Selected Answers for Core Connections Integrated I


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1 Selected Answers for Core Connections Integrated I
2 Lesson a: = 2 6 and then = 5. b: Yes, reverse the order of the machines ( = 5 and then = 2 6 ) and use an input of = a: 54 b: c: 2 d: a: b: It grows b adding two tiles each time. Figure 4 Figure 5 c: 1; The top and right tiles are removed, since the pattern is to add two tiles to epand each figure a: 59 b: 17 c: 72 d: 6 e: 24 f: 25 g: 25 h: 25 i: a: = 1 b: = 3 c: = 9 Lesson (Da 1) a: Figure 4 b: 42 tiles. Add 4 tiles to get the net figure a: = 0 b: all real numbers c: = 14 d: no solution a: 5 18 b: c: 3 5 d: a: $18 b: Yes, it is proportional because 0 gallons cost $0. c: 8.4 gallons d: Tpical response: The line would get steeper a: 17 b: 8 c: 8 d: Core Connections Integrated I
3 Lesson (Da 2) a: 5 b: 19 c: a: The negative number indicates the elevation is below sea level. b: The elevation decreases, that is, becomes more negative. c: 2700 m; 675 m; 0 m d: See graph at right. e: Yes, the table and resulting graph go through (0, 0) and doubling (or tripling) the time doubles (or triples) the elevation. This is a decreasing proportional relationship. elevation (m) time (min) a: = 3 b: = 5 c: = a: 84 and no real solution. b: He cannot get an output of 0 with = He can get an output of 0 b putting a 4 in = 2. Lesson a: m = 5 b: a = 4π a: 2 b: 30 c: 13 d: a: 4 b: 5 c: a: 100, obtuse b: 170, obtuse c: 50, acute a: b: The graph is a curve, going up that is as increases, increases. The points are not connected, there is no intercept or intercept and negative values of either variable are not possible. c: Possible answers: ma = 10 feet (the highest she can jump), min = 0 feet Selected Answers 3
4 Lesson a: 8 b: 10 c: 2 d: no real solution a: 2 b: 8 c: 2 t no a: 7 10 b: c: d: a: a = 123º, b = 123º, c = 57º b: all = 98º c: g = h = 75º Lesson a: Not a function because more than one value is assigned for between 1 and inclusive b: Appears to be a function c: Not a function because there are two different values for = 7 d: function a: intercepts ( 1, 0) and (1, 0), intercepts (0, 1) and (0, 4) b: intercept (19, 0), intercept (0, 3) c: intercepts ( 2, 0) and (4, 0), intercept (0, 10) d: intercepts ( 1, 0) and (1, 0), intercept (0, 1) a: 2 tiles b: 19 c: Figure a: = 7 b: = 1 c: = 9 d: = one point and two points of intersection are possible 4 Core Connections Integrated I
5 Lesson a: es b: 6 6 c: a: 3 b: 12 c: a: 1 b: c: 0 d: a: Yes, it is correct because the two angles make up a 90 angle. b: = 33, so one angle is = 23 while the other is 2(33) + 1 = 67. c: = a: 9465 people per square mile b: 5.4 billion people Lesson a: h 2 b: 7 c: 9k 10 d: n 8 e: 8 3 f: a: Hale is correct. You cannot add unlike terms. b: Hale is incorrect. The bases differ a: Not in scientific notation because 62.5 should be b: Not in scientific notation because 1000 should be 10 3 and it uses a instead of an c: Not in scientific notation because 0.39 should be a: 12 b: 18 c: a: = 2 b: = c: = 0 d: no solution Selected Answers 5
6 Lesson a: 1 4 b: 1 c: = 1 25 d: a  c: (a) and (b) are functions because each onl has one output for each input. d: a: D: all real numbers, R: 1 3; b: D: all real numbers, R: 0 ; c: D: 2, R: all real numbers a: b: The unshaded triangle is half the area of the rectangle (0.5(8)(17) = 68 sq. in.), so the shaded area is the other half. Lesson = b 3 a a: 2 b: 4 c: 5, 2, 0, 2, 4 d: 2 e: a: 60 b: 127 c: See solutions on the diagram at right Core Connections Integrated I
7 Lesson Δ Δ = The equation in part (b) has no solution. Possible reason: There are the same number of terms on each side of the equation, so if ou tr to solve, ou end up with an equation such as 11 = 4, which is impossible a: 10 b: 4 c: undefined d: No solution; ou cannot divide b a: b: c: d: Lesson a: Line a: = 2 2, Line b: = b: It would lie between lines a and b, because its intercept is at (0, 1). c: It would slant downward but would have the same intercept as the line from part (b) See graph at right. Approimatel 79% a: b: c: a: 15 b: 64 p 6 q 3 c: 3m Graphs (a) and (b) have a domain of all real numbers, while graphs (a) and (c) have a range of all real numbers. Graphs (a) and (b) are functions. Final % AP Score Selected Answers 7
8 Lesson a: m = 5 3, b = (0, 4) b: m = 4 7, b = (0, 3) c: m = 0, b = (0, 5) a: m = 2 b: m = 0.5 c: undefined d: m = a: correct b: c: d: correct a: 4 b: 16 c: = d: It would get steeper a: While walking double (or triple) the distance, the would encounter double (or triple) the number of dogs. If the walked zero blocks, the would encounter zero dogs. The dogs in the area are evenl spread out along the blocks. b: 17 dogs 12 blocks = dogs 26 blocks ; so 37 dogs would be reasonable. c: 1.42 dogs per block Lesson A ver strong positive nonlinear association with no apparent outliers See graph at right. The number of people must be whole numbers, and Mikko probabl did not keep track of parts of burgers, so the points should not be connected; that is, there is no possible data between the points. If a line is drawn to model the trend, it should be straight rather than go through all the points. # of burgers eaten a: m = 1 2 b: (0, 4) c: See graph below. # of people at the BBQ a: 15 b: 4 c: 3 d: m because the denominator cannot be 0. 8 Core Connections Integrated I
9 Lesson a: The dependent variable is (distance in meters) and the independent variable is (time in seconds). b: See graph at right. Mark won the race, finishing in 5 seconds. c: Barbara: = , Mark: = 4 d: 5 meters ever 2 seconds, or 5 2 meters per second. Distance (m) Mark Carlos Barbara e: 2 seconds after the start of the race, when each is 6 meters from the starting line. Time (sec) b, c, d, f a: 43 b: 25.5 c: = a: The slope represents the change in height of a candle per minute, m = 0 cm per minute b: The slope represents the gallons per month of water being removed from a storage tank, m = 900 gallons per month a: 9 b: 1 64 or c: 10 9 d: $50 per week, A = 50w +100, A = (50)(52) +100 = a: = 2 +1 b: : (0.5, 0), : (0, 1) Selected Answers 9
10 Lesson a: (4, 0) and (0, 2) b: (8, 0) and (0, 4) a: = 12 b: w = 0 c: = 8 d: no solution a: It is the slope of the line of best fit drawn on the graph. Its units are mpg/1000 pounds. b: It is the intercept of the line of best fit. Its units are mpg. c: Moderatel strong negative linear association with no apparent outliers. d: About 25 mpg a: G = 5, Figure 0 = 3 b: G = 2, intercept = 3 c: G = 3, intercept = 14 d: G = 5, intercept = 3 e: a a: No. On Da 0 the height is not 0. If the number of das is doubled (or tripled), the height is not doubled (or tripled). b: c: Das () Height cm () cm 2 das or 1.5 cm/da d: = Core Connections Integrated I
11 Lesson miles 1 hour 1 gallon 25 miles 1 hour 60 minutes 45 minutes = 1.95 gallons. Considering precision of measurement, the car uses about 2 gallons of gas a: 3, (0, 5) b: 5 4, (0, 0) c: 0, (0, 3) d: 4, (0, 7) The sum of the first four planets distances = miles, which is less than the distance to Jupiter a: 1 b: 1 2 c: 3 2 d: The line travels downward from left to right, so m = f () = Lesson a: = b: Answers var, but solutions should lie on = Possible points: (0, 0.5), (1, 2), (10, 15.5) $ per second There is no association between number of pets and age Answers var. Tpical responses: 3 5, 3 5, and ( 1 ) a: 4 b: 3 c: 1 d: 2 Selected Answers 11
12 Lesson = a: 8 b: 1 c: 2 d: 17 e: 45 f: feet/second a: See graph at right. u = p where p is the price in dollars and u is the number of unpopped kernels. The slope represents the change in price for each unpopped kernel. The intercept represents the number of unpopped kernels in a free (unpopped) bag. b: 21 kernels See graph at right. (c) # Unpopped Price ($) (a) (b) Lesson = m = He should thaw out 3 pounds of hamburger a: 6 b: 2 c: a: d: undefined e: = pounds 2 months or 2.5 pounds/month b: = , where = months and = pounds 12 Core Connections Integrated I
13 Lesson The flag would need to be a rectangle. The height of the clinder would match the height of the rectangle along the pole, and the clinder s radius would match the width of the rectangle See solution at right. f() = = 67, = 9, so 5(9) 2 = 43 miles f() = a: b: c: d: a: See graph at right. = where is the test score and is the number of tired behaviors observed. b: = Test Score Number of Tired Behaviors Selected Answers 13
14 Lesson a: Reflection b: Translation, or two reflections over parallel lines c: Rotation, or rotation and translation d: Rotation, or rotation and translation e: Reflection f: Reflection and translation, or rotation and translation, or reflection, rotation, and translation a: m = 3 b: (0, 2) c: = a: = 8º, right angle is 90 b: = 20º, straight angle is a: domain: all real numbers, range: 1 b: 3, range: 2 c: domain: all real numbers, range: 0 d: domain: all real numbers, range: a: b: c: 17 d: a: 1 5z2 b: 72 2 c: 1 216g 9 14 Core Connections Integrated I
