4. Give a verbal description of the elements in region " (R") in the diagram. a) not in A c) in Aand in B

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1 MGF 1106 Version C Fall Which Venn diagram below shows A œ A? A A a) c) A b) d) A 2. Suppose A œ {ßß$}, œ {ß} and C œ {}. Which of the following is NOT correct? a) A C œ {1,2,3} c) A Á {3} b) C œg d) A œ {ß} 3. The complement of the shaded set on the Venn diagram is: A w w a) A c) A b) A d) A Venn diagram for problems % and &: A R1 R2 R3 R4 4. Give a verbal description of the elements in region (R) in the diagram. a) not in A c) in Aand in b) in Abut not in w d) not in A 5. Region 4 in the diagram is: a) A c) aa b b) A d) U w Final Exam C R. Pyle MGF 1106 Fall 2000 page 1 of 6

2 Information for problems 6, 7, and. In a group of potential computer buyers À 20 people were considering buying Dell 25 were considering buying Gateway 20 were considering buying Micron 10 were considering Dell and Gateway 13 were considering Gateway and Micron 11 were considering Dell and Micron 5 were considering all three 4 were considering none of these companies. 6. How many people were considering only Micron? a) 1 c) 5 b) 20 d) How many people were not considering Gateway? a) 6 c) 5 b) 4 d) 15. How many people were considering Gateway or Micron? a) 6 c) 3 b) 32 d) A negation of the statement If it snows, then I'll go to the beach. is: a) It snows, but I don't go to the beach. b) If it doesn't snow, then I won't go to the beach. c) If it snows, then I'll go to the beach. d) It doesn't snow, but I don't go to the beach. 10. Which form below is logically equivalent to µ P Ä Q? a) µ Q Ä P b) P µ Q c) µ (P Q) d) Q Ä µ P 11. In the truth table below, what should the values of A and be? : ; < Ð: ;Ñ < T T F F T F T A F T T T F F F a) A= T, = T b) A= T, = F c) A= F, = T d) A= F, = F 12. In the truth table below, find an incorrect column (col. 3 - col. 6). Final Exam C R. Pyle MGF 1106 Fall 2000 page 2 of 6

3 col. 3 col. 4 col. 5 col. 6 : ; µ (: ;Ñ µ:ä; : µ; ;Ä: T T F T F T T F F T T T F T T T F F F F T F F T a) col. 6 b) col. 5 c) col. 4 d) col In the argument below, which Form (if any) is represented? If Julie is a good swimmer, then she will win. She will win Julie is a good swimmer. a) Fallacy of the converse c) Fallacy of the inverse b) Invalid Disjunctive Syllogism d) None of the above applies 14. In the argument below, which Form is represented? He is either a Republican or a barbarian. He is a Republican. He is not a barbarian. a) Modus Ponens c) Invalid Disjunctive Syllogism b) Modus Tollens d) Law of Transitivity 15. Find a valid conclusion for the following premises: a~ TÄF b G µg a) T b) TÄF c) a µtäfb d) G 16. Find a symbolic negation of : a+ µ, b a) µ: a µ+, b c) µ: a µ+, b b) µ: a µ+, b d) µ: a+, b Final Exam C R. Pyle MGF 1106 Fall 2000 page 3 of 6

