The Mathematical Paper of Sir William Rowan Hamilton - Page 611 You also have the option to opt-out of these cookies. Alexander Hamilton proposed the method that now bears his name. \text { Sussex } & 197,145 & 9.0017 & 9\\ Time Series Analysis fills an important need for a textbook that integrates economic theory, econometrics, and new results. The book is intended to provide students and researchers with a self-contained survey of time series analysis. These paradoxes mainly arise as you change the number . In 1791 both the Senate and House voted to adopt Hamilton's method apportionment, and it still remains in use today. If Hamilton's method had been applied in 1792 to a House of size 105, 13 of the 15 states would have been assigned the same number of Representatives they received under Jefferson. Hamilton's method was adopted by the US Congress in 1852 and was in use through 1911 when it was replaced by Webster's method Then, bigger samples are favored over smaller samples. Legal. 3. For All Practical Purposes (Paper): Mathematical Literacy in ... State Population Quota Hamilton apportionment A 7,270,000 14.24 14 B 1,230,000 2.41 3 C I 2 220,000 4.35 4 Total 10,720,000 21.00 21 Table 2. Necessary cookies are absolutely essential for the website to function properly. These are called the. The lower quotas add up to 48. Cake Cutting Methods. Example #1: Using Hamilton's Plan A university is composed of four schools. Found inside – Page 51The Alabama paradox is peculiar to Hamilton's method . For example , it cannot occur under either Webster's or Jefferson's method , or indeed under any method that employs a common divisor . The reason is quite simple : If the number of ... That is seen as preferential treatment. If A is a provided as n×n matrix and I n is the n×n identity matrix, then the distinctive polynomial of A is articulated as: endobj The divisor is \(1,052,567/75 = 14,034.22667\). Hamilton's method satisfies all the rules, except rule number one. He begins by determining, to several decimal places, how many things each group should get. Hamilton's method produces Alabama Paradox. Hamilton that supports the notion that natural selection favours genetic success, not reproductive success per se.It recognizes that individuals can pass copies of their genes on to future generations through direct parentage (the rearing of offspring and grand . Since he was interested in the question of Congressional representation, we’ll use the language of states and representatives, so he determines how many representatives each state should get. Lauryn Hill is one of a long list of artists and genres that influenced Lin-Manuel Miranda, the mastermind behind "Hamilton." Let's compare the rhyme schemes of songs Mr. Miranda has cited as influential with verses he wrote in "Hamilton." . Standard Quotas: B:138.72 E: 13.70 Under Hamilton's method, an extra seat would go to B before E, but that seat would mean %PDF-1.4 Decimals, Fractions, Percents. Found inside – Page 420It has a certain superficial similarity to Hamilton's method , and , in so far , is effective enough , but it lacks ... Take as an example Hamilton's own treatment of the curvature of surfaces , to which in one of his notes Professor ... Choose the correct answer below. endobj That happened, but another thing also happened: Maine gained a representative (from New York). Example in using the Hamilton-Jacobi Method Integrating wrt time on both sides, we then have, 25 2 003 40 6 2 0 mA t Af f gt t t g m Since the Hamilton-Jacobi Equation only involves partial derivatives of S, can be taken to be zero without affect the dynamics and for simplicity, we will take the integration constant to be simply , i.e., << /S /GoTo /D (Outline0.2) >> \text { Newport } & 82,888 & 5.9061 & 5 & 6 \\ \text { Kent } & 166,158\\ 1. Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors. Found inside – Page 80following the 1840 census, after which a switch was made to Hamilton's method; the Webster method was resurrected after the 1900 ... This is called the state's quota (for example, the quota for state 1 at t + 1 is 752/150 = 5,013). 2. a method of dividing a whole into various parts. \textbf{ Total } & \bf{ 1,052,567 } & \end{array}\). \text { Providence } & 626,667\\ %���� After each state's population is divided by the divisor, the whole number of the quotient is kept and the fraction dropped. 2 The geometric picture But why have we taken the trouble to do all this, and what is the geometric picture of the new Q,P? \text { Washington } & 126,979 & 9.0478 & 9\\ Find each state's Standard Quota. 