SJAM MPM 1D Unit 5 Day 13

Transcription

1 Homework 1. Identify the dependent variable. a) The distance a person walks depends on the time they walk. b) The recipe for 1 muffins requires cups of flour. c) Houses need 1 fire alarm per floor.. Identify the independent variable. a) Photocopying costs drop 1 cent for every page over 50 pages. b) A seamstress needs to know how much fabric is needed for 10 outfits. It takes meters of fabric to make 1 outfit. c) A manager needs to know how many cartons are needed to package juice. Each carton holds 4 cans of juice.. True or False? The dependent variable is labelled on the horizontal axis and the independent variable is labelled on the vertical axis. 4. By inspection of the difference table, determine whether each relation is linear or non-linear. a) b) c) x y d) e) f) x y

2 5. The table shows the height above the ground for an object dropped from the Skylon tower in Niagara Falls, Ontario. Without graphing, determine whether this relation is linear or non-linear. State reasons. Time (s) Height (m) At top speed, caribou can run at 14 m/s. a) Copy and complete the table by determining the distances covered over time by the caribou running at top speed. b) Without graphing, determine whether this relation is linear or nonlinear. State reasons. Time Distance (s) (m) The first figure consists of one pentagon with equal sides and a perimeter of 5 units. The second figure consists of two pentagons and has a perimeter of 8 units. a) Complete a table of values showing the number of pentagons and the perimeter for each of the first five figures in the pattern. b) Without graphing, determine whether this relation is linear or non-linear. State reasons. 8. Vivian sells clothing and shoes in a store. She earns $400/week plus a commission of 5% of her sales. a) Write an equation for this situation, including appropriate let statements. b) Complete a table of values for sales of $0 to $5000 in multiples of $1000 c) Graph the relation. d) Using the equation, calculate Vivian s earning in one week when her sales total $4600.

3 9. To place a picture advertisement on a website, there is a fixed cost of $150 and a charge of $80 for each day that the ad is run. a) Write an equation for this situation, including appropriate let statements. b) Complete a table of values for 0 to 7 days c) Graph the relation. d) If you have an advertising budget of $5000, calculate how many days the ad can run. e) Describe how the graph would change if the fixed cost increased to $00. f) Describe how the graph would change if the charge per day increased to $ Maia earns $14/h as a lifeguard at a wave pool. a) Write an equation for this situation, including appropriate let statements. b) Graph this relation. c) Does the graph pass through the origin? Explain. d) Calculate how many hours Maia must work to earn $15. Verify your answer using the graph. 11. A large pizza with one topping costs $1.50. With two toppings, the cost is $ With three toppings, the cost is $ a) Create a table of values for the cost of the pizza for 1 to 4 toppings. b) Graph this relation. c) Determine the cost of the pizza with no toppings. d) Write an equation for this situation including appropriate let statements. e) Determine the cost of a 5 topping pizza. 1. A bacteria culture grows in a laboratory dish. The table shows the number of bacteria in the dish at various time intervals. a) Is this relation linear or non-linear? b) Graph the data. c) Determine how many bacteria would be in the dish after 90 minutes. d) Determine when the population will be bacteria. Time Number of (h) Bacteria

4 1. Calculate the slope of the line and then determine the equation of the line that passes through each set of points. a) (, 5) and (, 8) b) (-1, -) and (, 10) c) (-1, 5) and (4, -5) 14. For each relationship, construct a table of values and draw the graph. Use -, -1, 0, 1, and for the x-coordinates. 1 a) y x 6 b) y 4x c) y x Identify the slope and the y-intercept for each line. a) y 5x b) y 1x 7 c) y 4x 16. Graph each relation using the slope and y-intercept. a) y x 1 b) y x 5 c) y x For each situation, write an equation of the line in y mx b form. a) The slope is 8 and the y-intercept is. b) The slope is and the point (-, 1) is on the line. 5 c) The slope is and the point (-6, 5) is on the line. d) The x- and y-intercepts are and 4 respectively. 18. A car is expected to decrease in value according to the equation y 100x 40000, where y is the value of the car in dollars after ears. a) State the slope and interpret its meaning. b) State the y-intercept and interpret its meaning.

5 19. Mohammed has a part-time job and is paid according to the equation y 1.75x, where y is his earnings per item produced and x is the number of items. a) State the slope and interpret its meaning. b) State the y-intercept and interpret its meaning. c) How many items has Mohammed produced if his pay is $101.50? 0. Attendance at a movie theatre is recorded for one week starting on Monday. The daily attendance is recorded in the table. a) Draw a scatter plot. b) Describe the relationship. c) Draw a line of best fit. d) Does the data have positive, negative or no correlation. Showing Attendance For each of the scatter plots shown: a) Describe the correlation for each of the scatter plot. b) State a possible correlation value. c) State your confidence in making accurate predictions. i) ii) iii) iv). Arrange the following are correlation coefficients in order from most confidence to least confidence in relating two variables. -0.9, 0.86, -0.94, 0.1, 0.9

6 . The table shows the data collected for 15 students. The data shows how long the students studied for their final exam and their exam mark. a) Draw a scatter plot for the data. b) Describe the correlation. c) Predict a correlation value. d) Draw a line of best fit. e) Calculate the slope of the line of best fit. f) Determine the equation of the line of best fit. g) Predict the score of a student that studied for 5.5 hours. h) Enter the data on a Google sheet and compare your equation with the regression equation. Study Time Exam Mark (hours) (%)

7 Answers: 1. a) distance walked b) number of muffins made c) number of fire alarms. a) number of pages photocopied b) number of outfits made c) number of cans of juice. False. The independent axis is the horizontal axis, the dependent is the vertical axis. 4. a) linear b) non-linear c) linear d) non-linear e) linear f) non-linear 5. Non-linear. The first differences are not constant. 6. a) b) Linear. The first differences are constant. Time Distance (s) (m) a) b) Linear. The first differences are constant. Number of Perimeter pentagons a) Let P be her pay ($); Let s be her sales; P = 0.05x b) c) $60 Sales Pay ($) ($)

8 9. a) Let C be the cost for the ad ($); Let d be the number of days the ad is run C = 80d b) Days Cost ($) a) 60 days b) the graph would intersect the cost axis at a higher value c) the slope of the line would be steeper 10. a) Let P be the total pay ($); Let h be the number of hours worked; P = 14 h c) The graph passes through the origin because if she doesn t work, she doesn t get paid. d).5 hours 11. a) Toppings Cost ($) 0 1 c) $1 d) Let n be the number of toppings; Let C be the cost ($); C = n e) $ a) non-linear c) 0 d) just over 7 hours 1. a) m, y x 1 b) m 4, y 4x c) m, y x 7

9 14. a) b) c) x y x Y a) m = -5, b = b) m = 1, b = -7 c) m = 4, b = a) m =, b = -1 b) m = -, b = 5 c) m, b = a) y 8x b) y x c) y x 10 d) y x a) -$100/year, the amount the value of the car decreases per year b) $40 000, the initial value of the car 19. a) $1.75/item, the amount paid per item b) $0, no money is paid if no items are produced c) b) as the number of showings increases, the attendance increases d) positive correlation 1. i) weak positive correlation, r = 0.7, moderate confidence ii) no correlation, r = 0, no confidence iii) strong negative correlation, r = -0.9, high confidence iv) strong positive correlation, r = 0.9, high confidence , 0.9, 0.86, -0.9, 0.1. a) b) weak positive correlation c) r = 0.8 e) m =.5 %/hour f) y.5x 60 g) 79%