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MATH10120 Final: Math10120F14 Fall2007 Final1

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turquoisegnu128

31 Jan 2019

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Let u = {all students at notre dame}. F = {all students at notre dame who like to play football} B = {all students at notre dame who like to play basketball} S = {all students at notre dame who like to play soccer}. Which of the following sets is the set. {all students at notre dame who like to play basketball and soccer but not football}. (a) (b s) (b) (b s) f (c) (b s) f (d) (b s) (e) (b s) f. In a group of 70 circus performers, 40 are gymnasts (g), 35 are acrobats (a) and 20 are both. How many of the circus performers are neither gymnasts nor acrobats? (a) 20 (b) 5 (c) 6 (d) 10 (e) 15. T (a) (t s) r (b) (t s) r (c) (s t ) r (d) (t s) r (e) (s t ) r.

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PROBLEM 01: There are 100 students waiting in line to get student IDs. Of these, 50 are from Indiana, 45 are freshmen, and 20 are neither freshmen nor from Indiana. How many of the students are freshmen who are not from Indiana? A) 15 B) 50 C) 35 D) 65 E) 30 N) none of the above

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Practice 12-2 Conditional Probability 1. The table contains information about Education and Salary of Employees the 1205 employees at one business. Find Under S20,000 to Over each probability. Round to the nearest $20,000 $30,000 S30,000 tenth of a percent. Less than high school 69 36 2 a. P(employee has less than a high High School 112 98 14 school education) 102 103 143 b. P(employee earns under $20,000) Some college c. P(employee earns over $30,000 13 178 25 College degree and has less than a high school education) d. P(employee earns under $20,000 and has a college degree) given that th e employee has on ly a high school education, the probability that the employee earns over $30,000 f. given that the employee earns over $30,000, the probability that the employee has only a high school education or less 2. High school students in one school chose their favorite leisure activity. Find each probability. Round to the nearest tenth of a percent. Favorite Leisure Activities Sports Hiking Reading Phoning Shopping other 48 85 02 71 29 Female 39 Male a. P(sports female b. P(female l sports) c. P(reading l male d. P male l reading) g. male I shopping) h. P(female shopping) e. P(hiking I female) f. P(hiking l male) 3. The senior class is 55% female, and 32% are females who play a competitive sport. Find the probability that a student plays a competitive sport, given that the student is female. Draw a tree diagram. Find each probability 4. A softball game has an 80% chance of being canceled for a light drizzle and a 30% chance of being canceled for a heavy fog when there is no drizzle. There is a 70% chance of heavy fog and a 30% chance of t drizzle. a. Find the probability that the game will be canceled b. Find the probability there will be a light drizzle and the game will not be canceled. The students of a high school are 51% males: 45% of the m ales and 49% of the females attend concerts. a. Find the probability that a student attends concerts. b. Find the probability that a student is a female and does not attend concerts.

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If U and V are positive constants, find all critical points of the function. (Enter your answers as a comma-separated list.) F(t) = Ue t + Ve -t t = Find all critical points of f(x) = 20 x 2 e - 0.3x and classify them as local minima of ,maxima. x = (smaller value) This critical point is a . x = (larger value) This critical point is a . Consider f(x) = x 8 (7 - x) 9. Find f '(x) and simplify your answer. f '(x) = Find all critical points of f(x) and then use the first derivation test to determine local maxima and minima. f(x) has a at x = (smallest value) Local Maximum OR Minimum OR Neither f(x) has a at x = Local Maximum OR Minimum OR Neither f(x) has a at x = (largest value) Local Maximum OR Minimum OR Neither Find the inflection points of f(t) = t 4 + t 3 - 18t 2 +8. Give exact answer. t = (smallest value) t = (largest value) Sketch a possible of y = f(x), using the given information about derivation y' = f'(x) and y" = f"(x). Assume that the function is defined and continuous for all real x. Let f be a function f(x) > 0 for all x. Let g = 1/f. If f is increasing in an interval around x 0, what about g? g is increasing in an interval x 0. g is zero in an interval around x 0. g is decreasing in an interval around x 0. We cannot tell whether g is increasing or decreasing in an interval around x 0. g is constant in an interval around x 0. If f has a local maximum at x 1, what about g? g has a local maximum at x 1. g has both a local minimum and a local maximum at x 1. We cannot tell whether g has a local minimum or a local maximum at x 1. g has an inflection point at x 1. g has a local minimum at x 1. If f is a concave down at x 2, what about g? g is increasing at x 2. g is flat at x 2. We cannot tell whether g is concave up of concave down at x 2. g is concave down at x 2. g is concave up at x 2. You are given the graph of the second derivation function f" below. Which of the given have x-values that are inflection points of the function f? (Select all the apply.) A B C D E F G H I none of the above