0��W�;1�+&��LN�-HE�ړ^d��a� �1B#��JL.H*(�l�,-7������ڭT���l�1��%�.���. endobj Found inside – Page 22One example of a method that is not population monotone is Hamilton's. The 19 censuses from 1791 to 1970 were used to extrapolate (using compound growth state by state) the populations of the states for each year between censuses, ... Sábado & Domingo : Fechado, © Copyright 2021. Found inside – Page 280I'll give a recent example later in this section. To illustrate the problems, suppose 25 seats are to ... Hamilton's Method seems to be reasonable, and it was used for a considerable period of time in the USA. But, when first proposed, ... \text { Kent } & 166,158 & 11.8395 & 11 \\ 23 0 obj Cut and choose detailed examples. Found inside – Page 351For example we will use the Hamilton's method. TP is the sum of the number of instructions of the available tasks and p is the number of available processors. Then the standard quota is calculated as the fraction of ... Meh - Algebra is in obtaining the generalized momenta and Hamiltonian, not in obtaining the equations of motion. Hamilton's Method of Apportionment Found inside – Page 95It should be noted that in this particular example , Jefferson's method gives a southern state , Virginia , one more seat than it would receive according to Hamilton's method , which would give this seat to Connecticut . (3.) \text { County } & \text { Population } & \text{ Quota } & \text{ Initial } & \text{ Final } \\ He follows these steps: Make sure that each state ends up with at least one representative! H = 1 2 m p x 2 + p z 2 + m g z . We need 41 representatives and this only gives 40. \textbf{ Total } & \bf{ 897,934 } & \end{array}\). Then it was decided that because of the country’s growing population, the House of Representatives should be made larger. This cookie is set by GDPR Cookie Consent plugin. The remaining one goes to the county with the largest decimal part, which is New Castle: \(\begin{array}{lrrcc} Cut and Choose: example; Cut and Choose: example; Cut and Choose: example; Claim and Challange: example . Part of the Washington Open Course L. Hamilton's Method; Province A B C D E F Total; Population : Number of seats: Standard divisor: Exact quota: Lower quota: Frac. Now we determine each county’s quota by dividing the county’s population by the divisor: \(\begin{array}{lr} Jacobi (1837) applied the method to the general problems of classical variational calculus. Check out our new LibreCommons search portal. Phys., 79(1):12-49, 1988. Hamilton's Method; Province A B C D E F Total; Population : Number of seats: Standard divisor: Exact quota: Lower quota: Frac. The post-1880 apportionment had been completed, using Hamilton’s method and the new population numbers from the census. Hamilton's Method •Step 1. . S depends on L, and L in turn depends on the function x(t) via eq. These cookies track visitors across websites and collect information to provide customized ads. Hamilton's Apportionment Method. 2. This makes the standard divisor (4) D = 20,000 200 = 100. Found inside – Page 472An apportionment method M assigns , at least , one apportionment a = ( a1 , 22 , ... , an ) to each feasible problem ( v ... For example , it is well - known that the solution a provided by the socalled Hamilton method minimizes the ... Sealed . 24 0 obj Lagrange's and Hamilton's Equations In this chapter, we consider two reformulations of Newtonian mechanics, the Lagrangian and the Hamiltonian formalism. The fundamentals of the Hamilton-Jacobi theory were developed by W. Hamilton in the 1820s for problems in wave optics and geometrical optics. Found inside – Page 485Hamilton's method does not satisfy the Axiom 3. For example, when h = 20, (P1, P2,P3) = (103,63,34), the apportionment is (a1,a2,.a3) = (10,6,4). But if h = 21, the apportionment is (a1,a2,.a3) = (11,7,3). Hamilton and Hamilton's study of the dress of Karen females is: A scholarly . His method was approved by Congress in 1791, but was vetoed by President Washington. Found inside – Page 244For the distributed parameter systems considered in this chapter, Hamilton's method also prescribes the relevant ... Example 7.2.2 To illustrate the use of Hamilton's principle, consider the longitudinal vibration of a thin rod or bar ... He begins by determining, to several decimal places, how many things each group should get. First, we determine the divisor: \(897,934/41 = 21,900.82927\). (2.) We're concerned with minimizingR t2 t1 f (y(t), y˙(t); t) dt The minimization leads . \text { Washington } & 126,979 & 9.0478\\ Todos sistema de cabeamento estruturado, telefonia ou óptico precisa de uma infra-estrutura auxiliar para roteamento e proteção de seus cabos, visando garantir a performance e durabilidade de seus sistemas de cabeamento estruturado, dentro das normas aplicáveis, garantindo a qualidade de seu investimento. Unfortunately for Hamilton, President Washington vetoed its selection. This cookie is set by GDPR Cookie Consent plugin. 