argument uses a set of facts or assumptions called premises, to support a conclusion.c. A fallacy is a deceptive argument, in which the conclusion is not well supported by the premises.2. Fallacies in thinkinga. Appeal to common practice: many people believe P is true, so P is true. EX: Morepeople drive Fords, so Ford is the best car.b. False Cause: A came before B, therefore A cause B. EX: You placed a crystal on your head, and since you did this that is why your headache went away. Lecture 53. Simpson’s ParadoxThis occurs when:- When combining, or aggregating, data masks underlying patterns - When a factor distorts the overall picture, but distortion goes away when underlying data is examined 4. Example The following data shows the hitting records of two major league baseball players for 1995 and 1996. Complete the batting averages, which are usually as a decimal to 3 places. Then answer the questions at the bottom. 1995 1996Jeter- 48 At Bats, 12 hits Jeter- 582 At Bats, 183 hitsJustice- 411 At Bats, 104 hits Justice- 140 At Bats, 45 hits To find the batting averages, you would take the hits and divide them by their at bats. Which would equal, .250 for Jeter in 1995 and .253 for Justice in 1995. In 1996, .314 was Jeter’s average and .321 was Justice’s average. Question 1: Which batter had the higher average in 1995? Answer: JusticeQuestion 2: Which batter had the higher average in 1996?Answer: JusticeQuestion 3: Which batter had the higher average over the 2-year period? (To find this answer you would add the hits from both years together and divide it by the added number of at bats for both years). Jeter’s Average = .310Justice’s Average = .270Answer: Jeter had the higher average over the 2-year periodThe answer to the last question is not aligned with the answers to the first couple of questions, because it looks as if though Justice would have the higher average over the 2 year period, but Jeter actually does. This is why it is a Simpson’s Paradox. Lecture 61. Fallacies in thinkinga. False dilemma/ limited choice: incomplete list of options b. Hasty generalization: ( more than 1 instance) A and B are linked 1 or a few timesc. Appeal to emotion: i. Positive: you should do it (good idea)ii. Negative: you should not do it (bad idea)d. Personal attack: you attacking someone / someone else’s business e. Straw man: creating a weak argument to argue withf. False authority: “ I’m not a doctor, but I play one on TV”g. Circular reasoning/ begging the question: 2 ideas argued to argue each other Lecture 71. Inductive Reasoning a. Premises: 1+5 = even #, 3+9 = even #, 11 + 27 = even #b. Conclusion: Therefore, adding 2 numbers results in an even #2. Examplesa. If you are a college student, you can ride the bus for free. i. Hypothesis: You are a college student ii. Conclusion: You can ride the bus for freeb. All nurses take blood pressure. Helen is a nurse, therefore she can take blood pressurei. Valid claimLecture 81. Logic and truth tables a. Negation of a statement is the assertion that means the opposite of the original statement i. P= he likes dogs, Not P= he does not like dogsii. The negation of P is false when P is true ( By its definition, the negation of a true statement is false and the negation of a false statement is true iii. When a negation uses ALL, you change 2 things. When it uses NONE, you change 1 thing1. EX: All cats are not afraid of dogs, would be negated to all cats are afraid of dogs. b. Conjunction of 2 statements is the assertion that both statements are truei. P= baseball is 90% mental, Q= the other half of baseball is physical. ii. The conjunction of p and q is that baseball is 90% mental and it is physical c. Disjunction of a statement means that it is inclusive and is only true if both statements happen i. P= this medication may cause dizziness, Q= this medication may cause fatigueii. The disjunction of this statement is that this