Second Semester Final Review IMP3 Name Simplify the expression and write the answer without negative exponents. 1) (-9x3y)(-10x4y6) 1) 2) 8x 9y10 2x8y7 2) 3) x 7 x6 3) 4) 3m -4n-4 2p-5 4) 5) 3x -8 x3 5) 6) (x5)-3 6) 7) (x-3y6)-3 7) 8) 9x-4 7y-4-3 8) Find the slope of the line through the given points. If the slope is undefined, so state. 9) (-7, -9) and (-7, 3) 9) Solve for k if the line through the two given points is to have the given slope. 10) (2, 4) and (4, k), m = 3 2 10) Write the equation in slope-intercept form. 11) -4x = 3y + 6 11) Find the point-slope equation for the line with the given properties. 12) Slope = - 5, through (1, -5) 12) 3 Two points on L1 and two points on L2 are given. Determine whether L1 is parallel to L2, L1 is perpendicular to L2, or neither. 13) L1: (1, 3), (3, 4); L2: (-2, 3), (2, 5) 13) 1
14) L1: (2, 2), (3, 0); L2: (3, -2), (5, -1) 14) Determine whether the two given lines are parallel, perpendicular, or neither. 15) 3x = 5y + 20 y = 3 5 x - 1 15) Graph the inequality. 16) -2x - 3y 6 16) 17) x > 2 17) Find the solution to the system of equations by substitution. 18) x + 2y = 2 7x - 6y = -6 18) 19) x + 6y = -45-6x + 5y = -17 19) Solve the system of equations using the addition method. 20) 5x + 6y = -7-5x - 13y = 21 20) 21) 5x + 35y = 35 9x - 5y = -5 21) 2
22) x + y + z = -7 x - y + 5z = -21 4x + y + z = -22 22) 23) 4x + y + 3 2 z = 14 23) 3 x + 3z = -3 2 x + 4y = -10 24) The Little Town Fine Arts Center charges $25 per adult and $13 per senior citizen for its performances. On a recent weekend evening when 469 people paid admission, the total receipts were $7345. How many who paid were senior citizens? 24) 25) A ceramics workshop makes serving bowls, platters, and bread baskets to sell at its Winter Festival. A serving bowl takes 3 hours to prepare, 2 hours to paint, and 8 hours to fire. A platter takes 15 hours to prepare, 3 hours to paint, and 4 hours to fire. A bread basket takes 4 hours to prepare, 14 hours to paint, and 7 hours to fire. If the workshop has 101 hours for prep time, 55 hours for painting, and 82 hours for firing, how many of each can be made? 25) Determine the solution to the system of inequalities. 26) x 0 y 0 x + y 6 10x + 5y 50 5x + 10y 50 26) Multiply. 27) (-4x + 5)(-4x + 7) 27) 28) (6x - 5y)(7x - 9y) 28) Multiply. Assume that all variables represent natural numbers. 29) (x2n - y)(x3n- 6y2n) 29) 3
Multiply. 30) (8m + 7)(8m + 7) 30) Multiply the polynomials. 31) (4x2-2x + 3)(x - 6) 31) 32) (x - 11)(x2 + 7x - 5) 32) Solve the equation by the quadratic formula. 33) 3x2 + 12x + 1 = 0 33) 34) 2x2 = -6x - 2 34) 35) (x + 5)(x - 4) = 4 35) 36) 6x2 = -12x - 3 36) 37) The expected future population of a small town, which currently has 7900 residents, can be approximated by the formula y = 7900(1.8)-0.2t where t is the number of years in the future. Find the expected population of the town 30 years in the future. 37) 38) Austin invested $12,000 in an account at 8% compounded quarterly. Find the amount in Austin's account after a period of 4 years. 38) Write the equation in logarithmic form. 39) 52 = 25 39) Write the equation in exponential form. 1 40) log = -2 40) 4 16 41) Luis invests $1000 into an account earning interest at a rate of 7% compounded annually. Find the amount in the account at the end of 10 years. 41) 42) Find out how long it takes a $3300 investment to double if it is invested at 9% compounded 42) monthly. Round to the nearest tenth of a year. Use the formula A = P 1 + r nt. n 43) A secured elevator allows access by pressing the correct sequence of letters on a control panel. If the control panel contains the 26 letters of the alphabet and a five-letter code must be entered (repetition is not permitted). How many different codes are possible? 43) 4
