Apportionment Using the Hamilton Method
Dawn Ambrose
Argosy University- On-line
MAT109 A01
Instructor: Marcus Vandiver

Apportionment Using the Hamilton Method
Using the Hamilton method of apportionment, determine the number of seats each state should receive.

Using the numbers you just calculated from applying the Hamilton method, determine the average constituency for each state. Explain your decision making process for allocating the remaining seats. As can be seen in the chart above, the additional seats were given to the states with the higher fractional parts (states # 1, 2, 3, 8 and 10). Explain how changes in state boundaries or populations could affect the balance of representation in this congress. Provide an example using the results above. The changes in state boundaries could affect the balance of representation in congress because if the population was to increase, the number of seats for the state would decrease and vice versa, if the population declined, the state could gain a seat or remain the same. How and why could an Alabama Paradox occur?

The Alabama Paradox means that if the total number of items to be apportioned increases, the group or state may loss an item. Explain how applying the Huntington-Hill apportionment method helps to avoid an Alabama Paradox. The Huntington- Hill apportionment method was an equal proportions method. It had a fixed house to avoid conflict and by using a fixed house number, the Huntington- Hill method helped to avoid an Alabama Paradox. Based upon your experience in solving this problem, do you feel apportionment is the best way to achieve fair representation? Be sure to support your answer. Yes, I believe apportionment is the best way to achieve fair representation because Huntington- Hill’s method seems to be working. I agree with a set number in the house because the population is forever changing. Just because a state has fewer people, does not mean they should not have the same or close to...

...
Apportionment
Maranda Jackson
Instructor: Terry VanNoy
General Education Mathematics
Argosy University
2/26/2014
Methods of apportionment are mathematical techniques used to allocate resources such as police officers in a certain city or congressional seats. These techniques are quite complicated and are based on several variables depending on which method one is choosing to use. Two of the most famousmethods for solving apportionment problems are known as The HamiltonMethod and The Huntington-Hill Principle. In this paper we will start by discussion the HamiltonMethod by pretending that 10 different states are to be assigned 100 congressional seats by usingapportionment.
The HamiltonMethod of Apportionment
The HamiltonMethod is a "common sense" method that Alexander Hamilton used to apportion the very first United States congress. With that being said, one could pretend that they have to divide or apportion 100 congressional seats among 10 states of the Union. To do this using The HamiltonMethod the population for each of the 10 states would have to be known. Then the population for all 10 states would need to be totaled. Once...

...CHAPTER 14: APPORTIONMENT
I. Basics
Example 1: Suppose a country consists of five states (North, South, East, West and Central) and representation in the National Assembly should be in proportion to each state’s population. The latest census figures are:
|North | 9279 |
|South | 7217 |
|East | 5155 |
|West | 3093 |
|Central | 2062 |
|Total |26,806 |
If there are 26 seats in the Assembly, how should they be apportioned among the five states?
Solution: Let’s start by dividing the total population by the number of seats: ____1031_______ . This tells us how many citizens each member of the National Assembly represents and is called the standard divisor.
The number of seats each state is entitled to, called its quota, is
North’s quota is _____9____ South’s quota is __7_______ East’s quota is ____5_____
West’s quota is ______3___ Central’s quota is _____2____
The two formulas above can be combined to yield:
Example 2: Suppose a later census is taken and the following population figures are revealed.
How should the 26 seats be apportioned among the 5 states?
Solution: Notice the quotas aren’t whole numbers any more. Round them off, you say? Std. Divisor = 1000
|State |Population |Std. Quota |Quota |Rounded quota |
|North | 9061...

