13.1.1: Chapter 1
- Page ID
- 117736
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Try It
ⓐ yes ⓑ yes ⓒ no ⓓ yes
ⓔ no
ⓐ no ⓑ yes ⓒ yes ⓓ no
ⓔ no
16
23
86
1
ⓐ 9 ⓑ 64 ⓒ40
ⓐ 216 ⓑ 64 ⓒ 185
ⓐ ⓑ
ⓒ ⓓ
ⓐ ⓑ
ⓒ ⓓ
ⓐ ⓑ
ⓐ ⓑ
ⓐ ⓑ ⓒ
ⓓ
ⓐ ⓑ ⓒ
ⓓ
16
9
ⓐ ⓑ 2 ⓒ
ⓐ ⓑ 3 ⓒ
ⓐ 2 ⓑ ⓒ ⓓ 10
ⓐ 3 ⓑ ⓒ ⓓ 11
ⓐ ⓑ
ⓒ ⓓ
ⓐ ⓑ
ⓒ ⓓ
3
13
ⓐ 23 ⓑ 60 ⓒ ⓓ
ⓐ 39 ⓑ 39 ⓒ −28 ⓓ −7
ⓐ 81 ⓑ
ⓐ 49 ⓑ
ⓐ 4 ⓑ 21
ⓐ 9 ⓑ 6
31
67
The difference in temperatures was 45 degrees.
The difference in temperatures was 9 degrees.
ⓐ ⓑ
ⓐ ⓑ
4
2
272
2
ⓐ ⓑ ⓒ 7
ⓐ ⓑ
ⓒ
ⓐ ⓑ
ⓐ ⓑ
ⓐ 25.8 ⓑ 258 ⓒ 2,580
ⓐ 142 ⓑ 1,420 ⓒ 14,200
ⓐ ⓑ
ⓐ ⓑ
ⓐ 0.09, 0.87, 0.039 ⓑ 17%, 175%, 8.25%
ⓐ 0.03, 0.91, 0.083 ⓑ 41%, 225%, 9.25%
ⓐ 6 ⓑ 13 ⓒ
ⓐ 4 ⓑ 14 ⓒ
ⓐ ⓑ
ⓒ ⓓ
ⓔ
ⓐ
ⓑ
ⓒ
ⓓ
ⓔ
ⓐ
ⓑ
ⓐ
ⓑ
ⓐ 0 ⓑ undefined
ⓐ 0 ⓑ undefined
Section 1.1 Exercises
Divisible by 2, 3, 6
Divisible by 2
Divisible by 3, 5
24
280
440
5
58
29
149
50
5
ⓐ 64 ⓑ 16 ⓒ 7
21
9
ⓐ ⓑ
ⓒ ⓓ
ⓐ ⓑ
ⓒ ⓓ
ⓐ ⓑ
ⓐ ⓑ
Answers will vary.
Answers will vary.
Section 1.2 Exercises
ⓐ ⓑ ⓒ ⓓ
ⓐ ⓑ ⓒ ⓓ
0
8
15
1
ⓐ ⓑ ⓒ
32
ⓐ 6 ⓑ ⓒ ⓓ
22
ⓐ 16 ⓑ16
ⓐ 45 ⓑ45
0
4
6
ⓐ ⓑ ⓒ
ⓓ
ⓐ ⓑ ⓒ
ⓓ
ⓐ ⓑ
ⓐ ⓑ
ⓐ
ⓑ
21 yards
Answers will vary.
Answers will vary.
Section 1.3 Exercises
ⓐ ⓑ
ⓐ ⓑ
ⓐ ⓑ
ⓐ ⓑ
ⓐ ⓑ
Answers will vary.
Answers will vary.
Section 1.4 Exercises
ⓐ 5.78 ⓑ 5.8 ⓒ 6
ⓐ 0.30 ⓑ 0.3 ⓒ 0
ⓐ 63.48 ⓑ 63.5 ⓒ 63
2.5
55200
8
12
ⓐ ⓑ ⓒ ⓓ ⓔ
ⓐ none ⓑ
ⓒ
ⓓ none
ⓔ
Answers will vary.
Answers will vary.
Section 1.5 Exercises
0
undefined
undefined
Answers will vary.
Answers will vary.
Review Exercises
Divisible by
120
4
3
ⓐ ⓑ
ⓐ ⓑ ⓒ ⓓ
ⓐ 8 ⓑ ⓒ ⓓ 22
ⓐ 40 ⓑ 40
ⓐ ⓑ ⓒ ⓓ 17
28
9
ⓐ ⓑ
75
488.1813
no real number
undefined
Practice Test
ⓐ ⓑ
1
−160
ⓐ 0 ⓑ undefined