44) Four different colored flags will be placed on a pole, one beneath another. The arrangement of the colors indicates the message. How many messages are possible if 4 flags are to be selected from 11 different colored flags? 44) 45) Mrs. Sartori, a teacher, decides to give identical prizes to 4 of the 10 students in her class. In how many ways can she do it? 45) 46) D.J Bob, a disc jockey has 34 records that he wants to play during the next hour, but he has time to play only 12 of them. Write the expression used to determine how many different ways he can select a group of 12 records to play. 46) Use the binomial theorem to expand the expression. 47) (x + 5)4 47) 48) (4x + 3)3 48) 49) Mr. and Mrs. Smith are planning to have 6 children. How many ways can they have 4 boys and 2 girls? 49) Round your answer, as needed. 50) In a business class, 10% of the students have never taken a statistics class, 35% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. What is the probability that both of the first two groupmates you meet have studied at least one semester of statistics? 50) 51) In one town, 50% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats. 51) 52) A study conducted at a certain college shows that 51% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that 9 randomly selected graduates all find jobs in their chosen field within a year of graduating. 52) 53) A study conducted at a certain college shows that 56% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 9 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. 53) 54) The American Red Cross says that about 45% of the U.S. population has Type O blood, 40% Type A, 11% Type B, and the rest Type AB. Among seven donors, what is the probability that no one is Type B? 54) 55) You roll a fair die four times. What is the probability that you roll at least one 6? 55) Provide an appropriate response. 56) Pepsi is running a sales promotion in which 12% of all bottles have a "FREE" logo under the cap. What is the probability that you find two free ones in a 6-pack? 56) 5
Use a tree diagram to find the indicated probability. 57) In one town in the Pacific Northwest, only 23% of days are sunny. A company's records indicate that on sunny days 2.1% of employees will call in sick.when it is not sunny, 1.4% of employees will call in sick. What percent of employees call in sick on a randomly selected day? 57) 58) 3.3% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 94% of those who have the disease will test positive. However 4.4% of those who do not have the disease will also test positive (false positives). What is the probability that any given person will test positive? Round your answer to three decimal places if necessary. 58) Find the expected value of the random variable. Round to three decimal places. 59) You pick a card from a deck. If you get a face card, you win $5. If you get an ace, you win $30 plus an extra $60 for the ace of hearts. For any other card you win nothing. Find the expected amount you will win. 59) 60) You roll a pair of dice. If you get a sum greater than 10 you win $50. If you get a double you win $30. If you get a double and a sum greater than 10 you win a $80. Otherwise you win nothing. You pay $5 to play. Find the expected amount you win at this game. 60) Find the indicated probability. 61) An archer is able to hit the bull's-eye 49% of the time. If she shoots 10 arrows, what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others. 61) 62) A tennis player makes a successful first serve 48% of the time. If she serves 8 times, what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others. 62) 63) Suppose that 10% of people are left handed. If 8 people are selected at random, what is the probability that exactly 2 of them are left handed? 63) Find the probability of the outcome described. 64) A beginning archer is able to hit the bull's-eye 39% of the time. If she shoots 6 arrows, what is the probability that she gets at most 3 bull's-eyes? Assume each shot is independent of the others. 64) Find the indicated probability. 65) Suppose a computer chip manufacturer rejects 3% of the chips produced because they fail presale testing. If you test 5 chips, what is the probability that none of the chips fail? 65) 66) A basketball player has made 70% of his foul shots during the season. If he shoots 4 foul shots in tonight's game, what is the probability that he makes all of the shots? 66) 6