15 Lesson The slopes are 1 2 and 2 3. Since the slopes are not opposite reciprocals, the lines must not be perpendicular a: b: = 78, so = 12 and the rectangle is 15 cm b 24 cm. c: (2 12)(12 + 3) = = = 800 ; The fling fo bat is about 800 times heavier than the bumblebee bat a: b: c: d: a: It looks the same as the original. c: Solution should be an value of 45k where k is an integer. d: circle Lesson A (4, 3), B (6, 1), C ( 2, 5), D ( 4, 1) Rigid transformations preserve length and ΔGHJ and ΔABC do not have the same side lengths. The do however appear to have the same angle measures = 52, so = 2. Side lengths are 19, 10, and a: = b: = c: = a: 1 b: 5 c: d: undefined a: = 6 b: = 1 c: = 8 d: = 16 Selected Answers 15
16 Lesson a: (9, 3); 10 square units b: (3, 3); 20 square units c: ( 2, 7) d: ( 52, 1483); 208,680 sq units (a) and (b) are perpendicular, while (b) and (c) are parallel a: Multipl b 6. b: = 15 c: = a: b: minutes a: The orientation of the heagon does not change. b: The orientation of the heagon does not change. c: There are 6 lines of smmetr, through opposite vertices and through the midpoints of opposite sides. Lesson (3, 1), (7, 1) a: One possibilit: 4(5 + 2) = 48 b: = 2 c: 144 square units a: = b: The resulting line coincides with the original line; = c: The image is parallel; = d: The are parallel, because the all have a slope of 4 3. e: = = Moderate negative linear association with no outliers. The data appear to be in two clusters, probabl indicating two classes of vehicles a: 12 b: 59 c: 7 d: 9 e: 13 f: 5 16 Core Connections Integrated I
17 Lesson a: = 6 b: c: d: See graph at right f () = Problem 378 does, possible response: the b in its equation is 3 versus 1 in problem a: ( 5, 1) b: (3, 5) c: (11, 0); The rectangle is moved parallel to the given line. d: 12 square units a: Calculate the output for the input that is 4 less than c. b: Calculate the output for the input that is half of b. c: 12 more than the output when the input is d. Lesson ( + 8)( + 3) = a: = 4.75 b: = 94 c: 1.14 d: a = a: 15 3 b: c: 5 d: = 915; = 17 weeks a: Using side AB as the base, Area Δ = 1 2 bh = 1 2 (5)(6) = 15 square units b: A ( 8, 4), B ( 8, 1), and C ( 2, 0) c: B ( 4, 1) d: A ( 4, 8) a It should be a triangle with a horizontal base of length 4 and a vertical base of length 3. b: 4 3 c: An equation of the form = b. Selected Answers 17
18 Lesson a: (12 +1)( 5) = b: (2m 2 4m 1)(3m + 5) = 6m 3 2m 2 23m 5 c: (2 + 5)( + 6) = d: (3 5)(2 + ) = a: b: c: a: (3, 4) b: (10, 9) a: 20 square units b: 2600 square units; subtract the  and coordinates to determine the length of the two sides Yes, he can. a: = 2 b: Divide both sides b a: d: 8 3 = b: c: 7 5 = e: f: Core Connections Integrated I
19 Lesson a: 2 = 4 b: For each, = 6. c: + 3 = 8, = Part (c) is correct; = The all are equivalent to a: b: c: d: a: b: A l B P c: d: Q C D m a: = ; inches/hr and inches b: 12.5 inches Selected Answers 19
20 Lesson a: = 4 b: = 21 c: = 16 3 d: = a: = + 2; grams/inch and inches b: 28 grams a: A ( 6, 3), B ( 2, 1), and C ( 5, 7) b: B (8,13) c: A (3, 6) a: A (3, 6) b: 2d 3 = 19; d = 11 candies a: = 3 b: = 5 c: = 2 d: = 3 Lesson a: = 2 b: = 1.5 c: = trees a: 1 2 bh = 1 2 = (7)(5) = 17.5 square units b: ( 6, 5), (1, 5), and ( 1, 0) Reasoning will var. a = 108, b = 108, c = 52, d = a: b: A A l c: d: l C D Q m a: = 5 b: = 2 c: = 0 d: = Core Connections Integrated I
21 Lesson a: Strong positive linear association with one apparent outlier at 2.3 cm. b: She reversed the coordinates of (4.5, 2.3) when she graphed the data. c: An increase of 1 cm length is epected to increase the weight b 0.25 g. d: (11.5) 4.3 g e: We predict that when the pencil is so short that there is no paint left, the pencil is epected to weigh 1.4 g a: 6 4 b: c: 2 4 d: ards apart 47. The better route to save time is the 122 miles at a slower pace of 65 miles per hour (although ou onl save approimatel three minutes) minutes on the freewa or minutes if taking the scenic route a: = b: = f() = input () output (f()) Lesson The predicted price for a 2800 sq ft home in Smallville is $264,800 while in Fancville it is $804,400. The selling price is much closer to what was predicted in Smallville, so she should predict that the home is in Smallville Cadel is correct because he followed the eponent rules. Jorge is incorrect; the problem onl contains multiplication, so there are not two terms and the Distributive Propert cannot be used. Lauren did not follow the eponent rules a: 14 b: 16 c: If is the age of the van, then + ( + 17) = 41 or if is the age of the truck, then + ( 17) = a: It is a reflection across both the  and aes or a rotation of 180 degrees. (The reflection is not across the line =.) The side lengths and angle measures have been preserved. (Area and perimeter have also been preserved.) b: No, the new triangle is not the result of rigid transformations, it has been stretched. The side lengths are not preserved a: b: Selected Answers 21
22 Lesson a: The form is linear, the direction is negative, the strength is moderate, and there are no apparent outliers. b: = 5 1.6; where is the number of months taking the supplement and is the length of the cold in das; about 2.6 das c: = 0.7 das. The cold actuall lasted 0.7 das longer than was predicted b the linear model. d: The intercept of 5 means that we epect a person who has not taken an supplement to have a cold that lasts five das; more generall, the average cold is five das long a: = b: (12, 0) a: ( + 3+ ) = b: ( + 8)( + 3) = a: 2 b: 86 c: 3 d: 1 e: 8 f: a: = or 5.95 b: = a: The total volume of both drink sizes combined. b: The total number of drinks served that da. c: The total volume of drinks served that da. 22 Core Connections Integrated I
23 Lesson (Da 1) a: The slope means that for ever increase of one ounce in the patt size ou can epect to see a price increase of $0.74. The intercept would be the cost of the hamburger with no meat. The intercept of $0.23 seems low for the cost of the bun and other fiings, but is not entirel unreasonable. b: One would epect to pa (3) = $2.46 for a hamburger with a 3 oz patt while the cost of the given 3 oz patt is $3.20, so it has a residual of $3.20 $2.46 = $0.74. The 3 oz burger costs $0.74 more than predicted b the LSRL model. c: The LSRL model would show the epected cost of a 16 oz burger to be (16) = $ oz represents an etrapolation of the LSRL model; however, $14.70 is more than $2 overpriced m = 2 3, (3, 0), (0, 2); See graph at right a: b: H I Z N t G J M F E L c: 10 K A B D C (a), (b), and (d) a: 1 8 b: b4 c: d: a: = 1 3 b: = 35 8 Selected Answers 23
24 Lesson (Da 2) a: Answers will var. Students ma sa negative because intown prices can be higher than prices in the outskirts, or outoftown families ma grow some of their food. Students ma sa positive because transportation costs make outoftown prices higher, or outoftown families eat at restaurants less. The association is probabl prett weak. b: The intercept is halfwa between and 7.67, so the equation is g = d. c: For each additional mile from church, we epect families to pa $140 less for groceries this ear. d: $ a: = 7 b: = 1 c: = 9 d: = a: cm b: cm a: 15 2 b: 8 c: 6 2 d: All equations are equivalent and have the same solution: = = Core Connections Integrated I
25 Lesson (Da 1) a: = , where is the number of months take the supplement and is the number of das to cold will last b: = and = , based on a maimum residual of c: 0 to 1.4 das. The measurements had one decimal place. d: Between 4.6 and 6.2 das. The intercept is the number of das a cold will last for a person who takes no supplements. e: Students should predict that a negative number of das makes no sense here. Statistical models often cannot be etrapolated far beond the edges of the data. f: A negative residual is desirable because it means the actual cold was shorter than the model predicted a: = 12 7 b: = m/min for cockroach versus 30 m/min for centipede or 80 cm/s for cockroach versus 50 cm/s for centipede. The cockroach is faster = 2 + 6; 206 tiles a: 3 b: a: 4 7 b: 1 c: 2 = 1 2 d: 6 3 e: d: Selected Answers 25
26 Lesson (Da 2) a: See scatterplot at right. = Students need to round to four decimals, because if the round to fewer decimals, the LSRL gets too far awa from the actual points due to the lack of precision. b: See table at right; sum of the squares is in = a: = 2 b: = a: 127 b: 10 c: 1 32 or d: a: It is a parallelogram, because MN // PQ (both have a slope of 2 5 ) and NP // MQ (both have a slope of 3). b: (1, 7) = 11 4 Distance from wall (in) Residual (in) c: Possible response: Reflect M N P Q across the ais and then rotate it 180º Core Connections Integrated I
27 Lesson a: See graph at right. b: = where is the length of the paint (cm) and is the weight of the pencil (g). c: See graph below right. d: Yes, the residual plot appears randoml scattered with no apparent pattern. e: Predicted weight is (16.8) = 5.5 g, residual is = 0.5 g. The measurements had one decimal place. f: A positive residual means the pencil weighed more than was predicted b the LSRL model a: 1 60 b: c: 1 24 d: a: 3( 4) = b: (3 + 5)( 4) = a: m = 2 7, b = 2 b: m = 1 3, b = 6 c: m = 5, b = 1 d: m = 3, b = $36.88; $8.85/foot a: = 2 b: = 1 Selected Answers 27
