Math 083 Review for Final Exam Name Please show work for all calculated answers. Show work in a neat and organized manner. 1) Using the frequency table for a monthly budget, find all of the relative frequencies (rounded to 3 decimal places) and percentages (rounded to tenths of a percent). a) Expenditure Dollars Spent Relative Frequency Percentage food $ 450 rent $1100 utilities $ 150 other $ 200 b) The relative frequencies should add to. c) The percentages should add to. 2) Tickets were purchased for a dance recital. The pie chart is shown below. a) Approximate the percentage of adult tickets purchased. b) Which is the most reasonable percentage for the senior tickets purchased? 20% 25% 30% 45% 50% 60% c) If 33.3% of the tickets were purchased for children and a total of 600 tickets were purchased, how many child tickets were purchased? 3) Using the histogram at the right of male heights in inches: a) How many males were there? b) What is the interval with a midpoint of 72 inches? c) What is the interval with a frequency of 7? d) What percent have heights of at least 71 inches? e) What percent of males have heights of less than 69 inches?
4) Using the Venn diagram on classic films people own, answer the following: a) How many people were surveyed? The Godfather Casablanca b) How many own all 3 films? 45 18 28 c) How many own The Godfather and Casablanca, but do not own Star Wars? 12 5 16 d) How many own Star Wars? e) How many own exactly one of these films? 12 31 f) How many own The Godfather and Star Wars? Note they may or may not own Casablanca. Star Wars 5) You currently have $5,000 and can earn 1.5% annual interest. a) If you earn simple interest, write a mathematical expression that would find the amount you have after n years. b) If you earn compound interest, write a mathematical expression that would find the amount you have after n years. c) How much will you have in your account if you deposit $2000 and it earns 2% interest compounded annually for 10 years? 6) You have a nice meal at a restaurant and wish to leave an 18% tip for the check of $35.75. a) What is the tip? b) What is the total cost of the meal? 7) Fill in the following chart: words inequalities Using the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, list the appropriate numbers at least 8 at most 3 more than 10 fewer than 7 strictly between 5 and 11 between 6 and 9, inclusive no more than 4
8) Write interval notation for each of these: a) x 20 b) x < 15 c) 10 x 20 9) Practice with integers and fractions. Reduce to lowest terms. a) 11 - (-4) d) -14 - (-6) g) - 4 2 b) - (-7) e)!12 5 + 7 10 h) -5-9! c) 3 3 $ # & f) " 7%! 2$ # & " 7%! 7 $ # & i) " 12% 12 7 / 3 10) A softball team has decided to have custom T-shirts made. They have two screening shops from which to choose. a) Wave Graphics charges a set-up fee of $30 and then charges an additional $6 per shirt. Give the expression that represents the total cost to order T shirts from Wave Graphics. Shirts Ordered 0 Wave Graphics Cost Shirt Shop Cost 4 8 b) The Shirt Shop does not charge a set-up fee. They just charge $9 per shirt. Give the expression that represents the total cost for T shirts from the Shirt Shop. 12 16 20 24 c) Complete the table. d) For what value(s) of T will the cost for ordering from the two companies be the same? e) Explain the circumstances under which you would choose to order from Wave Graphics. f) What is the independent variable and what is the dependent variable?
11) Whatever happened to 1-pound bags of coffee? Two brands of coffee are Eight O Clock and Dunkin Donuts, but it is hard to compare them because they come in different sized bags. Compare the following: Eight O Clock Coffee comes in a 12 oz bag for $5.99. Dunkin Donuts Coffee comes in a 16 oz. bag for $7.49. Which is the better buy and why? 12) A polygraph test is sometimes used to detect if someone is lying, but it is generally not admissible in court because of its dubious accuracy. A polygraph test is given to 100 people, and the test is wrong for 28 of them. What is the empirical probability that the polygraph test is wrong for a randomly chosen person? What is the probability that it is right? What is the difference between theoretical and empirical probability? 13) The table at the right represents the minutes per week that each student surveyed used the Math Center on two selected weeks. student week 1 week 8 a) Calculate the mean, median, and mode for week 1. b) For week 1, what is the relative difference between the largest number of minutes and the smallest? c) What is the percent decrease for student G from week 1 to week 8? 14) Using the following equivalents to obtain conversion factors, change $25 in U.S. currency to Japanese Yen. These conversions were for 05/01/2015. 1 Euro = 1.10 U.S. dollars 1 Euro = 133.85 Japanese Yen A 75 85 B 90 100 C 75 90 D 90 90 E 125 135 F 55 70 G 90 65 H 55 90 15) a) Solve and check: 3x 5 =!6 b) Solve and check (using both parts of the check): 2-5x > x - 16 c) Solve the following for b, then check your answer: A = ( b + ) B h 2
16) An account earns 2% simple interest each year. Your original deposit is $3500. a) How much interest would you earn after 10 years? b) How much money would be in your account after 10 years? 17) An account earns 2% compound interest each year. Your original deposit is $5600. a) How much interest would you earn after 20 years? b) How much would be in your account after 20 years? 18) Using the histogram at the right: a) How many of the test scores are at least 85? b) What is the modal interval for the test scores? 19) These graphs are for three plants whose heights are measured in inches. a) Which plant was planted as a seed? b) At what rate is the first plant growing? c) Which plant is growing more slowly than the other two? d) How tall was Plant #2 when it was placed in soil?
