9.4: Appendix D- Solutions to Practice Problems

Last updated
Save as PDF

Page ID: 51944

Amy Lagusker
College of the Canyons

$ \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}}} $

$\newcommand{\avec}{\mathbf a}$ $\newcommand{\bvec}{\mathbf b}$ $\newcommand{\cvec}{\mathbf c}$ $\newcommand{\dvec}{\mathbf d}$ $\newcommand{\dtil}{\widetilde{\mathbf d}}$ $\newcommand{\evec}{\mathbf e}$ $\newcommand{\fvec}{\mathbf f}$ $\newcommand{\nvec}{\mathbf n}$ $\newcommand{\pvec}{\mathbf p}$ $\newcommand{\qvec}{\mathbf q}$ $\newcommand{\svec}{\mathbf s}$ $\newcommand{\tvec}{\mathbf t}$ $\newcommand{\uvec}{\mathbf u}$ $\newcommand{\vvec}{\mathbf v}$ $\newcommand{\wvec}{\mathbf w}$ $\newcommand{\xvec}{\mathbf x}$ $\newcommand{\yvec}{\mathbf y}$ $\newcommand{\zvec}{\mathbf z}$ $\newcommand{\rvec}{\mathbf r}$ $\newcommand{\mvec}{\mathbf m}$ $\newcommand{\zerovec}{\mathbf 0}$ $\newcommand{\onevec}{\mathbf 1}$ $\newcommand{\real}{\mathbb R}$ $\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$ $\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$ $\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$ $\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$ $\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$ $\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$ $\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$ $\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$ $\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$ $\newcommand{\laspan}[1]{\text{Span}\{#1\}}$ $\newcommand{\bcal}{\cal B}$ $\newcommand{\ccal}{\cal C}$ $\newcommand{\scal}{\cal S}$ $\newcommand{\wcal}{\cal W}$ $\newcommand{\ecal}{\cal E}$ $\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$ $\newcommand{\gray}[1]{\color{gray}{#1}}$ $\newcommand{\lgray}[1]{\color{lightgray}{#1}}$ $\newcommand{\rank}{\operatorname{rank}}$ $\newcommand{\row}{\text{Row}}$ $\newcommand{\col}{\text{Col}}$ $\renewcommand{\row}{\text{Row}}$ $\newcommand{\nul}{\text{Nul}}$ $\newcommand{\var}{\text{Var}}$ $\newcommand{\corr}{\text{corr}}$ $\newcommand{\len}[1]{\left|#1\right|}$ $\newcommand{\bbar}{\overline{\bvec}}$ $\newcommand{\bhat}{\widehat{\bvec}}$ $\newcommand{\bperp}{\bvec^\perp}$ $\newcommand{\xhat}{\widehat{\xvec}}$ $\newcommand{\vhat}{\widehat{\vvec}}$ $\newcommand{\uhat}{\widehat{\uvec}}$ $\newcommand{\what}{\widehat{\wvec}}$ $\newcommand{\Sighat}{\widehat{\Sigma}}$ $\newcommand{\lt}{<}$ $\newcommand{\gt}{>}$ $\newcommand{\amp}{&}$ $\definecolor{fillinmathshade}{gray}{0.9}$

Chapter 2

Section 2.2

1063 feet
5 pounds, 8 ounces
$100 trillion

Section 2.3

There are 5 trikes and 2 bikes
21 cents
56 seconds
7 pieces; yes
$\dfrac{1}{5}$ are chickens
$198.65

Section 2.4

$\overline{V I I I V} D C C L I X$
2020
1982
MDCCLXIV
$\bar{L}$
20089

Section 2.5

The character 4 does not exist in base four
“Five-four-two base six”
0, 1, 2 10, 11, 12, 20, 21, 22 100, 101, 102
Answers vary

Section 2.6

1. $7565_{\text {nine}}$
2. $30_{\text {four}}$
3. $10201_{\text {three}}$
4. $1001001_{\text {two}}$
1. $46_{\text {ten}}$
2. $111_{\text {ten}}$
3. $73_{\text {ten}}$
4. $123256_{\text {ten}}$

Section 2.7

Eighty-ones
Six hundred twenty-fives
Six thousand sixty-ones
Thirty eight thousand four hundred sixteens

Section 2.8

$404_{\text {six}}$
$1011_{\text {two}}$
$2121_{\text {three}}$
$104542_{\text {eight}}$

Chapter 3

Section 3.2

50 + 80 + 6 + 1 = 137
1000 – 300 + 16 = 716
95 + 800 = 895
761 – 450 = 760 – 450 + 1 =311