28 Lesson a: A ver strong positive linear association with no outliers. See graph at right. b: See plot below right. Yes, the residual plot shows random scatter with no apparent pattern. c: r = 0.998; There is a ver strong positive linear association Hourl Wage ($) Eperience (ears) a: With each one degree of temperature increase, we predict an increase of 410 park visitors. b: The residuals are positive, so we epect the actual values to be greater than the predicted values, hence the predictions from the model ma be too low. c: The residual is about 17 thousand people; the LSRL predicts thousand people. actual = 7; the actual number of people in attendance was about 17,900. d: The predicted attendance is between 11,800 and 25,800 people. f: The residual plot shows a clear curve; the linear model is not appropriate. For temperatures in the 80s, the model predicts too low an attendance; for temperatures in the mid 90s, the model predicts too high an attendance. The range for predicted attendance in part (d) is ver large and therefore not useful a: 8 25 b: 6 c: d: a: D: 2 2, R: 3 2 ; b: D: = 2, R: all real numbers; c: D: 2, R: all real numbers a: Onl graph (a) a: 2 b: c: = 2 ($) Eperience (ears) = Core Connections Integrated I
29 Lesson a: = b: Yes. There is random scatter in the residual plot with no apparent pattern. c: r = and R 2 = 90.7%; 90.7% of the variabilit in the length of a cold can be eplained b a linear relationship with the amount of time taking the supplement. d: A residual plot with random scatter confirms the relationship is linear. It is negative with a slope of 1.581, so an increase in one month of supplements is epected to decrease the length of a cold b das. The association is strong: 90.7% of the variabilit in the length of a cold can be eplained b a linear relationship with the amount of time taking the supplement. There are no apparent outliers a: With a car readil available, these teens might simpl be driving more, and the etra time on the road is causing them to be in more crashes. b: Families that can afford the considerable epense of bottled water can also afford better nutrition and better healthcare a: incorrect, 100 b: correct c: incorrect, 8m 6 n = Answers var, but the answer should have the same number of terms on both sides of the equation, and the constant terms on each side should not be equal a: 1 b: 3 c: 2 Selected Answers 29
30 Lesson (Da 1) 56. a: Months Rabbits b: Months Rabbits a: Sample answers: (3, 0) and (3, 1); All points on this line have an coordinate of 3. = 3 b: = 1 c: = = 1; It will create a fraction with a denominator of zero, which is undefined pounds 4 ounces a: It is a reflection across the ais. A ( 1, 1), B (1, 1), C ( 4, 1) b: A (4, 5), B (2, 3), C (7, 3) a: Man nighttime jobs involve working in bars, casinos, or restaurants where smoking is prevalent. Night emploment is generall considered less desirable, so people who work at night ma have less mone and therefore less access to medical care. b: This might be connected to gender. Men as a group eat more meat and do not live as long as women. Also, if the meat is highl processed like hotdogs, it might be the additives that are harmful and not the meat itself. 30 Core Connections Integrated I
31 Lesson (Da 2) a: curved b: See table and graph at right. c: The graph is curved; the intercept is 1000; there is no intercept; the function is increasing from left to right; negative values and negative values are not possible. Time (das) Number of cells ,000 Number of Cells a: 5 2 = 25 b: 3 51 c: 1 d: Time (das) Jackie squared the binomials incorrectl. It should be: = , = 2 +1, 8 = 10, and = a: = b: = c: = See graph at right. a: See graph above right. A ( 2, 1), B ( 5, 0), C ( 5, 2), D ( 2, 6) b: See graph at right. A (1, 2) and C ( 2, 5) c: 13.5 square units Selected Answers 31
32 Lesson a: = 1 b: = a: = 4 3 b: Yes; ( 3, 4) is a solution to the equation from part (a) a: R 2 = 0.815; 81.5% of the variabilit in fuel efficienc can be eplained b a linear relationship with weight. b: The negative slope means there is a negative association. An increase of 1000 pounds in weight is epected to decrease the fuel efficienc b 8.4 miles per gallon a: = b: 30 ounces a: minutes; 24 2 = 12 minutes b: Speed (blocks per minute) Time to Get to Friend s House (minutes) c: The time decreases. d: No. The table and resulting graph do not go through (0, 0). If Meredith s speed is 0 blocks per minute, then it does not take 0 minutes to get to her friend s house. Furthermore, doubling (or tripling) the speed does not double (or triple) the time No; (12, 108) is not a solution to the equation Core Connections Integrated I
33 Lesson a: Answers var but should be close to b: Approimatel 228 cm. Since DeShawna measured to the nearest centimeter, a prediction rounded to the nearest centimeter is reasonable. c: 72 cm d: 166 meters e: 138 meters; 114 meters a: 10(0.555) = 5.55 feet b: 10(0.555)(0.555) 3.08 feet c: 10(0.555) feet f() = a: College admission rates and student aniet have a plausible negative association. However, admission rates could be plunging because the average number of universities a tpical student applies to has increased dramaticall with the widespread use of online college applications. It is more likel that student aniet and the ease of online applications is fueling lower universit admission rates. The total number of students attending college ma actuall be the same or even be increasing. b: For a small part of the population, those with celiac disease, gluten is a serious health problem. Those people aside, it is possible there is a link between gluten and obesit. Gluten is found in man grains. Grains are used to make man highl processed food products that are loaded with sugar and fats. Perhaps it is the sugar and fats in these foods causing obesit rather than the gluten a: = 34 b: = a: an isosceles triangle b: a rectangle Selected Answers 33
34 Lesson a: One possible answer is that their growth grows linearl. b: Answers var. Sample: The sequence of differences between terms turns out to be almost the same as the sequence itself. Or, add the two previous terms to get the net term a: Eponential, because the ratio of one rebound to the net is roughl constant ( 0.6). b: 475, 290, 175, 100, 60; Roughl geometric, because it has a multiplier (though students ma sa it is neither because the multiplier is not eact) pencils a: 3 b: = ounces bh = 1 2 (200)(270) = 27, 000 square units a: 500 liters b: liters a: 1.03 b: 0.8z c: = a: The output for the input that is 4 less than c. b: The output for the input that is half of b. c: 12 more than the output when the input is d a: 20 4 = 29 7; 3 hours b: 8 lil pads a: G + D + C + E + S or B + L + F b: either L G+D+C+E+S or L B+L+F c: either D+E G+D+C+E+S or D+E B+L+F 34 Core Connections Integrated I
35 Lesson a: Yes, the 90 th term or t(90) = 447. b: no c: Yes, the 152 nd term or t(152) = 447. d: no e: No, n = 64 is not in the domain of a sequence Justifications var a: 3, t(n) = 3n + 1 b: 5, t(n) = 5n 2 c: 5, t(n) = 5n + 29 d: 2.5, t(n) = 2.5n a: Descriptions var, but students ma sa the are multipling b 1.1 or growing b 10% each ear. b: $ a: Sample solution at right below. The intercept and slope could var the slope might even be negative but the coordinates and the position of the points relative to each other are precise feet b: The model made predictions that were closer to the actual values for taller swimmers. Swim time(s) Height (cm) Selected Answers 35
36 Lesson a: 3.5, 1, 5.5, 10 b: Evaluate the equation for n = 15. c: t(n +1) = t(n) ; t(1) = t(n) = 3n + 2 ; t(n +1) = t(n) + 3; t(1) = a: b: a: 144, 156, 168, 180 b: 264 stamps. c: t(n) = 12n d: n = 31.67; She will not be able to fill her book eactl, because 500 is not a multiple of 12 more than 120. The book will be filled after 32 months There is a weak, negative, linear association: as dietar fiber is increased, blood cholesterol drops % of the variabilit in blood cholesterol can be eplained b a linear association with dietar fiber a: 10, m = 18, m b: m = 40 months Lesson a: geometric, multipl b 12 b: arithmetic, add 5 c: other (quadratic) d: geometric, multipl b a: 3, 6, 12, 24, 48 b: 8, 3, 2, 7, 12 c: 2, 1 2, 2, 1 2, º = 2 + 9º; = 7º cm a: 8m 5 b: 2 3 c: 2 35 d: a: = 2 3 b: = 3 1 c: = d: Core Connections Integrated I