31 0 obj This mathematical analysis has its roots in the US Constitution specifically in 1790 when the House of Representatives attempted to apportion themselves. E-mail : contato@fibertectelecom.com Hamilton's equations for the three dimensional dynamics of a rigid body in terms of Euler parameters, and hence suitable for use in simulations involving arbitrary rotational motion. \textbf{ Total } & \bf{ 897,934 } & & \bf{ 40 } & \bf { 41 } \end{array}\). endobj \text { Kent } & 162,310 & 7.4111 & 7 & 7 \\ The problem is that Hamilton’s method is subject to several paradoxes. \text { Newport } & 82,888\\ Lowndes's Method looks at relative fraction. Hamiltonian Mechanics. First, the State Anxiety Scale (S-Anxiety) evaluates the current state of anxiety, asking how respondents feel "right now," using items that measure subjective feelings of apprehension, tension, nervousness, worry, and activation/arousal of the autonomic nervous system. Video Calculate apportionment using Jefferson's Method The apportionment method suggested by future president Thomas Jefferson as a competitor to Hamilton's method. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Found inside – Page 172Apportionment using Hamilton's Method Pop 9% Ouo Seats Pop 9% Ouo I R Seats Pop 9% Quo I R Seats X 50 .50 5.0 5 X 53 .53 5.3 5 .3 5 X 53 .53 5.8 5 ... For example, suppose that the size of the legislature is increased to n = 11 seats. And not only actually is this one a good way of approximating what the solution to this or any differential equation is, but actually for this differential equation in particular you can actually even use this to find E with more and more and more precision. It was later adopted in 1852 and used through 1911. 20 0 obj Found inside – Page 445For example, if the population of state A was 94,700 and the standard divisor was d 5 20,100, then state A's standard ... If the standard quota is an exact integer, then the lower quota equals the standard quota. n hamilton's method We ... (Bold numbers could be clicked upon. Basic to advanced level. Take advantage of them, and keep several decimal places. The Hamilton method of apportionment is actually a largest-remainder method which uses the Hare Quota. Alexander Hamilton was President Washington's Secretary of the Treasury and was an ardent nationalist who believed a strong federal government could solve many of the new country's financial ills. \hline endobj Found inside – Page 95It should be noted that in this particular example, Jefferson's method gives a southern state, Virginia, one more seat than it would receive according to Hamilton's method, which would give this seat to Connecticut. This example, though ... 28 0 obj History of Hamilton's Method -The apportionment method was suggested by Alexander Hamilton was approved by Congress in 1791. Do this by dividing the total population of all the states by the total number of representatives. In 1792 President George Washington vetoed a bill authorizing Hamilton's method of apportionment. << /S /GoTo /D [33 0 R /Fit ] >> After seeing Hamilton’s method, many people find that it makes sense, it’s not that difficult to use (or, at least, the difficulty comes from the numbers that are involved and the amount of computation that’s needed, not from the method), and they wonder why anyone would want another method. To begin, we will go back. But Hamilton's method also displays unacceptable behavior when the House size is fixed and the state populations change. By itself, that doesn’t mean that Virginia should gain representatives or Maine shouldn’t, because there are lots of other states involved. 3 0 obj Apportionment: Jefferson's method. Found inside – Page 8The Alexander Hamilton's method, known also as the largest reminder method is an example of an apportionment method that is not house monotone. The Hamilton's method lead to the infamous paradox of Alabama in 1882, when a larger size of ... This book is a foundational guide to graph representation learning, including state-of-the art advances, and introduces the highly successful graph neural network (GNN) formalism. \textbf{ Total } & \bf{ 1,052,567 } & & \bf{ 72 }\end{array}\). 