Review for Exam 3. Please show all work neatly. Remember your UNITS! 1) These graphs are for three plants whose heights are measured in inches.

Transcription

1 Math 083 Review for Exam 3 Name Please show all work neatly. Remember your UNITS! 1) 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? 2) 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) 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?

2 3) Suppose the cost of an international call has an initial connection fee of $10, plus $.29 per minute. a) Choose two letters for the variables and describe them in words. b) If you only have $20 to spend, how many minutes can you talk? Write and solve an equation. c) Give your answer in a sentence. 4) 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 may 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.

3 5) 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. 6) The graph at the right shows the number of women in the U.S. House of Representatives beginning in a) Identify the meaning of the two variables: Y represents N represents b) What does the point (8, 24) represent? c) Using the equation for the Least Squares line, approximately how many women were in the House in 1995? (graph based upon data from Pew Research) d) Using the equation, in what year would you estimate there to have been 30 women in the House? e) What is the slope of the Least Squares line? f) Interpret this slope in context.

4 7) Which of the following represent linear relationships? a) x y b) x y c) x y ) On her 4 th birthday Charlotte decided she wanted to let her hair grow out. Four months later her hair was 25 cm long. On her 5 th birthday, her hair was 35 cm long. We define two variables: x is the number of months that have passed after her 4 th birthday and y is the length of her hair in centimeters. a) Give the coordinates of the two points described above. b) Assuming the growth is linear, determine the slope and interpret its meaning. c) Using y = mx + b, the slope, and one point, find the y-intercept and interpret its meaning. d) Assuming the growth remains linear and she does not cut her hair, how long will Charlotte s hair be on her 6 th birthday? 9) A jet has a fuel tank containing 40,000 gallons of jet fuel when it takes off on an international flight at midnight. The plane consumes 3000 gallons of fuel per hour. a) Identify two variables to represent this situation by choosing two letters and describing what each represents. Be sure to include units. b) Write a linear equation using these two variables. c) Use your equation to determine the number of hours into the flight when the jet s fuel tank contains 4,000 gallons of jet fuel.

5 10) Mountain climbers use a general rule of thumb which estimates that the temperature will drop 3.5 degrees Fahrenheit for every 1000 ft of elevation. The temperature is 73 o F at an elevation of 4000 feet, but we will record the elevation in thousands of feet. Thus, we will use 4 to represent 4000 feet. a) Identify two variables to represent this situation. Choose two letters and describe what each represents. b) Write a linear equation using these two variables. c) Use your equation to determine the temperature at 10,000 feet. d) Use your equation to determine at what elevation (to the nearest foot) the temperature will be freezing (32 o F). e) Convert your answer in part (d) to miles, rounded to hundredths, using a conversion factor. Recall that 5280 feet = 1 mile. 11) 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. Currently an ounce of 24-karat gold costs $1179 per ounce. How much would you expect an ounce of 14-karat gold to cost? Use a proportion to solve this. (Assume it is mixed with copper and its cost is negligible.) 12) Using the information in problem 11, how much pure gold (in grams) would be in an 18-karat gold ring that weighs 8 grams? Use a proportion.

6 For each of these, let f = the frequencies heard, and let h = hours studying (a) Write two separate inequalities, and (b) write a compound inequality. 13) 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. 14) Cats hear frequencies between 55 and 77,000 hertz. What frequencies do cats OR dogs hear? 15) 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? From ALEKS: 16) Owners of a recreational area are filling a small pond with water. Let x represent the number of minutes you are adding water and let y represent the total number of liters of water in the pond. y = 22x Give the initial amount of water in the pond and the amount of water after filling the pond for 10 minutes. 17) If y = -5x + 20, identify the slope and coordinates of the y-intercept. Graph each of these: 18) Graph: y = 3x 19) Graph: y = 1 2 x + 5

7 20) Graph: y = -2x ) Graph: y = -2 3 x ) Graph: y = 4 23) Find the slope of a line that passes through the points (1, 2) and (3, 5). Then find the equation of the line in slope-intercept form. 24) Find the slope of a line that passes through the points (-6,5) and (-3,1). Then find the equation of the line in slope-intercept form. 25) Find the equation of the line in slope-intercept form. 26) Find the equation of the line in slope-intercept form.

8 Applications: 27) The table shows the relationship (Life Expectancy) between the number of years a person might be expected to live and the year he or she was born. Birth Year (x1) Life Expectancy (y1) (40) (50) (60) (70) (80) (85) (90) (95) (98) a) Use Desmos.com to plot the values in the table. (Use 40 for 1940, 50 for 1950, and so on). Describe the relationship between birth year and life expectancy. b) We wish to find the line of best fit for the data in the table, use the Desmos.com y1~mx1+b command to find m and b. Write the equation of the line of best fit. c) Use the equation for the line of best fit to predict the life expectancy of someone born in Show your work. How does your answer compare to the actual life expectancy of someone born in 2016 (You will need to look this value up online to make the comparison), was the predicted value an overestimate or underestimate? d) In what year will we have a life expectancy of 100 years? 28) Write a scenario that is described (modeled) by the linear equation y = -10x ) Write a scenario that is described (modeled) by the linear equation y = 0.50x + 3.