37 Lesson (Da 1) a: 1.03 b: 0.75 c: 0.87 d: a: #1 is arithmetic, #2 is neither, #3 is geometric b: #1 the generator is to add 3, #3 the generator is to multipl b = a: = 2 b: undo, then look inside; = a: Create a scatterplot; compute and draw the LSRL; verif linearit with a residual plot; describe form, direction (including the slope and intercept in contet), strength (including an interpretation of r and R 2 ), and possible outliers; draw upper and lower bounds to the model used for prediction. b: See graphs below. = The linear model is appropriate because the residual plot shows no apparent pattern. The slope is 1.60, meaning that an increase of 1µm in the length of the organelle is epected to decrease the diameter of the cell b 1.60 µm. The intercept of means that a cell with no organelle has a length of µm; this is possible even though it is an etrapolation. The correlation coefficient is r = and R 2 = 86.1%, so 86.1 percent of the variabilit in the diameter of the overall cell can be eplained b a linear relationship with the diameter of the organelle. There are no apparent outliers. The upper bound can be given b = , and the lower bound b = Diameter of Cell (µm) Length of Organelle (µm) Residuals (µm) Length of Organelle (µm) Technicall, Mathias can never leave, either because he will never reach the door or because he cannot avoid breaking the rules. The equation for this situation is = 100(0.5), where is the number of minutes that have passed and is the distance (meters) from the door. Selected Answers 37
38 Lesson (Da 2) minutes or 1 hour 52 minutes, miles per hour a: Sequence 1: 10, 14, 18, 22, add 4, t(n) = 4n 2; Sequence 2: 0, 12, 24, 36, subtract 12, t(n) = 12n + 36; Sequence 3: 9, 13, 17, 21, add 4, t(n) = 4n 3 b: Yes, Sequence 1: 18, 54, 162, 486, multipl b 3, t(n) = 2 3 (3)n ; Sequence 2: 6, 3, 1.5, 0.75, multipl b 1 2, t(n) = 48( 1 2 )n ; Sequence 3: 25, 125, 625, 3125, multipl b 5, t(n) = 1 5 (5)n c: Answers var, but the point is to have students create their own equation and write terms that correspond to it a: = 16 5 b: no solution c: = 2 d: = = a: 1 b: 2 c: undefined d: a: 7 2 = 49 sq cm b: 0.5(10)4 = 20 sq in c: 0.5(16 + 8)6 = 72 sq ft Lesson a: all numbers b: 1, 2, 3, 4, c: 0 d: 1, 2, 3, 4, a: No; the 5 th term is 160, and the 6 th term is 320. Justifications var. b: Yes, a: a 4 = a = 23 b: a 5 = a = 29 c: 5, 11, 17, 23, a: The total number of batters that Kasmir faced. b: The average number of strikeouts per inning pitched b Kasmir. c: The total number of innings plaed b the Coopersville Mad Hens. d: The fraction of the total innings plaed that were pitched b Kasmir. e: The average number of pitches per inning for Kasmir a: b: = 3 38 Core Connections Integrated I
39 Lesson a: = b: = c: r = C 2π 68. a: 6(13 21) = b: ( + 3)( 5) = c: 4( ) = d: (3 2)( + 4) = There is a moderatel strong negative association, meaning that the more a student watches TV, the lower his/her grade point average is predicted to be. 52% of the variabilit in GPAs can be eplained b a linear relationship with number of hours spent watching TV. However, we are careful not to impl a cause. Watching less TV will not necessaril cause a rise in GPA a: arithmetic b: t(n) = 4n + 3 c: No, n = Yes; both points makes the equation true If = the width, 2() + 2(3 1) = 30, width is 4 inches, length is 11 inches. Lesson a: = b: = a: a = 0 b: m = 2 c: = 10 d: t = The will be the same after 20 ears, when both are $ a: 43 b: a: ( 1, 9) (3, 5) b: Possible response: Reflect over the ais and then rotate clockwise (or counterclockwise) 180º around the origin. Selected Answers 39
40 Lesson a: In 7 weeks. b: George will score more with 1170 points, while Sall will have a: no solution b: = ( 1, 3) From an earlier lesson, association does not mean that one variable caused the other. One possible lurking variable is per capita wealth: wealthier nations ma tend to have more TVs and also better health care a: 17, 14, 11, ; a n = 20 3n b: 20, 10, 5, ; a n = 40( 1 2 )n a: = 3 b: = 1 Lesson a: The units of measurement, centimeters. Side #2 =, Side #3 = 2 1 b: + + (2 1) = 31 c: = 8, so Side #1 = Side #2 = 8 cm and Side #3 = = 15 cm ,600,000 miles per da; 66, miles per hour She combined terms from opposite sides of the equation. Instead, line 4 should read 2 = 14, so = 7 is the solution a: geometric b: 5 5 = 3125 c: a n = 5 n C AC 2 = = 58, AC = The length of AC is rounded up to 8 because the original measurements were whole numbers. 40 Core Connections Integrated I
41 Lesson a: a + c = 150 b: 14.95c v = m miles a: = +5 2 b: w = p 9 a c: m = (4n+10) 2 = 2n + 5 d: = b a: 0.85 b: 1500(0.85) 4 $783 c: a n = 1500(0.85) n ears a: 3, 1, 1, 3, 5 b: 3, 6, 12, 24, 48 Lesson a: ii b: 4 touchdowns and 9 field goals a: See answers in bold in table and line on graph. b: Yes; ( 3, 3) and ( 2, 1) both make this equation true a: geometric b: curved ( 3, 3) c: t(n) = 2 5 (5)n Kat is correct; the 6 1 should be substituted for because the are equal a: 1 8 b: b4 c: d: a: Calculate the output for the input that is 6 times w. b: Calculate the output for the input that is 2 less than h. c: 10 more than 4 times the output of f when the input is a. Selected Answers 41
42 Lesson From the graph, 3.7 and 6.3, when students look at the table of values the can justif that since f(3) = 5.5 and g(3) = 4.95 and then f(4) = 6.6 and g(4) = 6.85 that the two functions must have the same value between = 3 and = 4 and that value must be between 5.5 and a: h = 2c 3 b: 3h + 1.5c = 201 c: 28 corndogs were sold Yes; adding equal values to both sides of an equalit preserves the equalit a: = 2.2 b: = 6 c: = 10.5 d: = a n = t(n) = 32 ( 1 2 )n a: = b: = 2 5 Lesson a: (5, 3) b: (2, 6) a: You end up with 10 = 10. Some students ma conclude that it is all real numbers or infinite solutions. b: The two lines are the same. c: Since the equations represent the same line when graphed, an coordinate pair (, ) will solve both equations a: Let p represent the number of pizza slices and b represent the number of burritos sold. Then 2.50p + 3b = 358 and p = 2b a: a: b: 82 pizza slices were sold. b: 20(1.05) 5 = $25.52 c: t(n) = 20(1.05) n ; 20 represents the current (initial) cost and 1.05 represents the percent increase. 90 mi 1.5 h = 330 mi ; = 5.5 hours b: 90 = 1.5r, r = 60 mph, 330 = 60t, t = 5.5 hours c: es a: 8 25 b: 6 c: d: Core Connections Integrated I
43 Lesson a: (3, 1) b: (0, 4) c: (10, 2) d: ( 4, 5) The are both correct. The equations represent the same line, and so both coordinate pairs are solutions to both equations hours a n = t(n) = 4 3 n a: = 2 b: = a: b = m b: = b m c: t = I pr d: t = A p pr Lesson a: b: a: ( 5, 1) b: (3, 1) c: no solution a: not a function, D: 3 3 and R: 3 3 b: a function, D: 2 3, R: r 0; Answers will var for LSRL, but the average number of pairs appears to be about 3.8, which is an LSRL of = a: 3 18º = 74º; = 30.67º b: 3 9º = + 25º; = 17º; m 2 = 3(17º) 9º = 42º a: m = 12 b: = 24 c: = 16 5 Selected Answers 43
44 Lesson a: (0, 1 3 ) b: ( 6, 2) c: no solution d: (11, 5) n = p and n + p = 168; 56 nectarines are needed a: Yes, because these epressions are equal. b: 5(3) + = 32, = 2, = a n = t(n) = 6n = a: b: c: = 3 d: = 2 Lesson (Da 1) a: infinitel man solutions b: ( 1 3, 2 3) c: (1, 2) d: (8, 7) a: It is a line. It can be written in = m + b form. b: Answers will var. Possible solutions: (0, 2), (1, 5), (2, 8), c: = 3 + 2; Yes, because the points are the same a: p: = 2 + 8; q: = b: Yes, because ( 2, 4) is the point of intersection. c: The slopes indicate that the lines are perpendicular. d: ( 2, 4) a: 5, 10, 20, 40, 80 b: a n = 5 2 ( 2)n a: b: a: M ( 3, 3), J ( 1, 1), N ( 1, 6) b: M (3, 3), J (1, 1), N (1, 6) c: 5 square units 44 Core Connections Integrated I
45 Lesson (Da 2) n + d = 30 and 0.05n d = 2.60, so n = 8. There are 8 nickels C a: no solution b: = 5, = a: = 5 b: = 2 3 c: no solution d: = a: 0.85 b: 1500(0.85) 4 $783 c: a n = 1500(0.85) n ; 1500 represents the current (initial) cost represents a 15% decrease Let s = number of slices on an etralarge pizza; 4s + 3 = 51. An etralarge pizza has 12 slices. Lesson Answers var. One triangle ma be obtained from the other b reflection of UVW over line UV, followed b a translation of V to Z, and then a rotation about V so that the sides coincide. A possible congruence statement is ΔUVW ΔXZY Yes, the triangles are congruent. B the Pthagorean Theorem, the three side lengths are equivalent, and b the Triangle Angle Sum Theorem, the three angle measures are equivalent. The left triangle ma be mapped onto the right triangle with a translation and a rotation a: 5 2 or 2.5 b: = 17.5 mm, because = = a: It can be geometric, because if each term is multiplied b 1 2, the net term is generated. b: See graph at right. c: No, because the half of a positive number is still positive a: (4, 12) b: infinitel man solutions Selected Answers 45
46 Lesson (Da 1) Scale factor is = 9 ft, = 8 ft, z = 3.8 ft Answers var; a possible congruence statement is ΔHAN ΔJOE. Reflection across AN and translation of A to O (possibl followed b a rotation) maps ΔHAN to ΔJOE The lines are parallel, so the do not intersect. Therefore, there is no solution a: A ( 2, 7), B ( 5, 8), C ( 3, 1) b: A (2, 7), B (5, 8), C (3, 1) c: Reflection across the ais If Nina has n nickels, then 5n (2n) = 84, and n = 5 nickels a: = 0, 1, 2 and = 2, 0, 1 b: 1 1 and 1 2) c: 2 and 2 d: D: all real numbers and The are not congruent. Although b the Triangle Angle Sum Theorem all the corresponding angles are congruent, the 44cm sides are not corresponding sides No. AAA is not a congruence condition a: no solution b: (7, 2) c: ( 1, 2) d: (3, 1) a: 90 cm b: cm c: t(n) = 160(0.75) n See graph at right. t(n) d = 55t and (325 d) = 70t or 325 = 55t + 70t, where d = distance Esther traveled (miles) and t = time Esther traveled (hours). 2 hours 36 minutes n 46 Core Connections Integrated I