...Bioresource Technology 100 (2009) 1192–1196
Contents lists available at ScienceDirect
Bioresource Technology
journal homepage: www.elsevier.com/locate/biortech
Optimization of culture conditions for hydrogen production by Ethanoligenens
harbinense B49 using response surface methodology
Wan-Qian Guo a, Nan-Qi Ren a,*, Xiang-Jing Wang b, Wen-Sheng Xiang b, Jie Ding a, Yang You a,
Bing-Feng Liu a
a
b
State Key Laboratory of Urban Water Resource and Environment, Harbin Institute of Technology, Harbin 150090, PR China
Research Center of Life Science and Biotechnology, Northeast Agricultural University, Harbin 150030, PR China
a r t i c l e
i n f o
Article history:
Received 16 May 2008
Received in revised form 28 July 2008
Accepted 28 July 2008
Available online 14 September 2008
Keywords:
Hydrogen production
Ethanol fermentation
Response surface methodology
Ethanoligenens harbinense B49
Culture conditions
a b s t r a c t
The design of an optimum and cost-efﬁcient medium for high-level production of hydrogen by Ethanoligenens harbinense B49 was attempted by using response surface methodology (RSM). Based on the Plackett–Burman design, Fe2+ and Mg2+ were selected as the most critical nutrient salts. Subsequently, the
optimum combination of the selected factors and the sole carbon source glucose were investigated by
the Box–Behnken design. Results showed that the maximum hydrogen yield of 2.21 mol/mol glucose...

...Mitchell v. Lovington Good Samaritan Center, Inc., 555 P.2d 696 (1976).
Facts: The appellee was terminated from the Lovington Good Samaritan Center, Inc. on June 4, 1974. On June 12, 1974 Mrs. Mitchell applied for unemployment compensation benefits. She was initially disqualified from seven weeks of benefits by a deputy of the Unemployment Security Commission. Mrs. Mitchell then filed an appeal, and the Appeal Tribunal reversed the deputy’s decision. Mrs. Mitchell’s benefits were reinstated on August 28, 1974. On September 13, 1974 the Center appealed the decision made by the Appeal tribunal to the whole Commission. The Commission overruled the Appeal Tribunal and reinstated the seven week disqualification period. Mrs. Mitchell then applied for and was granted certiorari from the decision of the Commission to the District Court of Bernalillo County. The District Court reversed the Commission’s decision and ordered the benefits to be reinstated. From the judgment of the District Court, the Center appeals.
Issue: The issue is whether Mrs. Mitchell’s actions constituted misconduct under § 59-9-5(b), N.M.S.A. 1953.
Rule: The term ‘misconduct’ is not defined in the Unemployment Compensation Law. The Wisconsin Supreme Court found that in a prior case no statutory definition of misconduct existed, and they formulated a definition for such. The Supreme Court of New Mexico adopts that definition, and hold that Mrs. Mitchell’s acts constituted misconduct.
Applying: Mrs....

...is cooled
by radiation and convection to its surroundings.
I decided to use 4th order Runge Kutta method to
solve the problem.
Objective
To solve the first order nonlinear ordinary
differential equations using numerical
method.
To understand the 4th order Runge Kutta
method and its applications.
Problem statement
Steel ball bearing radius 0.02m, ρ =
dT
7800kg/m3
A T 4 Ta4 mC
dt
The radiation equation is
The convection equation is
Assumed T0= 1200K and Ambient
temperature,
Assumed that all heat transfer in
radiation and convection only.
Mathematical model
Combining both convection and radiation
equation to form a new rate of heat lost
equation:
After subsitution of the constants, the
equation reduced to:
Preliminary Solution
Rewrite the equations:
=(((-2.20673*(10^-13))*(T^4))-((1.60256*(10^-2))*(T))
+(4.8095))
f(t,T)=(((-2.20673*(10^-13))*(T^4))-((1.60256*(10^-2))*(T))
+(4.8095))
Set
Runge Kutta 4th Order Solution
1
Ti 1 Ti k1 2k 2 2k3 k 4 h
6
k1 f (ti , Ti )
1
1
k 2 f (ti h, Ti k1h)
2
2
1
1
k3 f (ti h, Ti k 2 h)
2
2
k 4 f (ti h, Ti k3 h)
MATLAB IMPLEMENTATION
Result
Discussion and conclusion
The steel ball bearing will reach temperature
1000K at 15.3 seconds
The time taken for the ball bearing to cool from
1200K to 1000K is obtained by using the 4 th
order Runge Kutta method to analyze...