20) When people buy gold jewelry, it is described in terms of karats. A karat is the unit that measures the purity of gold. This is the same as the percentage of pure gold. Pure gold is 24-karat gold, thus, it is 100% gold. Usually we mix gold with a metal like copper, silver, or zinc to make jewelry (because pure gold is too soft). Each karat indicates 1/24th of the whole. So, if a piece of jewelry is made of metal that is 18 parts gold and 6 parts copper, that is 18-karat gold. Thus, 18-karat gold is 18 / 24 pure gold and is 75% gold. a) Currently an ounce of 24-karat gold costs $1179 per ounce. How much would you expect an ounce of 14-karat gold to cost? (Assume it is mixed with copper and its cost is negligible.) b) Using the information above, how much pure gold (in grams) would be in an 18-karat gold ring that weighs 8 grams? 21) A small aircraft has taken off from an airport. The elevation of the plane was recorded at various times during the flight. Record each as an ordered pair, then plot them on the graph provided. Flight Time x (minutes) Altitude y (feet) 0 0 2 1000 4 2000 10 4000 20 3000 30 3000 40 3000 50 2000 60 0 Ordered Pair (x, y) a) What was the highest altitude reached during this flight? b) What was the cruising altitude during this flight? c) How long was the entire flight? d) During what time interval(s) was the altitude increasing? e) During what time interval(s) was the altitude decreasing?
22) The graph at the right shows the number of women in the U.S. House of Representatives for years beginning with 1980. a) Using the equation for the Least Squares line, approximately how many women were in the House in 1995? b) Using the equation, in what year would you estimate there to have been 30 women in the House? c) Find the slope of the line and interpret the slope in context. d) Find the y-intercept of the line and interpret the y-intercept in context. 23) In the graph below the input x is the number of units produced by a machine in a factory. The output y is the profit made by the sale of these x units in dollars. a) Give the coordinates of the x-intercept. b) Interpret the meaning of the x-intercept. c) Give the coordinates of the y-intercept. d) Interpret the meaning of the y-intercept. e) Determine the slope of the line. f) Interpret the meaning of the slope. g) Write the equation of the line in y = m x + b form. h) Use your line to determine how many units you would need to produce and sell to have $150 in profit. i) Use your line to determine the profit when 60 units are produced and sold.
24) The study time in minutes and the exam scores were obtained and graphed in the scatterplot. Then the least squares line was calculated. a) Using the equation, predict the exam score for a student who studies for 32 minutes. Round to the nearest point. b) Find the error (distance) between the point (38, 73) and the line. c) Find the percent difference between the estimate (line) and actual (point) values in part (b). Round to tenths of a percent. For 25 and 26, let f = the frequencies heard, and let h = hours studying (a) Write two separate inequalities, and (b) write a compound inequality. 25) According to Wikipedia humans can hear at frequencies between 31 hertz and 19,000 hertz. Dogs can hear frequencies between 64 hertz and 44,000 hertz. Find the frequencies that humans AND dogs hear. Cats hear frequencies between 55 and 77,000 hertz. What frequencies do cats OR dogs hear? 26) One student says that he will study at least 2 hours for the exam. A second student says she will study at least 5 hours for the exam. What inequality represents the hours that he OR she will study for the exam?