4 17. You are the editor of MathWorld, the exciting magazine of math (stop laughing!). The list of the 5 finalists for the annual really neato-math formula award is to be printed in this months' edition. In how many ways can the 5 formulas be printed? Is this a permutations or combinations problem? a) Permutation b) Combination 1. In how many different ways can 4 flags be placed on a flag pole? a) % b) Pa%ß 1 b c) % d) Ca%ß% b 19. Which of the following is a situation in which a permutation is involved? st nd a) The top 3 horses at a horse race (not distinguishing who is 1,2,etc). b) Election of President and Vice-president of a club (recounts not included, ha!) c) You select two ice-cream toppings from a list of five. d) None of the above is a permutation. 20. Given that the sample space of a 3 coin toss is {TTT, TTH, THT, THH, HTT, HTH, HHT, HHH}; What are the odds that in a 3-coin toss you will get exactly 2 tails? a) 6 b) 6-to-2 c) 3:5 d) ) 21. What are the odds of rolling a number greater than 10 when 2 dice are rolled if you add the up faces of each die? 1 a) $' b) 2:1 c) $ d) 3: If you are to choose a single card from a deck of cards, what are the odds against choosing a card whose value is either 2 or 4? $ %! a) % b) $ : c) %%:) d) If the probability of winning in a Las Vegas gambling game is &, then which of the following are true: I. The odds of losing are 3-to-5. II. The odds of winning are 2-to- $. III. The probability of losing is 2-to-5. a) I and II b) I and III c) II and III d) other Final Exam C R. Pyle MGF 1106 Fall 2000 page 4 of 6

5 24. Consider a carnival game in which you pay $2 to toss 3 pennies. The results are: If the outcome has exactly 3 tails then you neither win nor lose. If the outcome has exactly 2 tails in it then you lose $1.00. If the outcome has exactly tail in it then you lose $1.00. If the outcome has exactly 0 tails in it then you win $3.00. Do you expect to lose or gain on each toss? (i.e What is the mathematical expectation?) a) lose b) win c) break even 25. What's the distance between aß b and a&ß' b? a) b) $ c) % d) & 26. If the slope of the line segment joining the points, a ß b and aß $ b is, what is? a) b)2 c)! d) % 27. Suppose the minute hand on an alarm clock is & inches long. How many inches does the tip of the hand move in $! minutes? a) 1 in b) in c) & 1 in d) 60 in 2. An equilateral triangle is always an isoceles triangle? a) True b) False 29. If a 5 foot ladder is leaning against a building and the ladder reaches 4 feet up the side of the building, how far away from the building is the base of the ladder? a) ( ft b) 6 ft c)3 ft d) % ft 30. What is the volume of a coke can (right circular cylinder of radius 2 inches and height 3 inches)? $ $ $ $ a) % 1in b) 121 in c) 101 in d)! 1in 31. What is the volume of a rectangular box measuring 3in 5in 4in? a)1! in 3 $ b) 0 in c) 25 in 3 d) None of the above 32. Congruent triangles are always similar triangles. a) True b) False Final Exam C R. Pyle MGF 1106 Fall 2000 page 5 of 6

6 33. Consider the following chart. How many people scored more than 17 points on the quiz? a) 11 b) 6 c) d) 5 Dr. Payne's Finite Math Quiz Score 34. What score is the mode? a) 0 b) 5 c) 15 d) Mary and ob each took separate exams. Mary's score was 0 with a z-score was 1 Þ$. ob's score was an 3 with a z-score of 1.3. Who did better with respect to his/her own class? a) Mary b) ob c) Neither The ages of 100 turtles were recorded for the Florida Department of Agriculture. The average age, was found to be 16 months with a standard deviation, = of 3 months. Use empirical results. 36. What percentage of the turtle population lies within 6 months of the average? a) '%% b) 95% c) 99.7% d) None of the above 37. How many turtles would be no older than 19 months? a) 20 b) 40 c) 50 d) None of the above 3. Find the percentage of the population of turtles which are older than 16 months but less than 19 months. a) 34% b) 95% c) 6% d) 99.7% An exam was taken in an introductory accounting class. There were 150 scores and the minimum passing score is 70 points out of 100 points on the exam. Assume that the class grades are approximately normally distributed with an average score of 70 with a standard deviation of 5. Use the z-table. 39. Find the percentage of the students who scored lower than a 75 on the exam. a) 64% b) 4.1% c) 15.9% d) 99.7% 40. Find the percentage of the scores are between 77 and 0? a) 15% b) 47.7% c) 5.% d) 34.1% Final Exam C R. Pyle MGF 1106 Fall 2000 page 6 of 6