47 Lesson a: The are congruent b ASA or AAS. b: DF = 20 feet = 18 8, = 32 9 = a: no solution b: b = 3, c = a: b: c: d: a: On average student backpacks get 0.55 pounds lighter with each quarter of high school completed. b: About 44% of the variabilit in student backpack weight can be eplained b a linear relationship with the number of quarters of high school completed. c: The largest residual value is about 6.2 pounds and it belongs to the student who has completed 3 quarters of high school. d: (10) = 8.34 lbs e: A different model would be better because it looks like there is a curved pattern in the residual plot = ; = 10 Selected Answers 47
48 Lesson a: ΔADC; AAS ; Reflection across AC. b: not enough information c: ΔTZY; AAS or ASA ; Rotate 180º about point Y a: The 90 angle is reflected, so m XZY = 90º. Then m YZY = 180º. b: The must be congruent, because rigid transformations (such as reflection) preserve angles measures and side lengths. c: XY X Y, XZ XZ, YZ Y Z, Y Y, YXZ Y XZ, and YZX Y ZX a: a 1 = 108, a n+1 = a n + 12 b: a 1 = 2 5, a n+1 = 2a n c: t(n) = n d: t(n) = 585(0.2) n a: 15º b: = 12º; m D = 4(12º) + 2º = 50º c: It is equilateral a: (1, 1) b: ( 1, 3) D 48 Core Connections Integrated I
49 Lesson a: ΔCED; ASA b: ΔEFG; AAS c: Not necessaril, the congruent sides are not corresponding. d: Not necessaril, AAA is not a congruence condition a: ( 1, 7) b: ( 1 2, 2) a: See scatterplot at right. Best score is 45 minutes + 77 strokes = 122 points. b: There is a weak to moderate positive linear association between Diego s run time and the strokes taken for each match. There looks to be an outlier at 92 minutes. Strookes Time (minutes) c: See graph at below right. d: m 0.7; Ever minute of increase in time is predicted to increase the number of strokes b about 0.7. e: The variables are moderatel associated, but that does not mean that one variable causes the other. It does seem reasonable that training for conditioning could improve Diego s aim and confidence in his golf swing, however the potential eists that a better more accurate swing could also reduce the amount of running required on the course. It is not clear what causes what, or if there is a third, lurking, variable. Strookes Time (minutes) a: W = V LH b: = 2( 3) c: R = E I d: = d = (8 + 2)(t 1) and d = (8 2)(t), where d = onewa distance of trip (miles) and t = time to travel upstream (hours); 30 total miles. Selected Answers 49
50 Lesson a: The triangles are congruent b SSS. b: Not enough information is provided. c: Not enough information is provided. d: The triangles are congruent b AAS or ASA a: = 3 b: = (2, 4) a: 6 b: 3 c: These triangles are not congruent. Corresponding sides AT and GI are not congruent a: 120,000 = 16,000M + 14,500J b: $ , 000M + $ , 500J = $1, 070, 000 or $ M + $ J = $1,070, Core Connections Integrated I
51 Lesson Possible responses include: Right triangle: right angle, Pthagorean Theorem for side lengths; Equilateral Triangle: all sides and angles same measure; Rectangle: all right angles, opposite sides equal; Parallelogram: opposite sides parallel and equal, opposite angles equal; Kite: adjacent sides equal; Trapezoid: one pair of parallel lines; Square: all right angles, all sides equal; Rhombus: all sides equal, opposite angles equal Yes, the triangles are congruent b SAS. The left triangle ma be mapped onto the right triangle with a translation up and to the right a: 10 units b: ( 1, 4) c: 5 units; it must be half of AB because C is the midpoint of AB a: The two equations should have the same slope and intercept. b: When solving a sstem of equations that has an infinite number of solutions, the equations combine to create an equalit, that is alwas true as 3 = 3. This is the result when the two lines coincide, creating infinite points of intersection Let = number of months; = ; 11 months; Yes it does a: There is a strong positive linear association between the high temperatures on consecutive das in Mitchell s area. The random scatter in the residual plot confirms the appropriateness of using a linear model. An increase of one degree on an da is epected to increase the temperature the following da b 0.85 F. 86% of the variation in tomorrow s high temperature is eplained b a linear relationship with toda s high temperature. There are no apparent outliers. b: The largest residual value is about 17ºF and it belongs to the da after the 69.8ºF da. c: (55) = 60.0ºF d: The upper bound is given b = , and the lower bound is given b = Mitchell predicts tomorrow s temperature will fall between 42.9ºF and 76.9ºF. Despite the strong relationship between the variables, Mitchell s model is not ver useful. Selected Answers 51
52 Lesson a: Yes, each side has the same length ( 29 units). See graph at right. b: BD is = ; AC is = 5 c: The slopes are 1 and 1. Therefore the diagonals are perpendicular a: (4.5, 3) b: ( 3, 1.5) c: (1.5, 2) a: = b: No, the coordinates are not solutions to the equation of the line a: = 8 b: = a: not necessaril congruent b: congruent (ASA or AAS ) c: congruent (HL or SSS ) d: not necessaril congruent a: The two equations should have the same slope but a different intercept. This forces the lines to be parallel and not intersect. b: When solving a sstem of equations that has no solution, the equations combine to create an impossible equalit, such as 3 = 0. However, if students claim that and disappear when combining the two equations, ou ma want to point out that another special case occurs when the resulting equalit is alwas true, such as 2 = 2. This is the result when the two lines coincide, creating infinite points of intersection. 52 Core Connections Integrated I
53 Lesson a: E(1, 3) and F(7, 3); AB = 9, DC = 3, EF = 6; EF seems to be the average of AB and CD. b: EF = 4, while AB = 6, and CD = 2 c: Sample response: The midsegment of a trapezoid is parallel to the bases and has a length that is the average of the lengths of the bases It is a parallelogram; the slopes of the pairs of opposite sides are 2 and (2, 5) b + 3h = 339, b = h + 15; 48 bouquets and 33 hearts a: arithmetic, t(n) = 3n 2 b: neither c: geometric, r = 2 d: arithmetic, t(n) = 7n 2 e: arithmetic, t(n) = n + ( 1) f: geometric, r = Write all equations in = m + b form and compare the slopes. (a) and (d) are parallel, (b) and (c) are perpendicular. Selected Answers 53
54 Lesson a: (8, 8) b: (6.5, 6) a: AAA; Not necessaril congruent. b: Congruent b SSS. c: FED BUG b HL or SSS a: X b: Y and Z a: It is a right triangle because the slopes of AB and AC ( 4 3 and 4 3, respectivel) are opposite reciprocals. b: B is at ( 2, 0). It is an isosceles triangle because B AB must be a straight angle (since it is composed of two adjacent right angles) and because BC B C (since reflections preserve length) Let b = # bos, g = # girls. 5b + 3g = 175, b + g = girls came to the dance a: p = 3.97v , where p is power (watts) and v is VO 2 ma (ml/kg/min). b: 280 watts. The measurements are rounded to the nearest whole number. c: = 13 watts d: r = 0.51; The linear association is positive and weak. e: There is a weak positive linear association between power and VO 2 ma, with no apparent outliers. An increase of one ml/kg/min in VO 2 ma is predicted to increase power b 3.97 watts. 26.7% of the variabilit in the power can be eplained b a linear relationship with VO 2 ma. 54 Core Connections Integrated I
55 Lesson (Da 1) 87. a: 1.25 b: 0.82 c: 1.39 d: a: 6, 18, 54 b: See graph shown above right. domain: positive integers c: See graph shown below right. d: The have the same shape, but (b) is discrete and (c) is continuous and the have different domains a: = 2 3 b: b = ac c: = c: t 2 = 2g a a: It is a square. Students should demonstrate that each side is the same length and that two adjacent sides are perpendicular (slopes are opposite reciprocals). b: C is at ( 5, 8) and D is at ( 7, 4). c: P = 4 20 = units, A = 20 sq. units a: ΔSQR; HL b: ΔGFE; ASA c: ΔDEF; SSS m = 13, b = If t represents time traveled (in hours) and r represents the rate of the freight train, 49.5 = rt and 61.5 = (r + 16)(t); t = 0.75 hours, so, the time is 4:10 p.m. Selected Answers 55
56 Lesson (Da 2) a: b: c: See graph at right. The graph is a curve with a intercept at (0, 1). There are no intercepts. The function is continuous and increasing. The domain is all real numbers. The range is > 0. There is an asmptote at = a: There is a strong negative linear association between the pressure and volume of these three gasses. There are no apparent outliers. The residual plot indicates a curved model might be better than the linear model. About 82% of the variation in the volume of the gasses is eplained b a linear relationship with pressure. On average for ever increase of one atmosphere (at a constant temperature) the volume decreases b 1.65 liters. b: 2.3 liters and it belongs to ogen at 2 atmospheres of pressure. c: 9.40 liters, 6.10 liters, and 2.82 liters d: The model would not work well. There is a curved pattern in the residual plot. In fact, b the ideal gas law, pressure and volume have an inverse relationship. After 8.19 atmospheres of pressure the linear model will start predicting negative volumes. Students ma know at some point the gasses will condense into liquids and have much different phsical characteristics = 90 ; 2.7 pounds These polgons are congruent b a rotation and translation. z = 15 units and = 3 units a: = b: all real numbers c: c = , 46, 47; + ( + 1) + ( + 2) = Core Connections Integrated I