Section 3.3

7 + 7 + 7 + 7
2 + 2 + 2 + 2 + 2 + 2
36.6034
179.1908

Section 3.4

7 coworkers; repeat subtraction
3 pieces of paper; Sharing

Section 3.5

The answers below are precise. Your answers must be close.
1. 16.5
2. 76
These answers must be precise.
1. 16.46
2. $49.35
3. 82
These answers are precise. Your answer must be close.
1. $6.48
2. $11.36
3. $16.39
Your answers must be exact.
1. 72
2. 72
3. Same answers
Your answers must be exact.
1. 866
2. 65322

Section 3.6

Answers vary. Here are some sample answers:

1 meter = the height of a short woman

1 inch = distance from nail to join on my thumb

1 foot = length from my elbow to my wrist

1 yard = The height of preschooler

Section 3.7

309.26
92.86%
114.06

Chapter 4

Section 4.2

Two possible ways to show $3 \dfrac{1}{2}$
1. Rectangles: $clipboard_e4a73c597e1870bdccb728ac233e0008c.png$
2. Number Line: $clipboard_e6357633ac51cd8836a92c1263cd78fd4.png$
$\dfrac{1}{9}, \dfrac{3}{8}, \dfrac{2}{5}, \dfrac{4}{7}, \dfrac{12}{13}$

Section 4.3

$\dfrac{53}{28}$
$\dfrac{11}{28}$
$\dfrac{6}{7}$
$\dfrac{3}{224}$
$\dfrac{257}{30}$ or $8 \dfrac{17}{30}$
$\dfrac{67}{30}$ or $2 \dfrac{7}{30}$
$\dfrac{171}{10}$ or $17 \dfrac{1}{10}$
$\dfrac{162}{95}$ or $1 \dfrac{67}{95}$

Section 4.4

Natural, Whole, Integers, Rational and Real
Rational and Real
Irrational
Natural, Whole, Integers, Rational, and Real
Irrational
Integers, Rational, Real
Whole, Integers, Rational and Real
Natural, Whole, Integers, Rational and Real
29
147
-277
-11
276
Distributive Property
Communitive Property of Multiplication
Reflexive Property
Transitive Property

Chapter 5

Section 5.2

1, 2, 4, 7, 8, 14, 28, 56
1, 5, 29, 145
1,2,4,8,16,32
50, 100, 150, 200
23, 46, 69, 92
8, 16, 24, 32
23,29,31,37
61,67,71,73,79
127, 131, 137, 139, 149
20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40
60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80
120, 121, 122, 123, 124, 125, 126, 128, 129, 130, 132, 133, 134, 135, 136, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150
$2^{2} \cdot 3^{3} \cdot 5$
$2^{2} \cdot 3 \cdot 5$
$5^{3}$

Section 5.3

Table 7.4.1
	2	3	4	5	6	8	9	10
67820	X		X	X				X
512	X		X			X
49
3463

Section 5.4

Section 5.5

360
75
14280
1800
2025
$\dfrac{131}{60}$
$-\dfrac{7}{144}$
$\dfrac{27}{13}$

Chapter 6

Section 6.2

55
46
121
140
95
90
Obtuse
Straight
Acute
Right
Acute
Equiangular
Acute scalene
Right scalene
$clipboard_eb90edd91ce663b8cee79d8fe5f6bb4b6.png$
Does not exist
Octagon
Heptagon
360
1617
1800
1260
Irregular
Regular
Regular
Irregular

Section 6.3

Area is amount inside a two dimensional shape, surface area is the area around a three dimensional shape, volume is the amount of space inside a three dimensional shape
1. $2 \text { units}^2$
2. About $2 \text { units}^2$
3. About $2.5 \text { units}^2$
1. $28 \text { units}^2$
2. $24 \text { units}^2$
1. $7 \text { units}^3$
2. $6 \text { units}^3$

Section 6.4

0.00795455 miles or $\dfrac{7}{880}$ miles
2.25 yards or $\dfrac{9}{4}$ yards
59840 yards
3276 inches

Section 6.5

$254.3 \text { cm}^2$
$28.3 \text { miles}^2$
$232.2 \text { cm}^2$
$153.9 \text { meters}^2$
$25.9 \text { cm}^2$
$60.4 \text { miles}^2$
$7.3 \text { miles}^2$
$2.9 \text { inches}^2$2
Triangular pyramid
Hexagonal prism
Cylinder
Rectangular pyramid
$59.2 \pi \text { ft}^2$
$116.4\pi \text { in}^2$
$462 \pi \text { km}^2$
$323.5 \text { ft}^2$
$99 \text { cm}^2$
$1152 \pi \text { m}^3$
$1.33 \pi \text { m}^3$
$1774.67 \pi \text { km}^3$
$273.84 \pi \text { ft}^3$
$27 \pi \text { mi}^3$
$168 \text {km}^3$
$1296 \pi \text { mi}^3$
$84 \text { m}^3$

Search

Text Color

Text Size

Margin Size

Font Type