...UTT MATH1002 Weeks 3&4 Notes
Systems of ODEs
First-order linear equations with constant coefficients
[pic]
[pic]
Let [pic]
[pic]
Taking Laplace transforms of (1) and (2)
[pic]
[pic]
From (3) and (4)
[pic]
[pic]
We solve this system algebraically for [pic]and [pic] and obtain [pic] by taking inverse transforms.
Example [pic]
[pic]
[pic]
We have
[pic]
[pic]
[pic]
From (5) and (6)
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
Since [pic]
[pic]
[pic]
From (II)
[pic]
[pic]
[pic]
[pic]
[pic]
Since [pic]
[pic]
Solution:
[pic]
[pic]
Example
[pic]
Advanced Engineering Mathematics (Kreyszig)
Tank T1 initially contains 100 gal of pure water.
Tank T2 initially contains 100 gal of water in which 150lb of salt are dissolved
The inflow into T1 from outside is 6 gal/min with 6 lb of salt. Obtain the salt content [pic] and [pic] in T1 and T2 respectively. Assume that the mixtures are kept uniform.
[pic]
[pic]
[pic]
Taking Laplace transforms
[pic]
[pic]
[pic]
[pic]
[pic]
By Cramer’s Rule
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
Similarly,
[pic]
[pic]
Taking inverse transforms
[pic]
[pic]
Example
[pic][pic]
Advanced Engineering Mathematics (Kreyszig)
The above mechanical system consists of two bodies of mass 1 on 3 springs of the...

...references to relevant items in the category frame, per chosen unit of content.
- Express the results as an overall distribution of the chosen content sample in terms of the frequency of occurrence of the sought-for referents.
This procedure is based on two main assumptions: first, that the link between the external object of reference and the reference to it in the text will be reasonably clear and unambiguous, and second, that the frequency of occurrence of chosen references will validly express the predominant “meaning” of the text in an objective way. The method produces a statistical summary of a much larger media reality, it has been used especially for comparing media content with a known frequency distribution in “social reality”.
LIMITs 362
ARTHUR ASA BERGER: Media Research Techniques !!!!???? Missing!!!!
“ Media Analysis Techniques
97 C.A. is a standard sociological technique that uses statistical methods to make inferences about what is found in the media (:97).
-Historical frame of ref to make comparisons between earlier samples, is there more or less X? if so, what does it mean?
Topic: the representation of young men in Irish advertising.
The topic only addresses age and gender: young men, it does not specify any research questions or context, which leaves the analyst not being certain about which are the variables or measurable elements of interest (Hornig:87). The field is advertising, regarding representations, no context...

...Methods of Research
Jennifer Whitehead
CJ490
8/12/14
Professor Price
Methods of Research
Scientist conducts research on a daily basis. The purpose of this research is exploration, description, explanation, and application. In the area of criminal justice things are getting researched all of the time. Take murder for example, the police have to explore to find out what actually happened. They have to describe the events leading up the the murder. They have to explain the facts to try and come up with a suspect. Finally, they have to use the process of application to put it all together so they can make an arrest. When using the different purposes of research it is important to examine each purpose by itself because each purpose has its own different aspect when it comes to research design.
The exploration stage is the first stage that researchers begin with when using research methods. “This stage is typically done for three purposes: to satisfy the researcher does curiosity and desires for better understand, to test the feasibility of undertaking a more extensive study, and to develop the methods to be employed in any subsequent studies.” (Crossman, 2014) A researcher will use the exploration stage of research when they want to find out about something that there is little known about. Take drugs for example; let’s say a researcher wants to find out how bad the drug problem is...

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