27) a) Graph: y = 2x d) Graph: y = -x + 4 b) Graph: y = 5 e) Graph: x =!3 c) Graph: y = 1 2 x + 3 f) Graph: y =!2 3 x! 2
28) We will compare these two options for flying to Las Vegas and parking a car at the airport: Long Beach airport has a fare available of $119.08 with parking for $12 per day John Wayne airport has a fare of $167.20 with economy parking for $7 per day. a) Let d = Let c = b) Write a formula for the cost for using Long Beach airport: c) Write a formula for the cost for using John Wayne airport: d) We wish to see how many days you d need to park for it to make sense to pay the higher airfare. After solving the system, answer this question in a sentence. 29) Percentages a) A 50-inch flat screen television has a regular price of $1299.99. During Black Friday it is on sale for 20% off. How much will you pay for this television on Black Friday? b) A 50-inch flat screen television has a regular price of $1299.99. During Cyber Monday, you will save 30%. How much will you save if you buy it on Cyber Monday? c) A 50-inch flat screen television has a regular price of $1299.99. It is currently on sale for $999.99. What percent are you saving? 30) From years of experience, a bagel shop has determined that at a price of p = $2.50, they will sell x = 400 bagels each week. If they lower the price to p = $2.00, they will sell 500 bagels each week. The costs of doing business for a company can be found by adding fixed costs (such as rent, insurance, and wages) and variable costs (which are the costs to produce the product you are selling). The portion of the bagel shop s fixed weekly costs allotted to bagels is $200, and the supplies to produce each bagel cost $0.75. a) Assuming this relationship is linear, write an equation that relates the price, p, to the number of bagels, x, that will be sold. Your equation should look like p = mx + b. b) The revenue generated by selling these bagels comes from the product of the price times the number of bagels sold. Write a revenue equation: R = c) Write an equation for the total cost of x bagels: C = d) Last, write the profit equation: P =
31) A video game company collected the following data: a) We wish to write a profit function: P(x) Begin with the factors from the x-intercepts. P(x) = - a ( ) ( ) b) Determine the value for a by using one of the other points. # of games profit 0-300 5 0 10 200 15 300 30 0 35-300 c) Check with any point you have not yet used. 32) This graph shows an auto parts maker s daily profit in y dollars for x parts sold. a) Give the coordinates of the y-intercept. b) Explain what it means. c) Give the coordinates of the x-intercepts. d) Explain what they mean. e) Use what you know about the factored form of a polynomial to find the equation of this parabola: y = - ( ) ( ) f) What is the maximum profit this business can generate in a day and how many parts do they need to sell to achieve this amount of profit?
33) Miscellaneous a) Find the product: (x - 3) (x + 8) f) Factor: x 2-6x - 40 b) F(x) = (x + 5) (x - 8); What is F(10)? g) Write 125,000 in scientific notation. c) Write 4.6 (10-4 ) in decimal notation. h) ( 3x 10 ) ( 4x 8 ) = d) ( 3x 6 ) 4 = i) 10x 16 15x 20 = e) 9x 15 6x 7 = j) ( x 4 ) 6 ( x 12 ) x 18 ( ) = 34)
35) 36)
37) 38) 39) If he made $3500, then how many copies of Math is Fun did he sell?
40) *Note: Choose one among: Always, Sometimes, and Never. 41) Let D be the dominant gene, you do not have allele for the disease. Let d be the recessive gene, you do have allele for the disease. After completing the Punnett square, tell what percent of the offspring will have the disease. a) Both father and mother are carriers. b) Father is carrier and mother has no recessive alleles. Father Father Mother Mother 42) A baseball diamond is really a 90-foot square. Let s say the catcher is throwing a ball from home plate to second base. Find the distance the ball is thrown, rounding to tenths of a foot.
43) A 9-ft ladder is placed against a wall with its base 4 ft from the wall. How high above the ground is the top of the ladder? a) Make a drawing with all the specifics. b) Round your answer to the nearest foot. 44) The value of Jennifer s stock portfolio is given by the function v(t) = 50 + 73t 3t 2, where v is the value of the portfolio in hundreds of dollars and t is the time in months. a) How much money did Jennifer start with? b) When will the value of Jennifer s portfolio be at a maximum? 45) The height h in feet of an object above the ground is given by h = -16t 2 + 64t + 190, where t is the time in seconds. Find the time it takes the object to strike the ground and find the maximum height of the object. 46) Evaluate: a) log 2 (32) = b) log 10 (10,000,000) = 47) Solve for the X: a) 4 = log 10 X b) 5 = log 3 X