36 1012141516y1010152020153025a) What is the equation for the line of best fit?-2zb) Draw the line of best fit on the following scatterplot.3025201510-2 -11 2 3 4 5 6789 10 il 12 13 14 15 16 17 12-5+Clear All Draw: Line

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 10EQ

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2) Here are some data on height (in meters) of mature sycamore trees. Construct a boxplot of these data. Do not use R: 31.7 13.7 21.0 29.6 30.9 3.3 30.2 47.3 29.9 17.8 15.6 23.2 22.6 3) Here are the weights (kg) of 14 male lions and 15 female lions (all adults). Construct a correct parallel boxplot for these data. Do not use R: males: 176.0 175.7 174.2 185.1 168.1 165.1 177.3 172.4 188.3 162.4 167.3 154.6 176.8 180.3 females: 105.8 98.1 128.3 114.7 113.6 135.0 125.3 113.5 110.7 109.2 104.1 153.4 105.2 130.4 135.0
Wishing to prove that / and m are skew lines. John began an indirect proofby supposing that / and m are intersecting lines. What possibility has Johnoverlooked?
Produce by hand a proof of ((A→B)→C) → (A→(B→C)) How many lines does the most natural box proof contain?
write a proof for the converse to theorem 2.6.2 Let l and m be two lines. If l and m are distinct and nonparallel, then there exists a unique point P such that P lies on both l and m
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Given four 2D points a0, a1, b0, and b1, create a robust procedure to determine whether the line segments a0a1 and b0b1 intersect.
Lengths of bus routes for any particular transit systemwill typically vary from one route to another. The article“Planning of City Bus Routes” (J. of the Institution ofEngineers, 1995: 211–215) gives the following informationon lengths (km) for one particular system:Length 62,8 82,10 102,12 122,14 142,16Frequency 6 23 30 35 32Length 162,18 182,20 202,22 222,24 242,26Frequency 48 42 40 28 27Length 262,28 282,30 302,35 352,40 402,45Frequency 26 14 27 11 2a. Draw a histogram corresponding to these frequencies.b. What proportion of these route lengths are less than20? What proportion of these routes have lengths of atleast 30?c. Roughly what is the value of the 90th percentile ofthe route length distribution?d. Roughly what is the median route length?
If ?1 is the line through ?(1,2,7) and ?(−2,3, −4) and ?2 is the line through ?(2, −1,4) and ?(5,7, −3), prove that ?1 and ?2 are skew lines (lines that do not lie in one plane) and find the distance between them.
Prove: In Fano’s Geometry, show that for a set of three lines not all containing the same point, there exists exactly one point in the geometry not on any of the three lines.
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A group of 11 students was selected at random and asked for their high school GPA and their freshmen GPA in college the subsequent year. The results were: Student High School GPA Freshmen GPA 1 2.0 1.6 2 2.2 2.0 3 2.6 1.8 4 2.7 2.8 5 2.8 2.1 6 3.1 2.0 7 2.9 2.6 8 3.2 2.2 9 3.3 2.6 10 3.6 3.0 We would like to know whether there is a linear relationship between the high school GPA and the college freshmen GPA, and we would like to be able to predict the freshmen GPA, if we know that the high school GPA of another student is, say, 3.4. Provide the two requested scatter plots for this data (put college freshman GPA on the Y (vertical) axis!). a) What would be your approximate 95% prediction interval for question (g)? b) Show your scatterplot with the predicted trend line below
Which of the following is always true about the lengths of the SHD and SD of skew lines? Choose the best answer. a. Shortest Horizontal Distance > Shortest Distance b. Shortest Horizontal Distance not equal to Shortest Distance c. Shortest Horizontal Distance >= Shortest Distance d. Shortest Horizontal Distance <= Shortest Distance e. Shortest Horizontal Distance < Shortest Distance f. Shortest Horizontal Distance = Shortest Distance

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3 6 10 12 14 15 16 y 10 10 15 20 20 15 30 25 a) What is the equation for the line of best fit? -2z b) Draw the line of best fit on the following scatterplot. 30 25 20 15 10