MATH 120 FINAL EXAM STUDY GUIDE 2025/2026 COMPLETE QUESTIONS WITH CORRECT DETAILED ANSWERS || 100% GUARANTEED PASS <BRAND NEW VERSION>

MATH 120 FINAL EXAM STUDY GUIDE 2025/2026 COMPLETE QUESTIONS WITH CORRECT DETAILED ANSWERS || 100% GUARANTEED PASS &lt;BRAND NEW VERSION&gt; 1. A box contains 20 chocolates, but only two of them are the dark chocolate that somebody likes. When it is said that the probability of drawing one of the dark chocolates at random is 0.1, what kind of probability is being stated? (7A) - ANSWER A theoretical probability, because both the total and desired numbers of objects are known 2. Suppose that four 6-sided dice are tossed. How many outcomes are possible? (7A) - ANSWER 6x6x6x6, because each of the four dice have six possible outcomes. 3. Each of the following states a probability for two events. In which case are the events dependent? (7B) - ANSWER The probability of choosing two pink roses from a vase with 25 roses. After the first rose is picked, there will be one less pink rose and one less out of the total in the vase. 4. You purchase 25 lottery tickets for which the probability of winning some prize on a single ticket is 1 in 100. What is your probability of having at least one winner among your 25 tickets? (7B) - ANSWER The probability is 1 - (0.99)^25 according to the "at least once" rule for independent events. 5. Benjamin Franklin bequeathed 4,400$ each to the cities of Boston and Philadelphia, in trust to gather interest for 200 years. When the trust came due in 1990, what was the approximate value of the Boston Trust - ANSWER Almost 5,000,000$ 6. How many companies are used to make up the current DJIA index - ANSWER 30 7. What is a Ponzi Scheme - ANSWER a fraudulent investment operation that pays returns to investors from their own money or money paid by subsequent investors, rather than from profit. 8. Using a fraudulent investment scheme, how long did it take Charles Ponzi to go from anonymity to being a well-known Boston Millionaire - ANSWER Six months after using the scheme in 1920 9. Upon his release from prison in 1934, what did Charles Ponzi tell reporters before he left - ANSWER "I went looking for trouble, and I found it" 10. Along with being a mathematician, in which profession did John Venn also serve - ANSWER Anglican Priest 11. Which location houses a stained glass window commemorating John Venn's work - ANSWER A university in Cambridge in one of the dining halls 12. How did Henri Poincare describe Cantor's work - ANSWER A grave disease infecting the discipline of mathematics 13. Leopold Kronecker tried to prevent Georg Cantor's work from being published because he thought mathematics should deal only with finite numbers and with a finite number of operations. Thus, Kronecker is well known for what remark? - ANSWER god made the integers, all else is the work of man 14. Into what personal belief did Georg Cantor invest an intense amount of study. - ANSWER Elizabethan literature 15. When was Pythagoras born? - ANSWER 569 BC 16. What was the name for the inner circle of followers in Pythagoras' society? - ANSWER Mathematikoi 17. Because this lack of biographical information (such as the date, place, and circumstances of both his birth and death) is unusual for ancient Greek mathematicians, some researchers have proposed which of the following? - ANSWER Euclid was not, in fact, an actual historical figure. 18. Eudid's Elements is divided into to how many books? - ANSWER 13 19. How do many scholars view the death of Hypatia? - ANSWER As the beginning of the downfall of intellectual life in Alexandria. 20. Why did some fanatical Christian sects consider Hypatia's teachings to be paganism? - ANSWER Because she was an intelligent, dignified, and forthright woman just before the beginning of the Dark Ages. 21. In which of the following books did Leonardo da Vinci make use of geometric techniques to create three-dimensional elements? - ANSWER Divina Proportione 22. Da Vinci was a polymath. What is a polymath? - ANSWER An individual whose knowledge spans a substantial number of subjects, known to draw on complex bodies of knowledge to solve specific problems. 23. Who wrote the Indiana House Bill #246 in 1897? - ANSWER Amateur Mathematician and Medical Doctor Edwin Goodwin 24. When the Indiana House Bill #246 came before the 1897 Indiana House of Representatives, what were the vote results? - ANSWER It passed 67-0. 