57 Lesson a: = 1.2(3.3) b: = b: All three graphs are increasing curves that are the same shape. All three graphs have an asmptote at the ais, but the have different intercepts. It would be incorrect to sa the have different steepness or different growths. See solution graph at right a: See table at right. The two sequences are the same. b: The coefficient is the first term of the sequence, and the eponent is n 1. c: See table at right. Yes, both forms create the same t sequence. t(n) d: Because he is using the first term of the sequence instead of the zeroth term. Dwane subtracts one because his equation starts one term later in the sequence, so he needs to multipl or add one less time a: Tpical response: The distance between A and D ( 10 ) equals the distance between B and D (also 10 ). b: = t t(n) c: Yes, the slope of BD is 1 3 while the slope of AC is 3. Since the slopes are opposite reciprocals, BD is perpendicular to AC. d: P = units. If AC is used as the base, then A = 20 sq. units Congruent b SSS. See flowchart at right d = 2(t + 5) and d = 6t; where d = distance traveled (miles) and t = time Jan biked (miles per hour); d = 15 miles PQ = SR given QR = RQ PQR SRQ segment congruent to itself SSS PR = SQ given a: (2, 4) b: (3, 3 2 ) Selected Answers 57
58 Lesson a: t(n) = (1.0625) n b: $504, Answers var, but should include a table, a graph, and a situation a: Each of the sides is 5 units in length. b: A = 20 sq. units, P = 20 units c: The slopes are 2 and 1 2. The are perpendicular because the slopes are opposite reciprocals. d: The point of intersection is (0, 2). It is the midpoint of the diagonal a: Michelle is correct. One wa to view this is graphicall: The intercept alwas has a coordinate of 0 because it lies on the ais. b: ( 4, 0) a: congruent (SAS ), = 79º b: cannot be determined c: congruent (AAS ), 5.86 units d: congruent (SAS ), cannot be determined a: no solution b: (0, 2) ounces, no it does not make sense because the blue blocks weigh 2 ounces, which is not possible See graph at right a: b: c: Boes a: 8 units b: ( 6, 1), (, ) (, ) a: 3 b: 3 c: 4 d: 1 Shoes a: 1 b: 2 c: 2 d: a: 228 shoppers b: 58 people per hour c: at 3:00 p.m (2 3)( + 2 4) = Core Connections Integrated I
59 Lesson rebound ratio is 80%; t(n) = 100(0.8) n ; See graph at right a: 0.40 b: $32, $2.05 c: V(t) = 80(0.4) t d: According to this model, it never will; in realit, a DVD plaer would have no value if it breaks. e: See graph at right. Value a: 4 b: 2 c: 3 d: weeks Time (ears) Yes, she is correct. The lengths on both sides of the midpoint are equal and that (2, 4) lies on the line that connects ( 3, 5) and (7, 3) a: congruent (SSS ) b: not enough information c: congruent (ASA ) d: congruent (HL ) a: 8%; 1.08 b: cost = 162(1.08) 7 = $ c: $55.15 (An answer of $50.41 means 0.92 was incorrectl used as the multiplier.) d: $475.83; Probabl not, because the model assumption that the percent increase is constant would probabl not be true for this long. Selected Answers 59
60 Lesson = 4(1.75) a: t(n) = (n 1) b: t(n) = 30 5 n d = r(5) and (d + 225) = 2r(5), where d = distance of slower car (km) and r = speed of slower car. The slower car is going 45 kilometers per hour, while the other car is going 90 kilometers per hour Sometimes true; true onl when = a: = = 5 3 b 2 b: = m c: r2 = A π AC = BC and AC is perpendicular to BC a: es b: no; most inputs have two outputs c: no; = 1 has two outputs 60 Core Connections Integrated I
61 Lesson a: = 281.4(1.02) 5, million people b: million people c: 34 million people. Population growth has slowed Note that students are not epected to have a particular method developed to solve these et. Rather, the are epected to devise a method that works. The will most likel use some form of substitution. a: a = 6, b = 2 b: a = 2, b = a: l = P 2w 2 b: π = C 2r c: r = 3 3V 4π a: The data appears randoml scattered. There is apparentl no association between time running a mile and heart rate. Onl 1% of the variation in heart rate can be eplained b a linear association with time running a mile. The LSRL is nearl horizontal. There are no outliers b: Answers will var. Eample responses: D Ran a fast mile but seemed to be giving little effort. This athlete might alread be in outstanding phsical condition or have an attitude problem. F Strong run and strong effort. Keep this plaer. N, O Ran slowl and gave little effort. Along with plaer M, we do not know these plaers potential or motivation. Cut? P The slowest of the group but with the highest effort. This plaer ma improve substantiall over time. Cost ($) Number of Das AC = 58 units; the midpoint is at (3.5, 2.5) a: sometimes true (when = 0) b: alwas true c: sometimes true (for all values of and for all ecept = 0) d: never true Selected Answers 61
62 Lesson a: = 2 4 b: = 4(0.5) a: a = 3, b = 5 b: a = 2, b = a: = 500(1.08) b: $ c: 0, 500 d: See answer graph above right See graph at right. Length of base = GJ = 4 units; height = 6 units. Area of triangle = 12 square units. J G H a: Let s = price of a can of soup and let b = cost of a loaf of bread, then Khalil s purchase can be represented b 4s + 3b = $11.67 and Ronda s b 8s + b = $ b: soup = $1.35, bread = $ a: true b: false c: true d: true e: false f: false a: The triangles should be b SSS but 80º 50º. b: The triangles should be b SAS but 80º 90º. c: The triangles should be b SAS but d: Triangle is isosceles but the base angles are not equal. e: The large triangle is isosceles but base angles are not equal. f: The triangles should be b SAS but sides Core Connections Integrated I
63 Lesson a: No; b observation, a curved regression line ma be better. See scatterplot at right. b: Eponential. The growth is similar to the flu outbreak in Chapter 1 (Lesson 1.1.2). c: m = d, where m is the percentage of mold and d is the number of das. Hannah predicted the mold covered 20% of a sandwich on Wednesda. Hannah measured to the nearest percent units a: false b: true c: true d: true = (0.5) e: true f: false g: true h: false % Mold Da a: = 15 5 b: = 151(0.8) f() f() Relationships used will var, but ma include alternate interior angles, Triangle Angle Sum Theorem, etc.; a = 26, b = 65, c = 26, d = a: Let = oungest child, + ( + 5) + 2 = 57; The children are 13, 18, and 26 ears b: Let = months, = insects, = , = 175 3; 14 months c: Let = amount paid, 8 5 = 3 ; $4.80 d: Let a = # adult tickets, s = # student tickets, 3s + 5a = 1770, s = a + 30; 210 adult and 240 student Selected Answers 63
64 Lesson ; 8.8% monthl increase; = 1000(1.088) CD = 22, BC = 7, and ED = 6; the perimeter is = 48 units a: f() = 8 ( 1 2 ) b: See graph at right a: = 28.5º; Triangle Angle Sum Theorem b: = 23º; relationships used varies c: = 68º; relationships used varies a: 3 2 b: 3 c: 6 d: 2 b: never; (0, 3); See graph at right a: 12, 7, 2, 3, 8; t(n) = 17 5n b: 32, 16, 8, 4, 2; a n = 64( 1 2 ) n Let represent the amount of mone the oungest child receives. Then = 775; $185, $370, and $ Core Connections Integrated I
65 Lesson a: p > 1 b: k < 2 c: 1 h or h p k h 98. a: alwas b: sometimes c: never d: sometimes e: alwas f: never 99. a: ( 8, 2) b: ( 5 3, 1) = 7.68(2.5) a: See graph at right. = b: See graph at right. The Ushaped residual plot indicates a nonlinear model ma be better. c: = 23.76(1.01) d: See plot at right. The residual plot shows no apparent pattern, so the eponential model is appropriate a: Congruent (SAS ) and = 2 b: Congruent (HL ) and = a: 25b36 55 a22 b: 3 9 Residuals (100 in 3 ) Volume (100 in 3 ) Volume (100 in 3 ) Residuals (in 3 ) Time (min) Time (min) Time (min) Time (min) 500 Selected Answers 65
66 Lesson a: k < 2 b: p 15 c: n > 1 2 c: t > d Either 15 or 15; es = 3( 1 3 ) Let t = number of Turks and k = number of Kurds. Then t + k = 66,000,000 and t = 4k. t = 52,800,000 and k = 13,200,000. There are 13,200,000 Kurds times; 141 times considering precision of measurement a: = 14, = 3 b: = 32, = 9 Lesson a: = 7 or 7 b: = 16 or 16 c: = 3, 17 d: = 7 or a: false b: false c: true d: false a: (4, 1) b: ( 1, 2) c: part (b) d: part (a) = 27( 1 3 ) $ a: units or 23 units using appropriate precision b: a: $0.16 per ear; $4.85 b: The multiplier is 1.04 or 4% per ear; $ Core Connections Integrated I
67 Lesson a: 3 b: 1 c: 4 d: a: < 4 b: 3 c: > 2 d: S $24, 000 $1575 ; $22,425 S $25, f () = 0.2(8) = AAS or ASA, ΔABC ΔDCB Corn: a n = t(n) = n + 2 ; Leah: a n = t(n) = 1 3 n + 3 Selected Answers 67