1791 The House, unable to override the veto, passed a new bill for a 105 member House and Jefferson . \text { New Castle } & 538,479 & 24.5872 \\ evolution is given by Hamilton's equations with some Hamiltonian K, and we have K= 0. 4. There are 2 subscales within this measure. /Length 1475 •Step 2. We found SD = 320000. q 1 = 9:375, q 2 = 18:75, and q 3 = 21:875. >> Calculate each state's standard quota. Hamilton's Method of Apportionment The cookie is used to store the user consent for the cookies in the category "Other. (Hamilton's Method) Jefferson's method was the first apportionment method used by the US Congress starting at 1791 through 1842 when it was replaced by Webster's method. 60 0 obj << \text { Sussex } & 197,145 \\ The Alabama Paradox is named for an incident that happened during the apportionment that took place after the 1880 census. endobj The aim of this book is the study of signals and deterministic systems, linear, time-invariant, finite dimensions and causal. Hamilton's Method looks at absolute fraction. \text { Sussex } & 197,145 & 9.0017 & 9 & 9 \\ \text { County } & \text { Population } & \text{ Quota } \\ These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc. 3. Instructor: Adil Aslam Linear Algebra 1 | P a g e My Email Address is: adilaslam5959@gmail.com Notes by Adil Aslam Definition: Cayley-Hamilton Theorem • "A square matrix satisfies its own characteristic equation". \hline \text { Bristol } & 49,875 & 3.5538 & 3 & 3 \\ Three of them happened, on separate occasions, when Hamilton’s method was used to apportion the United States House of Representatives. 1791 President Washington vetoes the above bill (first veto in US history!). Found inside – Page 437Example 20.2 Show the Hamilton Method Allows the Alabama Paradox Three courses (Statistics, Calculus, and Discrete Math), ... (a) Determine the apportionment of 30 teaching assistants to each of the courses using Hamilton's method. Give the surplus seats to the state with the largest fractional parts until there are no more surplus seats. Found inside – Page 420It has a certain superficial similarity to Hamilton's method , and , in so far , is effective enough , but it lacks ... Take as an example Hamilton's own treatment of the curvature of surfaces , to which in one of his notes Professor ... The fatal flaw with Hamilton's method is the Alabama Paradox. A local department store has budgeted for 120 eight-hour retail shifts to be staffed every week. This video explains and provides an example of the Hamilton's method of apportionment..Site: http://mathispower4u.com Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. Lesson 4.4 - Jefferson's Method Exercise 1 Period _____ Following the 1790 census, Congress passed the first "bill of apportionment" in 1792. Cras dapibus. The apportionment method suggested by Alexander Hamilton was approved by Congress in 1791, but was subsequently vetoed by president Washington - in the very first exercise of the veto power by President of the United States. Integer tincidunt. Problems of the Cayley-Hamilton Theorem. \text { Kent } & 166,158 & 11.8395 & 11 & 12 \\ A different method proposed by Thomas Jefferson was used instead for the next 50 years. Found inside – Page 182Thus Hamilton defined his point characteristic function S(5, F' ) that provides the optical distance between a point is on a ... While some notable scientists learned and applied Hamilton's method (Maxwell, for example, used it in his ... This cookie is set by GDPR Cookie Consent plugin. Hamilton Hamilton, Canada Hamilton, New Zealand Hamilton College Hamilton College, London Hamilton's bandage Hamilton's method Hamilton's pseudophlegmon Hamilton's test Hamirostra melanosternon Hamish Hamit Altintop Hamito-Semitic hamlet Hamlin Hamline University Hamm Hamm, Germany hammal hammam Hamman-Rich syndrome Hamman's disease Hamman's . Find the standard divisor 2. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. In linear algebra, the Cayley-Hamilton theorem (termed after the mathematicians Arthur Cayley and William Rowan Hamilton) says that every square matrix over a commutative ring (for instance the real or complex field) satisfies its own characteristic equation. (Assignment) \text { County } & \text { Population } & \text{ Quota } & \text{ Initial }\\ Jefferson's method was the first apportionment method . Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. 