15.11: Chapter 11
- Page ID
- 129940
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Your Turn
![A table shows the best director pairwise comparison matrix. The table has 6 rows and 7 columns. The row headers are opponent/runner, Scorsese (s), Phillips (P), Mendes (M), Tarantino (T), Bong (B), and points. Under opponent/runner it is labeled as Scorsese wins, Phillips wins, Mendes wins, Tarantino wins, and Bong wins. Under Scorsese (s) a symbol hyphen is labeled in a box, a box colored in blue and labeled as P S 3600, and the entire box is stricken out, a box labeled as M S 3100 is colored in yellow, a box colored in orange and labeled as B S 6600 and the entire box is stricken out. Under Phillips (P), a box colored in blue and labeled as S P 5100, a symbol hyphen is labeled in a box, a box labeled as M P 1900 is colored in blue, a box colored in yellow and labeled as T P 5100, a box colored in grey and labeled as B P 6300. Under Mendes (M), a box colored in yellow and labeled as S M 5600, a box labeled as P M 6800 is colored in blue, a symbol hyphen is labeled in a box, a box colored in blue and labeled as T M 8700, a box colored in yellow and labeled as B M 8700. Under Tarantino (T), a box colored in grey and labeled as S T 5600, a box labeled as P T 3600 is colored in yellow, a box colored in blue and labeled as M T 0, a hyphen is labeled in a box, a box colored in blue and labeled as B T 4700. Under Bong (B), a box colored in orange and labeled as S B 2100 and the entire box is stricken out, a box labeled as P B 2400 is colored in grey and the entire box is stricken out, a box colored in yellow and labeled as M B 0 and the entire box is stricken out, a box colored in blue and labeled as T B 4000 and the entire box is stricken out. Under points, it is labeled as 3, 1, 0, 2, 4.](https://math.libretexts.org/@api/deki/files/110087/CS_Figure_11_01_029.jpg?revision=1)
Family | Family’s Standard Quota |
---|---|
Hernandez | 175.6667 candies |
Higgins | 234.2222 candies |
Ho | 117.1111 candies |
Total | 527 |
The sum is very close to 527.
Each state would receive the following seats: Fictionville 1, Pretendstead 2, Illusionham 4, and Mythbury 28.
The apportionment is Fictionville 2, Pretendstead 2, Illusionham 5, and Mythbury 26.
/**/{\text{Original Standard Divisor}} \approx \fracCallstack:
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/**/{\text{New Population}} \approx 76,000,000 + 300,000 = 76,300,000/**/
/**/{\text{New House Size}} \approx \fracCallstack:
at (Bookshelves/Applied_Mathematics/Contemporary_Mathematics_(OpenStax)/15:_Answer_Key/15.11:_Chapter_11), /content/body/div/div/div/div[48]/div/p[3]/span/span[1], line 1, column 2
Callstack:
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There are /**/392 - 391 = 1/**/ new seats to be apportioned to New Mexico.
Check Your Understanding
The Hamilton method.
The Hamilton method.
The Jefferson method.
The Adams method.
The Adams method.
The Hamilton and Jefferson methods.
Webster’s method.
Larger