68 Lesson a: b: a: = 10 or = 16 b: = 1 3 or = c: no solution , so 5. Algeria can order an advertisement up to 5 inches high f () = 3(2) a: See graph at right. Weight is ver strongl positivel associated with time in a nonlinear manner with no apparent outliers. b: An eponential function is often useful for describing increasing change over the course of time. c: See graph at right. = (1.679) ; the intercept of (0, 0.08) seems reasonable since a mushroom with no time to grow will weigh almost nothing. d: 5.02 g a: 2 2 units b: ( 1, 6). The function would change the coordinate to, or more formall, (, ) (, ). c: (8, 5) d: The translation is a movement 10 units along an line parallel to = Line L: = ; line M: = ; point of intersection: (6, 5) Weight (g) Weight (g) Time (das) Time (das) 68 Core Connections Integrated I
69 Lesson a: See graph at right b b: No, it is not; it lies on the boundar to <, but the boundar is not part of the solution g 20; g 19.5, so 19 games ( 3, 6) ; 7.5% increase; See graph and eample table at right a: = b: = 24 c: = 2.5 d: = 0 or ABD CDB b SAS. Rotate ΔABD b 180º and then translate. Other sequences eist, but reflection is not an option unless it is followed b another reflection. (time) (price) Selected Answers 69
70 Lesson See solution at right a: 32 < b < 40 b: 33 or Let = amount of trash for each household (pounds); < 50,000; < 14.8; less than 14.8 pounds = 2.75(1.05) ; $ No; 3(7 2) = 15 and 15 > No; Bernie would pass Wendel after 36 seconds, when each was 81 meters from the starting line. Since the race was onl 70 meters, that would occur after the race was over a: f () = 2 4 Month () Population (f()) b: f () = 5 (1.2) Year () Population (f()) c: The function in part (a) is growing faster, the outputs in the table are larger for the same inputs, its multiplier is larger. 70 Core Connections Integrated I
71 Lesson a: Let r = the number of rulers sold and let c = the number of compasses sold; $1r + $2.50c $15 b: r + c 25 c: See graph at right. No, the club cannot sell a negative number of items. d: See graph at right. The points represent the possible sales of rulers and compasses that would allow the club to break even or make a profit while falling within the sales limit. Not all of the points in the solution region can be possible answers as ou can onl have whole number amounts of rulers and compasses a: 6 b: > 1 c: 2 < 7 d: 3 or > a: = 0 b: = 1 c: = 11 or = 6 d: = ; inches a: ( 2, 5) b: (1, 5) c: ( 12, 14) d: (2, 2) See graph at right a: eplicit b: t(n) = 3 + 4(n 1) or a n = 3 + 4(n 1) c: t(50) = a 50 = 193 Selected Answers 71
72 Lesson a: Subscribe to Sunda paper and subscribe to local paper. See table at right. b: 77% c: 84.4% No, because 1 is not greater than 1. Subscribes to weekl local paper Subscribes to Sunda paper es no es no ; or the time is between approimatel 3:16 and 3: ( 5, 1), ( 3, 7), and ( 6, 2) = 6(0.8) ; See graph at right a: d = 4(I 18) 3m m = 1 2 ; (0, 4) b: q = S 25 p c: n = PV RT a: See table at right % b: = 50% See graph at right. did not purchased washer purchase washer purchased drer did not purchase drer m 31 5 ; 26 m W M º a: Since the colon doubles ever da and it would be covered on Februar 21, then it is half covered on Februar 20. b: t(n) = a 2 n c: 100 = a 2 12 ; a = % d: n = 5, so t(5) 0.78% a: 3, 15, 75, 375 b: 10, 50, 250, Denali has 18 pieces of cand. Y J 32 15º T Q 72 Core Connections Integrated I
73 Lesson (46.4, 48.5, 50.4, 52.5, 55.9) a: = 8 b: = 9 2, 11 2 c: no solution a: If c = number of cars and t = number of trucks, 2c + 3t 500, c + t 200 b: Yes, if the make no more than 100 cars The team president is using the mean, and the fans are using the median. A few large outliers, such as superstar plaers, have ver high salaries = 1 2 (10) ,910,080 beats per ear The are not on the same line; m AB = 1 5, m BC = 1 3, m AC = a: 1.58, 2.50, 2.91, 3.49, 4.29) b: See solution graph at right. c: The median (center) is 2.91 points. The shape is smmetric. The IQR (spread) is Q3 Q1 = = 0.99 points. There are no apparent outliers. # of Students GPA a: See diagram below right. b: P(Senior given OceanView) = = 25% Let h = number of hats and let t = number of Tshirts; 5h + 8t In both cases, the account that pas 2% interest is better a: 2 2 b: m 3 n 3 c: 1 m 3 d: n a: P mm, A = 72 sq mm b: P = 30 feet, A = 36 square feet A Not OceanView Ocean View Senior (0.60)(0.10) = Not senior (0.20)(0.90) = Selected Answers 73
74 Lesson (Da 1) a: See solution graph at right. b: The median is 257 rpm. The graph is singlepeaked and skewed. The IQR is Q3 Q1 = = 10 rpm. 291 rpm is apparentl an outlier. c: The median. Because the data is not smmetric and has an outlier, the mean is not an appropriate measure of center. Frequenc rpm < Yes, b AAS. Reflection on an line, then rotation and translation If she deposits the mone for 5 ears, the simple 2.5% interest is better; if she deposits the mone for 25 ears, the 2% compounded interest account is better a: m = 3 b: m = 6 c: m = 5 d: m = a: = 3 or 11 b: = 14 c: = 2 e: = a: ( 1 3, 2) b: (4, 9) 74 Core Connections Integrated I
75 Lesson (Da 2) a: See sketch at right. The medians of the two groups are virtuall identical. Both groups have uniform distributions of ages. Neither group has an outliers. However, the ages in Group 7B are much more widel distributed (have much more variabilit) than the ages in Group 7A. The IQR for 7A is onl = 17 ears, while the IQR for 7B is more than twice as wide at ears. The minimum for 7A is 20 ears older than the minimum for 7B, and the maimum for 7A is 22 ears ounger than the maimum for 7B. Note that the small number of data points does not allow for bin widths on the histogram much narrower than 20 ears; it is not appropriate to create bin widths of 10 ears. b: Either. Since the data distributions are smmetric and there are no outliers, either measure of center is appropriate. 10 7A Age (ears) 8 7B Age (ears) a: = 4 or = 4 b: = 7.9 or = 1.5 c: = 5 6 or = d: = or = See graph at right a See graph at right. The graph is a continuous curve. It is decreasing with a domain of all real numbers and a range of > 0. The intercept is (0, 1). There are no intercepts. It is a function with an asmptote of = a: 9 2 b: c: 6 d: Let g = ground speed (mph) and w = wind speed (mph) = (g w)3.6 and 1809 = (g + w)3. Considering the precision of measurement, g = 553 miles per hour and w = 50 miles per hour. Selected Answers 75
76 Lesson See graph at right. The distribution of weights is smmetric with no outliers (as determined b the modified boplot). The mean is 40 kg with a standard deviation of 16 kg. The weights are rounded to the nearest whole number See solution graph at right a: = 20º, sum of angles is 180º b: = 60º, sum of angles is 180º = 0.6 ; See graph at right a: b: c: d: Let = time spent delivering Times (minutes); Let = time spent delivering the Star (minutes); + = 60 and 2 + = 91; = 31 and = 29. He delivers 62 Times and 29 Star papers Let a = # of adult tickets and s = # of student tickets, then 7a + 5s Core Connections Integrated I
77 Lesson a: Shifted down 7 units b: Shifted up 15 units c: Shifted up 13 units d: Shifted down 4 units a: Not necessaril congruent because SSA is not a congruence condition. b: Not necessaril congruent because AAA is not a congruence condition, and there is not complete information for an side a: See boplots below. Unequivocall, the farmer should plant in shade. The median crop is about 7 bushels higher in shade. The minimum, maimum, first quartile, and third quartile are all higher in shade. Both distributions are skewed in the same direction. The spread in data (IQR) is almost the same for both tpes of trees the middle bo is the same size for both boplots. The maimum of 127 bushels from one of the shad trees is almost certainl an outlier. sunn shad b: No. Neither of the boplots is smmetric; the distributions are skewed. The maimum on the shad plot ma be an outlier a: 3 b: 1 c: 4 d: See graph at right. The graph is a continuous curve. It is decreasing with a domain of all real numbers and a range of > 0. The intercept is (0, 1.5). There are no intercepts. It is a function with an asmptote of = See graph at right Let = time of Marisol; Marisol: = 2, Mimi: = 3( 1); solution: = 3 hrs, so 6 miles Selected Answers 77
78 Lesson f () 5 = See solutions on graph a: Team 2 works, on average, a little faster the median number of widgets per team member is slightl higher. The distributions for both teams are similarl smmetric. However, the members of Team 1 are much more consistent than those of Team 2. The variabilit (IQR) of Team 1 is almost half that of Team 2, and Team 1 s range is less too. Neither team had outliers. f() + 1 f() 2 b: Since both distributions are nearl smmetric with no outliers, it is appropriate to compare standard deviations. Since Team 1 had both IQR and range smaller than Team 2, we would epect that Team 1 has a smaller standard deviation. f() w 10 > 0.13 ; w < 9.87 or w > See graph at right (4 3) = , so = 4 and GH = 4(4) 3 = 13 units a: = 13 b: = 4 or 8 c: = 3 d: no solution 78 Core Connections Integrated I
