1.6.2: Exercise N.6
- Page ID
- 147907
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)(1) Imagine you are planning to draw an infographic that models the Pacific Ocean as a square with 3-centimeter sides, and the Great Pacific Garbage Patch as a square within that square.
(a) The area of the Pacific Ocean is 165 million km2. Use 15 million km2 as the area of the Garbage Patch. What is the ratio of the area of the Garbage Patch to the area of the Pacific Ocean?
(b) If the Pacific Ocean is represented by the square with 3-centimeter sides, what is the area of this square?
(c) If the ratio between the squares is the same as the ratio in Question 1(a), what should be the area of the square representing the Garbage Patch? Round to the nearest hundredth of a cm2.
(d) What should be the length of each side of the square representing the Garbage Patch? Round to the nearest tenth of a cm.
(e) What is the ratio of the sides of these two squares?
(f) What is the ratio of the areas of these two squares?
(2) Imagine you are planning to use circles to visually compare the populations of California (38,800,000), Texas (28,240,245), and New York (19,807,500). The size of each population will be represented by the area of each circle, not the radius. Round each answer to the nearest tenth.
(a) If the circle for New York will have a radius of 5 cm, what would be the size (area) of that circle (which represents the population of New York)?
(b) What should the area and radius be for the circle representing the population of Texas? Round answers to one decimal place.
(c) What should the area and radius be for the circle representing the population of California? Round answers to one decimal place.
(3) A diagram has circles such that the area represents the populations of various countries in the world. The circle for India has a radius of 3.2 cm and the circle for China has a radius of 3.4 cm. If 18% of the world’s population is in India, what percentage of the world’s population is in China? Round to the nearest percent.
(4) Your team has been tasked with drawing an infographic to show the increase in population of the United States between 1900 and 2000. During this time, the U.S. population increased by 269% (almost quadrupling in size). A member of your team created the infographic below to depict this increase. Write a few sentences which explain to this teammate why the infographic is inaccurate.
(5) Below is a map of the continental United States, showing the results of the 2012 presidential election.23 The darker shaded states are states in which the majority of voters voted for Barack Obama. In the lighter shaded states, a majority of voters voted for Mitt Romney. Looking only at the information provided on this map, which candidate would you say appeared to receive the majority of votes in the 2012 election? Fill in the blank: _________________________________.
(6) In the next map, the size of each state has been adjusted to reflect the number of people living in the state. The larger the state’s population, the larger the state appears to be on the map. Use this map to determine which candidate appeared to receive the majority of the votes in 2012. Fill in the blank: ________________________________.
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