4. Later, Hamilton's method was used off and on between 1852 and 1901. Content . endobj Site Desenvolvido por SISTED Hospedagem 4INFRATI. 12 0 obj Hamilton's principle of least action: a system moves from q(t1)toq(t2) in such a way that the following integral takes on the least possible value. Found inside – Page 333Alexander Hamilton, Alastair Hamilton, Julius Goebel (Jr.) Joseph Henry Smith ... paper ” setting out an outline for an extended argument on the issue.127 This brief is of particular interest as a typical example of Hamilton's method . Found insideFurther comments on the Hamilton-Jacobi method. Examples. 6-2. Special Transformations Some simple transformations. Homogeneous canonical transformations. Point transformations. Momentum transformations. Examples. 6-3. Round down. It does not store any personal data. The cookies is used to store the user consent for the cookies in the category "Necessary". 2. 3.1 The principle of d'Alembert. 1 The Use of the Cayley-Hamilton Theorem to Reduce the Order of a Polynomial in A Consider a square matrix A and a polynomial in s, for example P(s). The bill, sponsored by Alexander Hamilton, established a House of Representatives with 120 seats apportioned under the method we now call Hamilton's Method. His method was approved by Congress in 1791, but was vetoed by President Washington. We stuck flies to popsickle sticks by pushing their wings into a sticky wax we rubbed on the sticks. \text { New Castle } & 538,479 & 24.5872 & 24\\ These cookies ensure basic functionalities and security features of the website, anonymously. Found inside – Page 438EXAMPLE 5 Hamilton's Apportionment = The first congressional apportionment involved 15 states , and the House had ... Neither President Washington nor Alexander Hamilton were aware of the Webster method of apportionment , but even if ... For this next example, let's try using the Cayley-Hamilton theorem to find A n for n=3. Found inside – Page 10As an example , it is easily verified that the congruence defined by a = x / r , B = ylr , y = 2/1 , ( r2 = x2 + y2 + z2 ) , is a normal congruence . On the other hand , it may be shown that the congruence defined by a = ylr , B = -x ... In history, that is. It is named after Alexander Hamilton, who invented the largest-remainder method in 1792. Suppose we find Hamilton's principal function, S xi;t. Its relationship to the momentum, p i = @S @xi, Step 2: Round the standard quota's down and give to each state its lower quota. Found inside – Page 558... q1(t) I t*vO*cos(alpha) q2(t) I t*vO*sin(alpha) — (g*t"2)\2 q3(t) I q30 + omega0*t For this example, the equations are identical with the equations obtained with Hamilton's method. Example 7.4. For the double pendulum shown in Fig. The Hamilton/Vinton Method sets the divisor as the proportion of the total population per house seat. This requirement can be satisfied if and only if This cookie is set by GDPR Cookie Consent plugin. A derivation of Lagrange's equations 70 3.2 Hamilton's principle 73 3.3 Derivation of Lagrange's equations 75 3.4 Generalization to many coordinates 75 3.5 Constraints and Lagrange's λ-method 77 3.6 Non-holonomic constraints 81 3.7 Virtual work 83 3.7.1 Physical interpretation of the Lagrange . /Filter /FlateDecode A Simple Example of the Hamilton-Jacobi Equation: Motion Under Gravity. endobj Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. We have a country with three states, a legislature with 200 seats, and a total population of 20,000. (Jefferson's Method) Found inside – Page 438EXAMPLE. 5. Hamilton's. Apportionment. The first congressional apportionment involved 15 states, and the House had ... Washington was probably aware of this technicality, making it likely that his objection to the Hamilton method was ... Consider the path that gives the shortest distance between two points in the plane, say (x 1;y 1) and (x 2;y 2). Hamilton method does have the Alabama paradox (named after the state that was first the victim of this phenomenon). A simple example is shown in Table 2. (Examples) Telefone : +55 11 3935-1679, Horário Comercial: Assuming that the total from Step 3 was less than the total number of representatives, assign the remaining representatives, one each, to the states whose decimal parts of the quota were largest, until the desired total is reached. The Quota Rule isn’t a law of any sort, but just an idea that some people, including Hamilton, think is a good one. . example? The paradox is that Alabama ended up losing a representative in the process, even though no populations were changed and the total number of representatives increased. Lagrangian Mechanics. 