79 Lesson a: The 72 represents the temperature of the room. It is the horizontal asmptote. b: The equation would then be f (t) = 140(0.5) t + 68 as the horizontal asmptote would at = 68. It is the coolest the tea can get a: 3 b: 1 c: a: The IQR for W is more than for Z because the middle of the boplot for W is wider. The standard deviation for Z is greater because overall, including the outliers, the data for Z is spread out more than for W. Since mean is impacted b outliers more than median, the standard deviation (which is based on mean) is impacted b more b the outliers in Chip Z. Mean and standard deviation are not appropriate for Chip Z because the shape is skewed and there are outliers. b: Chip Z appears to be the more energ efficient. It has 0 a lower median use of current. Also, for most of the 135 data sets tested, chip Z uses the same or slightl less current than chip W. Chip Z has smaller IQR: it is more consistent in current usage. However, all these benefits ma be offset b the two high outliers belonging to Chip Z that might indicate a reliabilit problem a: 3 4, shift down 1 units b: 3 + 5, shift up 8 units c: 3 25, shift down 22 units d: 3, shift up 3 units a: < 1 b: Chip W Electrical Current (ma) Chip Z Electrical Current (ma) c: m 2 d: no solution a: SAS ; 90ºclockwise rotation followed b a translation, JKH NLM b: SSS ; reflect on line AC, then 180ºrotation, then translate; ABC FDE c: Not necessaril congruent d: AAS ; 180ºrotation about point R; PRQ SRT a: Y R+G+B+Y b: G+B R+G+B+Y c: 0 R+G+B+Y or 0 Selected Answers 79
80 Lesson Possible response: Construct a circle of an radius. Then choose a point on the circle and mark off two radius lengths in each direction along the circle circumference. Connect the original point to each of the other two points a: $4.10 b: $ a: = 39% b: = 56% c: = 77% d: See the relative frequenc table below. Yes, the juniors and seniors are much less likel to be carring a backpack. Freshmen Sophomore Junior Senior Backpack 73% 73% 56% 54% No Backpack 27% 27% 44% 46% a: a = 0 b: m = c: = 10 d: = 9, a: Room temperature. The hot water will approach room temperature but will never cool more than that. b: The asmptote would be lower, but still parallel to the ais. If the temperature outside was below zero, the asmptote would be below the ais a: m > 5 b: 6 c: > 7 d: no solution a: (1, 1) b: ( 2, 1 2 ) t(n) = 188n ; t(5) = Core Connections Integrated I
81 Lesson She should construct an arc centered at P with radius k so that it intersects n and m each once (call these intersections R and S). She should then construct two more circles with radius k, centered at R and S. The fourth verte lies where these two circles intersect a: 3 d: One third of the students will have heard the rumor at 2 p.m. since each hour the number that have heard the rumor triples. c: t(n) = a 3 n d: t(7) = a 3 7 = 1; a = e: = 3 s, where s is the total number of students in the school; s = 6561 students a: Making percentages based on the column totals for comparison will help Kenn see past the variation that comes with the overall popularit of having cupcakes at various tpes of celebrations. b: The row and column totals are shown below. The column percentages are also shown below. Comparing across each row, the Birthda and Wedding celebrations seem ver similar in the tpes of cupcakes ordered. Halloween and the 4 th of Jul celebrations seem substantiall different from the other celebrations, with a stronger preference for Fudg Fantas on Halloween and an inclination toward Fruit Fun on the 4 th of Jul. Birthda Wedding Halloween 4 th of Jul Fudg Fantas FluffFetti Fruit Fun , ,973 Birthda Wedding Halloween 4 th of Jul Fudg Fantas 48% 51% 68% 40% FluffFetti 29% 27% 19% 24% Fruit Fun 23% 22% 13% 36% 100% 100% 100% 100% a: 8( 3) + 2; shifted down 2 units b: 8( 3) + 3.5; shifted down 0.5 units c: 8( 3) + 12; shifted up 8 units d: 8( 3) + 3.5; shifted up 3 4 units a: 2 b: > 1 c: 9 d: > 10 Selected Answers 81
82 f() + 2 f() f() a: = 11 3 b: = Let a = the number of apples; Let p = the numbers of pears; a + p = 11, 0.60a p = $5.60; 7 apples and 4 pears Answers var, but likel answers are 6(m 2), 2(3m 6), 3(2m 4), and 1(6m 12). 82 Core Connections Integrated I
83 Lesson b a: 0.463, 53.7% decrease b: f () = 20(0.463) c: See graph and table at right. f() a: (1.5, 5) b: = c: = = 7.5 units terms a: 12 b: 10 < < 10 c: < 0 d: < 5, > a: 2 5, shifted down 2 units b: 2 3.5, shifted down 0.5 units b: 2 + 5, shifted up 8 units d: , shifted up 3 4 units a: = 4 or 2 b: = 7 c: = a: There is no solution, so the lines do not intersect. b: = c: Yes; both lines have the same slope (are parallel) a: = 23500(0.85) ; $ b: = (1.12) ; 138,570,081 Selected Answers 83
84 Lesson Let s = the amount of mone invested in stocks (dollars); Let b = the amount of mone invested in bonds (dollars); 0.03s b = 430 and s + b = 10,000; Marius invested $3500 in stocks and $6500 in bonds = 4.75( + 3) ; 9 5 pounds a: f () = 5(1.5) b: f () = 0.5(0.4) A > a: intercepts ( 2, 0) and (0, 0); intercept (0, 0) b: intercepts ( 3, 0) and (5, 0); intercept (0, 3) c: intercepts ( 1, 0) and (1, 0); intercept (0, 1) a: 2 < < 2 b: 2.5 c: = 1 4 d: no solution e: = 12 f: Let t = number of toppings; 1.19(3) t = 4.55; t = a: 2a 2 5ab 3b 2 b: Core Connections Integrated I
85 Lesson a: See graph at right. b: ( 2.5, 1.1) c: = a: annual multiplier = which is a 5.6% decrease b: f() = 60(0.944) c: f(15) = f() g() a: iv b: ii c: v d: i e: iii b is the onl histogram with a narrow range, so it matches to ii. The two skewed histograms are straightforward to match. c has a uniform distribution, so the quartiles on the boplot must be of even length, as in v. d has a lot of data at the two edges, and the data in the middle is more spread out, so the whiskers of the boplot must be narrow, and the bo must be wide, as in i emploees a: < 2 b: 6 c: > 4 d: See graph at right a: = 1.5 b: = miles width = 60 mm; area = 660 mm 2 Selected Answers 85
86 Lesson (Da 1) a: There is a strong positive linear association between the depth of a water well and the cost to install it. There are no apparent outliers C b: On average, ever foot deeper ou drill the well, the cost increases b $ c: The coefficient of correlation is 0.929, Rsquared = About 86% of the variation in the cost of drilling a water well can be eplained b a linear association with its depth. d: $1395 represents the cost of a well that has no depth. It would be roughl the cost of the pump. e: (80) = $2567, (150) = $3593, (200) = $4325 f: From part (e), the predicted cost is $2567. Actual $2567 = $363; actual cost was $2930. g: A linear model looks the most appropriate because there is no pattern in the residual plot Yes, b HL ; grams; the coin is significantl less than this range, so its legitimac could be questioned, though there ma be reasons that it has lost weight since See graph at right = 1 or = 1 ; = 6 5 hours = hours = 1 hour and 12 minutes Mr. Greer distributed incorrectl. The correct solution is = a: See graph at right. b: f () = 10(2.3) c: = 42, 000(0.75) 5 = 9967 d: 60 = 25(b) 10 ; b = 1.09, 9%increase s = a + 150, 3s + 5a = 4730; 685 students 86 Core Connections Integrated I
87 9( Lesson (Da 2) FG = 3.5 cm, BC = 14 cm minutes a: Congruent (SAS ), ΔABD ΔCBD b: Congruent (ASA or AAS ), ΔABC ΔDEF a: t(n) = 3n + 10 or t(n) = 7 3(n 1) b: t(n) = n 1 or t(n) = (3) n m m = 5000; m = 8.6; It will be full after 8 months; there will not be enough room for songs in the 9 th month a and d a: = 6 3 b: = 7 ( 1 2 ) f() f() f() a: ( 1, 2) b: (4, 4) c: (3, 4) Selected Answers 87
88 9( Lesson f () = 3(0.2) See graph at right. The distribution is smmetric with no outliers. The mean is 50.7 cm and the standard deviation is 2.6 cm. The lengths were measured to the nearest tenth of a centimeter (12 + 7) = 30 4, so = Let p = amount of powder blue and s = amount of spring blue. Then 0.02 p + 0.1s = 0.04(1) and p + s = 1, so p = 0.75 gallons and s = 0.25 gallons a: 4 b: > 20.5 c: 0 d: > 19 or < See graph at right Let = time (months); = ; = 11 months = = 2 + 5; 105 tiles 88 Core Connections Integrated I
89 9( Lesson A relative frequenc table is below. There is almost no difference between the amount of cheese at Taco Shack and at the competitor. An difference can easil be eplained b natural sampletosample variabilit. No association. The Taco Shack owner does not need to adjust the amount of cheese, and should consider other reasons for the difference in perception minutes NUMBER OF TACOS Taco Shack competitor <15 grams cheese 11% 10% between 15g and 25g cheese 60% 61% >25 grams cheese 29% 29% Both (a) and (d) are equivalent. One wa to test is to check that the solution to 4(3 1) + 3 = makes the equation true (the solution is 3 2 ) a: t(n) = See graph at right. 1 ( 2 ) n 1 b: t(n) = 7.5 2(n 1) a: 3 b: 2 c: 1 d: 0 e: 1 f: does not eist g: a: > 3 or < 3 b: c: = 2 or 3 d: = u = 4, v = a: 92 4 b: 22 c: 2 Selected Answers 89
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