Math 082 Final Examination Review

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1 Math 08 Final Examination Review 1) Write the equation of the line that passes through the points (4, 6) and (0, 3). Write your answer in slope-intercept form. ) Write the equation of the line that passes through the points ( 9, ) and (3, 4). Write your answer in slope-intercept form. 3) Write the equation of the line that passes through the points (11, 7) and ( 3, 14). Write your answer in slope-intercept form. 4) Graph the line: 5) Graph the line: 6) Graph the line: y x y x 3 3 y x 4 5 7) For the line x 10y 5, find: a) The y-intercept b) The x-intercept 8) For the line 3x y 6, find: a) The y-intercept b) The x-intercept 9) For the line 1x 8y 6, find: a) The y-intercept b) The x-intercept 10) Graph the linear equation: x y 6 11) Graph the linear equation: 7x 5y 35 1) Graph the linear equation: 3x 7y 4 13) Find the slope of the line 11x 5y 13 1

2 14) Find the slope of the line y 3 15) Find the slope of the line 8x 5y 11 16) Find the slope of the line 8y 5x 11 17) Solve the following system of equations by graphing: x y 1 x y 8 18) Solve the following system of equations by graphing: 5x y 7 x y 4 19) Solve the following system of equations by graphing: 5x 3y 3 x 3y 9 0) Solve the following system of equations by using the addition method: x y 1 x y 8 1) Solve the following system of equations by using the addition method: 5x y 7 0.5x y ) Solve the following system of equations by using the addition method: 5x 3y 3 x 3y 9 3) Solve the following system of equations by using substitution method: y 3x x 3y 7 4) Solve the following system of equations by using the substitution method: x y 3 y x 5 5) Solve the following system of equations by using the addition method: 3x 5y 4 7x 11y 6) Adult tickets for a play cost $5.50 and children tickets cost $.00. For one performance, 398 tickets were sold. Receipts for the performance were $ Find the number of children tickets sold. 7) Two investments earn an annual income of $86. One investment earns an annual simple interest rate of 5%, and the other investment earns an annual simple interest rate of 6%. The total

3 amount invested is $1500. How much is invested in each account? 8) Two burgers and one order of fries contain 34 grams of fat. Two orders of fries and one burger contain 41 grams of fat. Find the number of grams of fat in each item. 9) Simplify: (3y 11y 13) (3y y 1) 30) Simplify: 4( t 7t 11) (3t 7t 5) 31) Simplify: 3( x 7x ) ( x 7x 13) 3) Simplify: 7 3 ( 3 z )( 5 z ) 33) Simplify: 4 5 ( x )(3 x )( 4 x ) 34) Simplify: 7 4 ( t )( 3 t )( 4 t ) 35) Simplify by performing the following operation: (t 5)(3t 5) 36) Simplify by performing the following operation: (3x 1)( x 3) 37) Simplify by performing the following operation: (5x 7)(x 3) 38) Simplify, write answer with positive exponents: 3 (4 x ) 39) Simplify, write answer with positive exponents: ( 3 x y ) 40) Simplify, write answer with positive exponents: 5 4 ( 4 x y ) 41) Simplify, write answer with positive exponents: x y 8 8x y 4) Simplify, write answer with positive exponents: x y t x y t 43) Simplify, write answer with positive exponents: x y t x y t 3

4 44) Simplify: 3 8y 5 4y 45) Write: 4 a) in decimal notation b) in scientific notation. c) d) 11 8 (7 10 )(8 10 ) in scientific notation after simplifying in scientific notation after simplifying ) Factor out the GCF from the polynomial ) Factor out the GCF: 6x y 9x y 5 7 8z 1z 48) Factor out the GCF: r s 7r s 35r s 49) Completely factor: x 8x ) Completely factor: x 7x ) Completely factor : 81 4x. 5) Completely factor: x 3x ) Completely factor : a ab b. 3 54) Completely factor: x 6x 4x. 55) Completely factor: x 3xy 4y. 56) Solve the equation: x 6x ) Solve the equation: z z ) Solve the equation: x 10x ) Indicate whether or not the following pieces of information are qualitative or quantitative variables. If they are quantitative, indicate if they are continuous or discrete. a.) Your zip code b.) A student ID c.) The distance from the sun to the earth d.) The number of minutes you spend watching television each day. e.) Your social security number. f.) The number of books on your bookshelf. g.) Your daily checking account balance. 4

5 60) The table below ranks the top companies with the best reputation in the world. Identify the variable and determine whether each variable is quantitative discrete, quantitative continuous, or qualitative. Rank Home 017 Score 1 Switzerland Rolex Denmark Lego United States The Walt Disney Company Japan Canon United States Google ) The following frequency table represents the number new HIV/AIDS cases in the US in 008 according to race/ethnicity. What percent of the new cases were Hispanic/Latino (round to the nearest tenth of a percent)? 6) This pie chart shows the results of a survey that was carried out to find out how students travel to school. a. What is the most common method of travel? b. What fraction of the students travel to school by car? c. If 6 students travel by car, how many people took part in the survey? 5

6 63) Twenty students answered a survey about their majors. Their responses are below Nursing English Radiation therapy Nursing Chemistry Nursing English Nursing Radiation therapy Undecided Chemistry Nursing Political science Undecided Nursing Political science Nursing Radiation therapy Nursing English a. Construct a frequency table b. Draw a bar graph c. How many students participated in this survey? d. What percent of students are nursing major? 64) The following tables show the employment in stem occupation in 000 and009 for females. Year 000 Year 009 Computer and math Engineering Physical life science Stem manager a. Calculate the relative frequencies for each year. b. Compare the relative frequencies in year 000 and 009. Is there any significant change in stem occupation for females? 65) Is the following dotplot of a unimodal or bimodal distribution? 6