25. Every square is a rhombus. - ANSWER True 26. A square has exactly two right angles. - ANSWER False 27. Every square is a rectangle. - ANSWER True 28. In the provided triangle, x = 17.2 m, y - 13.7 m, z - 9.0 m, and h - 7 m. What is the perimeter? - ANSWER 39.9 29. In the provided triangle, a - 24.0 cm, b - 12.0 cm, c - 29.1 cm, and h = 9 cm. What is the area? - ANSWER 108 30. In the provided triangle, x = 19.5 m, y = 15.0 m, z - 9.6 m, and h = 6 m. What is the area? - ANSWER 58.5 31. In the provided triangle, a = 24.0 cm, b = 11.7 cm, c = 27.3 cm, and h - 8 cm. What is the perimeter? - ANSWER 63 32. A flag pole that is 15 feet tall casts a shadow that is 23 feet long. At the same time of day, the shadow of a nearby tree is 32.1 feet long. How tall is the tree? - ANSWER 20.9 33. A 6-ft tall man notices his shadow is 5 feet long. At the same time of day, he measures the shadow of a nearby water tower and finds it to be 23.3 feet long. How tall is the water tower? - ANSWER 28 34. Jon walked 98 feet in 14.6 seconds. What is his speed in miles per hour? (1 mi = 5280 ft) - ANSWER 4.6 35. An equilateral triangle has three equal angles. - ANSWER True 36. An equilateral triangle can be a right triangle. - ANSWER False 37. A right triangle always has two acute angles. - ANSWER True 38. An equilateral triangle has three equal length sides. - ANSWER True 39. In the provided triangle, x - 18.5 m, y = 13.4 m, z = 9.1 m, and h = 6 m. What is the perimeter? - ANSWER 41 40. In the provided triangle, a = 21.0 cm, b - 11.8 cm, c - 27.6 cm, and h = 8 cm. What is the perimeter? - ANSWER 60.4 41. In the provided triangle, x = 19.5 m, y = 14.1 m, z - 8.3 m, and h - 6 m. What is the area? - ANSWER 58.5 42. A supplier of parts to the automobile industry is launching a new brake pad intended to wear down more slowly while delivering the same performance. The company performs a study that incorrectly maintains the null hypothesis. What type of error is this? - ANSWER Type 2: The supplier maintained the null when it should have rejected it. 43. When assessing the significance of a study, we're asking: - ANSWER What is the likelihood that we incorrectly reject the null? 44. You're surprised to learn that instead of ~$100, a 0.30 carat costs ~$800 carats. Which explanation would make sense? - ANSWER The linear regression is not accurate at predicting the cost of diamonds below 0.40 carats. There is a fixed cost associated with procuring the diamond and offering it for sale, meaning that small diamonds have a relatively high price. The diamond is very high quality as measured by other metrics (e.g., cut, clarity, color). **All of the above.** 45. If a residual is negative, what does it mean about the observed value? - ANSWER The predicted value is greater than the observed value. 46. If the expected value of a diamond is $3,500, but the observed value is $3,800, what is the residual? - ANSWER $300 47. If the correlation between the price of two stocks is 0.83, what does this indicate? - ANSWER Strong positive correlation 48. If the coefficient of determination between the price of a house and it square footage is 65%, what percentage of the variation in the price of the house is explained by its size? - ANSWER 65% 49. If the correlation coefficient between the price of a car and its mileage is 60%, what percentage of the price of the car is explained by its mileage? - ANSWER 36% 50. If the regression line comparing the age of a used car to its price has the equation c = -3000a + 36000, what is the expected cost of an 8-year-old car? - ANSWER $12,000 51. If the regression line comparing the age of a used car to its price has the equation c = -3000a + 36000 and the residual is $3,000, what is the observed cost of an 8-year-old car? - ANSWER $15,000 52. If the regression line comparing the age of a used car to its price has the equation c = -3000a + 36000, what is the expected age of a car that costs $27,000? - ANSWER 3 years 53. If the r-squared of the regression line comparing the age of a used motorcycle to its cost is 64%, what is the correlation coefficient? - ANSWER -0.80 54. Using the test scores in the table below, what is the variance of the scores on the exam? (Round your answer to the nearest whole number.) - ANSWER 27 55. Using the test scores in the table below, what is the standard deviation of the scores on the exam? (Round