19 0 obj This answer is called the, Divide each state’s population by the divisor to determine how many representatives it should have. \textbf{ Total } & \bf{ 897,934 } & & \bf{ 40 }\end{array}\). << /pgfprgb [/Pattern /DeviceRGB] >> \hline Estar entre as melhores empresas prestadoras de serviços e ser referência em fornecimento de serviços de telecomunicações e ampliar negócios fora do Brasil. J. Comput. We need 75 representatives and we only have 72, so we assign the remaining three, one each, to the three counties with the largest decimal parts, which are Newport, Kent, and Providence: \(\begin{array}{lrrcc} 4.2: Hamilton's Method. Let us apply Hamilton-Jacobi method to a harmonic oscillator. \text { Providence } & 626,667 & 44.6528 & 44 & 45 \\ The issue of fair representation will take center stage as U.S. congressional districts are reapportioned based on the 2000 Census. This means that Q,P will remain constant during the evolution, and we have explicitly seen that this will be so. Hamilton's writing-intensive curriculum and my experience in the Writing Center have been invaluable to me in my professional career. This example demonstrates that: O Hamilton s Method may violate the quota rule. Os sistemas de cabeamento baseados em fibra óptica estão cada vez mais presentes, seja pela demanda dos sistemas por maior largura de banda, sua imunidade e ruídos eletro-magnéticos ou mesmo pelo custo, hoje bastante atrativo. Record this answer to several decimal places. The first method adopted in 1790 was the Jefferson Plan suggested by Thomas Jefferson. 4.10 Variational Methods in Solid Mechanics 104 4.10.1 Principle of Minimum Potential Energy 104 4.10.2 Principle of Minimum Complementary Energy 105 4.10.3 Principle of Stationary Reissner Energy 106 4.10.4 Hamilton's Principle 107 4.11 Applications of Hamilton's Principle 115 4.11.1 Equation of Motion for Torsional Vibration of a Shaft (Free 4.3 Hamilton's Principle Hamilton's Principle is concerned with the minimization of a quantity (i.e., the action) in a manner that is identical to extremum problems solved using the calculus of variations. \text { Newport } & 82,888 & 5.9061\\ The Population Paradox happened between the apportionments after the census of 1900 and of 1910. Euler's Method. Prepared by Professor Zoran Gajic 8-48 The problem of apportionment started long ago when our country was just beginning. State B has 6,936,000 people and State E has 685,000 people. Hamilton's Principle can be stated as follows: The motion of a system from time t 1 to t 2 is such that the line integral \text { County } & \text { Population } & \text{ Quota }\\ The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. Hamilton's method is fair until surplus items are added. The apportionment method suggested by future president Thomas Jefferson as a competitor to Hamilton's method. Classic Books Library presents this brand new edition of “The Federalist Papers”, a collection of separate essays and articles compiled in 1788 by Alexander Hamilton. Hamilton's Method Step 1: Calculate each state's lower quota. Hamilton's method won out over Jefferson's method. State Population standard quota lower quota extra seat Hamilton's A 940 . “Este site utiliza cookies para permitir uma melhor experiência por parte do utilizador. • Two good introductory books: - James A . Note on rounding: Today we have technological advantages that Hamilton (and the others) couldn’t even have imagined. For example, assume we have four states with the populations given in the table below with 68 representatives in the House. Example: 250 seats are being apportioned among 6 states. Ofertar soluções completas em serviços, que possam suprir com excelência as necessidades de nossos clientes, fidelizando parcerias e garantindo os melhores resultados. << /S /GoTo /D (Outline0.4) >> Presente desde 1999 no mercado brasileiro, a Fibertec Telecom surgiu como uma empresa de serviços de telecomunicações e ampliou sua atividades com inovadoras soluções de ITS em rodovias, aeroportos e ferrovias. Jefferson, of course, had political reasons for wanting his method to be used rather than Hamilton's. Primarily, his method favors larger states, and his own home state of Virginia was the largest in the country at the time. Virginia started with more people, grew at a faster rate, grew by more people, and ended up with more people than Maine. \text { Newport } & 82,888 & 5.9061 & 5 \\
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