Math 103, Section 11, Tuesday, February 22, 2011
Chapter 4 Handout
3
1. Submitted Homework Assignment
for Chapter 4 is at Sakai.
It is in the Assignments section and is called:
Assignment Chapter 4A
Please do Exercises Exercises 4, 14, and 20 , pages 144146 and
upload to Sakai.
Homework is due by Tuesday, February 22 at midnight.
Assignment Chapter 4B
Please do Exercises Exercises 26, 36, and 46 , pages 146147 and
upload to Sakai.
Homework is due by Thursday, February 24 at midnight.
Our first exam will be on Friday, March 4.
The exam will cover Chapters 1,2 and 4.
Quiz on Friday, February 25 covering Chapter 4
Extra credit problem:
Page 150, Project E, Parts 2 and 3
You do an apportionment using Hamilton’s Method with 105 seats and
you do an apportionment using Jefferson’s Method with 105 seats
and you compare the results. If you know Excel, I suggest you use
Excel.
Homework Solutions for Chapters 1 and 2 are at Sakai. Go to
Resources, Homework solutions.
Homework to be discussed on Tuesday, February 22. Exercises
27,37,47
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• Does the constitution stipulate an apportionment method? (Answer: no,
it just states that the number of seats in the House of Representatives
should be based on population census carried out every 10 years.)
• Who proposed the first apportionment bill (in 1792)? (Hamilton)
• Who vetoed that bill?
• What was the first ever presidential veto in U.S. History?
• What was the first method proposed in U.S. history? (Hamilton) What
was the first
method actually used in U.S. history? (Jefferson)
• When was Jefferson’s method discontinued? (1832 was the last year that
it was used)
• Why was Jefferson’s method discontinued? (In 1832 New York got 40
seats, but its standard quota was only 38.59 seats. An upper quota
violation).
• What methods were used after Jefferson’s method was discontinued?
(Webster’s and
Hamilton’s)
• What method is used today, since 1941? (HuntingtonHill)
• Does the constitution mandate the number of seats? (No)
• Has the number of seats M been the same throughout U.S. History? no
• Since 1941, how many seats does congress have? (M = 435)
• Which state recently challenged the use of HuntingtonHill? (Montana
in 1991 after
dropping from 2 seats to 1 seat.)
Adams’s method was never used.
Percentage decrease formula:
If you start with the number P and decrease it by x%, your new decreased
number S is:
S=Px%*P or S=(1x%)P
The new decreased number is (1x%) of the original number P.
Percentage increase formula
If you start with the number Pand increase it by x%, your new increased
number
S
is:
S
=P+x%*P or S= (1+x%)P
The new
increased number is (1+x%) times the original number.
Practice with increasing and decreasing
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 Spring '07
 Berkowitz
 Math, Partylist proportional representation, seats, Quota

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