your answer to the nearest whole number.) - ANSWER 5 Determine that the average score is 87% Calculate all of the differences between the scores and the average to get 9, 5, 4, 3, 0, -1, -1, -4, -5, -10 Square all of the differences to get 81, 25, 16, 9, 0, 1, 1, 16, 25, 100 Average the squared differences to get 27.4 as the variance Take the square root of the variance to get 5.23 as the standard deviation Round 5.23 to the nearest whole number to get 5 Answer: 5 56. Assume that 500,000 people take the GED exam (high school proficiency exam) each year and their scores form a normal distribution. If Danny scores two standard deviations below the mean, what percentile is he? - ANSWER 2.5th 57. Assume that 500,000 people take the GED exam (high school proficiency exam) each year and their scores form a normal distribution. If Tara scores one standard deviation above the mean, what percentile is she? - ANSWER 84th 58. Assume that 20 people take a math test, which is not enough for a normal distribution to form. If Conrad scores three standard deviations above the mean, what percentile is he? - ANSWER Not enough information to determine. 59. Assume that 20 people take a math test, which is not enough for a normal distribution to form. If Sarah scores at the median, what percentile is she? - ANSWER 50th 60. Assume that 20 people take a math test, which is not enough for a normal distribution to form. If Charlie scores at the mean, what percentile is he? - ANSWER Not enough information to determine. 61. Typically, in the early stages of a country's transition from an emerging nation to a developed nation, death rates fall while birth rates stay constant. What type of covariance do death rates and birth rates have? - ANSWER No Covariance 62. Typically, in the middle stages of a country's transition from an emerging nation to a developed nation, death rates fall while birth rates fall. What type of covariance do death rates and birth rates have? - ANSWER Positive Covariance 63. Typically, in the late stages of a country's transition from an emerging nation to a developed nation, death rates stay constant while birth rates fall. What type of covariance do death rates and birth rates have? - ANSWER No Covariance 64. If a company's profits increase when the economy slows, what type of covariance is there between this company and the broader economy? - ANSWER Negative Covariance 65. If the average height of a male in the U.S. is 70 inches and the standard deviation of male heights is 3 inches, what is the probability that a randomly selected male will be between 70 and 73 inches? (Assume a normal distribution.) - ANSWER 34% 66. If the average height of a female in the U.S. is 65 inches and the standard deviation of female heights is 2.5 inches, what is the probability that a randomly selected female will be between 60 and 62.5 inches? (Assume a normal distribution.) - ANSWER 14% 67. Simplify 8! - ANSWER 40,320 68. Divide 8! by 8. - ANSWER 5,040 69. Evaluate 17!/15! - ANSWER 272 70. Evaluate 17!/17*15! - ANSWER 16 71. How many different ways can five types of bread be displayed on a grocery store shelf? - ANSWER 120 72. How many different ways can 8 types of candy be displayed on a grocery store shelf? - ANSWER 40,320 73. A 12-sided die can be made from a geometric solid called a dodecahedron. Assume that a fair dodecahedron is rolled. The sample space is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Find P(Less than 3). A) 1/4 B) 2/3 C) 1/6 D) 1/12 - ANSWER D 74. According to a survey, 81% of teenagers could recognize a picture of legendary film star John Wayne. What is the probability that a randomly selected teenager could recognize John Wayne? A) 0.19 B) 0.81 C) 0.01 D) 0.23 - ANSWER C 75. A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). List all the outcomes of the sample space. A) {AA, AB, AC, BB, BC, CC} B) {A, B, C} C) {AA, AB, AC, BA, BB, BC, CA, CB, CC} D) {AB, AC, BA, BC, CA, CB} - ANSWER B 76. A survey asked respondents to indicate their level of satisfaction with government spending. The results are shown below. Response Number Very satisfied 608 Somewhat satisfied 3053 Dissatisfied 5303 Total 8964 77. Assume this is a simple random sample from a population. Use the Empirical Method to estimate the probability that a person is dissatisfied with government's spending? A) 0.635 B) 0.408 C) 0.33 D) 0.592 - ANSWER C