7 Formula Sheet - Final Exam VALID Arguments forms: Modus Ponens: :p; Law of Transitivity: :p; : ;p< ; :p< Disjunctive Syllogism: : ; Modus Tollens: :p; µ; µ; : µ: INVALID Argument forms: Fallacy of the Converse: :p; Invalid Disjunctive : ; ; Syllogism: : : µ; Fallacy of the Inverse: Logical Equivalences: DeMorgan's Laws œ :p; µ: µ; µ a: ; b a µ: µ; b anegation of Conjunctionb µ a: ; b a µ: µ; b anegation of Disjunctionb ~ a µ: b : adouble Negationb a:p; b a µ;pµ: b acontrapositiveb ~ a:p; b a: µ; b anegation of Implicationb a:p; b ~ : ; aimplication to Disjunctionb All statements below translate to :p; : a) if :, then ; b) ; if : c) : only if ; d) : is sufficient for ; e) ; is necessary for : f) whenever :, athen b ; g) ; whenever : Quantified Negation Statements: ~All a birds fly. b is Some birds do not fly or Not all birds fly. ~Some a birds fly. b is No birds fly. ~Not a all birds fly. b is All birds fly. ~No a birds fly. b is Some birds fly.

8 x x a < bx <xa < bx Formulae: P aß< b œ Gß< a b œ Special Addition Law of Probability P ae Fb œtaeb TaFb IF Aand are mutually exclusive events. Special Multiplication Law of Probability P ae Fb œt aeb TaFb IF Aand are independent events. Complements Rule P ai w b œ TaIb and P aib œ TaI w b for any event E. Outcomes for two dice: ridge Deck: {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, { A, 2, 3, 4, 5, 6, 7,, 9, 10, J, Q, K 31, 32, 33, 34, 35, 36, A, 2, 3, 4, 5, 6, 7,, 9, 10, J, Q, K 41, 42, 43, 44, 45, 46, A, 2, 3, 4, 5, 6, 7,, 9, 10, J, Q, K 51, 52, 53, 54, 55, 56, A, 2, 3, 4, 5, 6, 7,, 9, 10, J, Q, K } 61, 62, 63, 64, 65, 66} Remember: Hearts a b and Diamonds a b are RED Spades a b and Clubs a b are LACK Distance:.œ Éa b ac C b Midpoint: ˆ C C <3=/ C C ß Slope of a line: 7œ <? œ Arc length: Pœ 1 < )! Pythagorean Theorem: aright triangleb +, œ- where - is the length of the hypotenuse Volume and Surface area of rectangular solid: Z œ6a2ß Wœ6A A2 62 Area of a right triangle: Eœ 6A Area and Circumference (perimeter) of a circle: Eœ 1<ßGœ 1< Volume and Surface area of a right circular cylinder: Z œ 1<2ß Wœ 1< 1<2

9 . œ! 3 œ population mean 3œ œ! 3 œ sample mean 3œ Ÿ these formulas are the same = 3œ œ population standard deviation 5 Ë! Ð3. Ñ = œë! Ð3 Ñ 3œ œ sample standard deviation Ÿ these formulas are not the same D. -score œ 5 for population data D-score œ = for sample data Empirical Rule for Normal Data Sets: 6% within 1 st. dev 95% within 2 st. dev % within 3 st. dev rief Table Z For each positive Z, the P column gives the proportion (percentage) of data between Dœ! and DœZ. y the symmetry of the normal curve, proportions for negative Z values are the same as the corresponding positive Z values. z=0 z=z

10 Final Exam Answers C D C D 1. D A 21. D A 2. C D 22. C D 3. A 23. D C 4. C 24. A 5. C D 25. D A 6. A 26. C 7. D A 27. C D. C 2. A A 9. A 29. C D 10. A 30. C 11. C 31. D A 12. D A 32. A A 13. A 33. A 14. C D 34. C D 15. C D 35. C A 16. C D 36. C 17. A 37. D D 1. A 3. A 19. C 39. C 20. C D 40. C D