7 66) The frequency distribution below shows the number of magazines sold at a local store Number of magazines frequency a. How many magazines sold at a local store? b. What is the class width? c. Identify the lower class limit d. Identify the upper class limit e. Draw a Histogram 67) The following set of data represent the test score for Mr. apple English class 60, 64, 68, 7, 7, 78, 79, 80, 8, 84, 87, 85, 95, 98, 99 Create a frequency and a relative frequency table to display the data. Let your first lower limit be 60 and the class width be 10 68) The stem and leaf plot below shows the age of a group a. How many people are 44 years old or older? b. What is the total number of people? c. How many people are at most 30 years old? 69) Describe the shape of the distribution. Is it symmetrical, skewed left, or skewed right? 7

8 70) Construct a dot plot for the data below: ) Use the set of data to answer the following questions a. Calculate the mean b. Calculate the median c. Calculate the range 7) Determine which measure of center would be the most appropriate for the following situations (mean or median): a. A storeowner kept a tally of the sizes of suits purchased in her store. Which measure of central tendency should the storeowner use to describe the average size suit sold? b. The science test grades are posted. The class did very well. All students taking the test scored over 75. Unfortunately, 4 students were absent for the test and the computer listed their scores as 0 until the test is taken. 73) Multiple Choice: The number of sick days used by 100 employees at orange company was recorded. The mean number of the sick days is 13 days. Assume the distribution of the sick days is skewed to the right, which of the following value is the most likely the value of the median? a. 11 b. 15 c. 17 d ) The table below shows the waiting time for customers ( in minutes) for two different banks Bank A 5, 8, 8, 4, 9 Bank B 4, 4, 5, 6, 7 a. Find the range for each bank b. Compute the standard deviation for each bank c. Which bank has more consistent waiting time for customers? 8

9 75) The prices paid for a particular model of a new car has a mean of $18000 and the standard deviation is $400. A sample of 4 prices are listed Which price is two standard deviation of the mean? 76) A set of data items has a mean of 60 and the standard deviation of 10. Use the Empirical Rules to answer the following questions. a. What percent of scores are between 40 and 80? b. What percent of scores are greater than 70? c. What percent of scores are less than 30? d. What percent of scores are less than 70? 77) Upload speeds for a particular Internet provider are known to be unimodal and symmetric. The mean upload speed is 500 KBps with a standard deviation of 60 KBps. Use the Empirical Rule to answer the following questions. a. What percent of speeds were between 30 KBps and 680 KBps? b. 68% of speeds are between and. c. What percent of speeds are greater than 560 KBps? a. What percent of speeds are between 380 KBps and 440 KBps? 78) The distribution of time children spend watching television is unimodal and symmetric with respect to the mean. a.) If the middle 95% of the scores fall between 180 and 300 minutes, what is the standard deviation of the distribution? b.) What is the mean? c.) Using the Empirical Rule, how many minutes of television do the lower 50% of children watch each day? d.) Using the empirical rule, how many minutes of television do the upper 16% watch each day? 79) Find the z-score for the value 8, when the mean is 91 and the standard deviation is 9. 80) Heights of men have a mean of 173 cm and a standard deviation of 7 cm. heights of women have a mean of 16 cm and a standard deviation of 5 cm. Dwayne Jonson s height is 196 cm and Julia Robert s height is 176 cm. a. Find the z-score for each height b. Relative to the population of the same gender, who is taller and why? 81) A married couple is employed by the same company. The husband works in a department for which the mean hourly rate is $1.80 and the standard deviation is $1.0. His wife is employed in a department where the mean rate is $13.50 and standard deviation is $

10 a. Relative to their departments, which is better paid if the husband earns $14.60 and the wife earns $15.75? b. What would the wife need to earn to match her husband s z-score? 8) The test scores of 15 employees enrolled in a CPR training course are listed a. Find the five number summary b. Find the interquartile range c. Find the fences and examine the data for outliers 83) The following data represent the number of pop-up advertisements received by 10 families during the past month a. Find the mean. b. Find the median c. Find the 5-number summary. d. Draw a box-pot. e. Are there any outliers? 84) The following numbers represent the numbers from a five-number summary for the number of child abuse cases reported per county during a one-week period. Unfortunately, the numbers have been shuffled and are no longer in the right order. 14, 17.5, 8, 1.5, 1 a. Can you still determine which number is the first quartile, Q1? Explain your answer. b. The top twenty-five percent of reports are above what number? c. What percent of reports are between 1.5 and 14? 10

11 85) The following box-plots describe the high temperatures of the day (as measured at the weather station at BWI airport) for summers of a. Which month does not have any outlier temperatures? b. Which month typically has higher temperatures? c. Which month generally has the lowest high temperatures? d. True or False: The third quartile for June is smaller than the first quartile in July. 86) The boxplot below compares the annual income of three professions. a. What is the shape of distribution of the Musicians annual income? b. How much greater is the median of Nuclear Engineers than the median of Musicians? c. The bottom 5% of the Musician is below what value? d. Which quartile in the distribution of Police Officers annual income has the largest spread? e. What data has a larger variation, Explain? 11

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