Mathematics All Around (6th Edition)
6th Edition
ISBN: 9780134434681
Author: Tom Pirnot
Publisher: PEARSON
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Textbook Question
Chapter 11.1, Problem 2E
Five candidates running for mayor receive votes as follows:
Kinison,
a. Is there a candidate who earns a majority?
b. Who wins the election using the plurality method?
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Students have asked these similar questions
Problem 11 (a) A tank is discharging water through an orifice at a depth of T
meter below the surface of the water whose area is A m². The
following are the values of a for the corresponding values of A:
A 1.257 1.390
x 1.50 1.65
1.520 1.650 1.809 1.962 2.123 2.295 2.462|2.650
1.80 1.95 2.10 2.25 2.40 2.55 2.70
2.85
Using the formula
-3.0
(0.018)T =
dx.
calculate T, the time in seconds for the level of the water to drop
from 3.0 m to 1.5 m above the orifice.
(b) The velocity of a train which starts from rest is given by the fol-
lowing table, the time being reckoned in minutes from the start
and the speed in km/hour:
| † (minutes) |2|4 6 8 10 12
14 16 18 20
v (km/hr) 16 28.8 40 46.4 51.2 32.0 17.6 8 3.2 0
Estimate approximately the total distance ran in 20 minutes.
-
Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p − 1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
p-1
2
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
23
32
how come?
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
The set T is the subset of these residues exceeding
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p-1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
2
p-1
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
23
The set T is the subset of these residues exceeding
2°
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
how come?
Chapter 11 Solutions
Mathematics All Around (6th Edition)
Ch. 11.1 - Four candidates running for a vacant seat on the...Ch. 11.1 - Five candidates running for mayor receive votes as...Ch. 11.1 - The university administration has asked a group of...Ch. 11.1 - The university administration has asked a group of...Ch. 11.1 - The university administration has asked a group of...Ch. 11.1 - The university administration has asked a group of...Ch. 11.1 - The drama society members are voting for the type...Ch. 11.1 - The drama society members are voting for the type...Ch. 11.1 - The drama society members are voting for the type...Ch. 11.1 - The drama society members are voting for the type...
Ch. 11.1 - Before a conference on Trends in the next Decade,...Ch. 11.1 - Before a conference on Trends in the next Decade,...Ch. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - A small employee-owned Internet company is voting...Ch. 11.1 - Prob. 16ECh. 11.1 - Prob. 17ECh. 11.1 - A small employee-owned Internet company is voting...Ch. 11.1 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - In Exercises 23-26, refer to the preference table...Ch. 11.1 - Prob. 24ECh. 11.1 - In Exercises 23-26, refer to the preference table...Ch. 11.1 - Prob. 26ECh. 11.1 - In Exercises 27-30, refer to the preference table...Ch. 11.1 - In Exercises 27-30, refer to the preference table...Ch. 11.1 - In Exercises 27-30, refer to the preference table...Ch. 11.1 - Prob. 30ECh. 11.1 - Prob. 31ECh. 11.1 - Prob. 32ECh. 11.1 - Prob. 33ECh. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Prob. 37ECh. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.1 - Prob. 40ECh. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Prob. 43ECh. 11.1 - Math in Your Life: Between the Numbers Instant...Ch. 11.1 - In approval voting, a person can vote for more...Ch. 11.1 - Prob. 46ECh. 11.1 - Prob. 47ECh. 11.1 - Prob. 48ECh. 11.1 - Prob. 49ECh. 11.1 - Prob. 50ECh. 11.1 - Prob. 51ECh. 11.1 - Prob. 52ECh. 11.2 - Some of these exercises have no fixed solution...Ch. 11.2 - Some of these exercises have no fixed solution...Ch. 11.2 - Determining the legal drinking age. A state...Ch. 11.2 - Voting for the president of a club. A chapter of...Ch. 11.2 - Choosing a location for a research facility. Teach...Ch. 11.2 - Locating a new factory. The Land Mover Tractor...Ch. 11.2 - Reducing a budget. Due to a decrease in state...Ch. 11.2 - Voting on an award for best restaurant. A group of...Ch. 11.2 - Use the following preference table for Exercises 9...Ch. 11.2 - Use the following preference table for Exercises 9...Ch. 11.2 - Complete the preference table so that the Borda...Ch. 11.2 - Complete the preference table so that A is the...Ch. 11.2 - Prob. 13ECh. 11.2 - Make a preference table similar to the one given...Ch. 11.2 - Complete the preference table so that the...Ch. 11.2 - Does the plurality method satisfy the majority...Ch. 11.2 - Does the plurality-with-elimination method satisfy...Ch. 11.2 - Prob. 18ECh. 11.2 - Presidential election. One of the several...Ch. 11.2 - Prob. 20ECh. 11.2 - Prob. 21ECh. 11.2 - A run off election. Repeat Exercise 21 using this...Ch. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Voters are choosing among five options. Make a...Ch. 11.2 - Make a preference table, similar to the one given...Ch. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Prob. 32ECh. 11.2 - Prob. 33ECh. 11.2 - Prob. 34ECh. 11.2 - One of the voting methods we have been discussing...Ch. 11.3 - Prob. 1ECh. 11.3 - Prob. 2ECh. 11.3 - In Exercises 1-12, the weight represent voters A,...Ch. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - In Exercises 1-12, the weight represent voters A,...Ch. 11.3 - In Exercises 1-12, the weight represent voters A,...Ch. 11.3 - In Exercises 1-12, the weight represent voters A,...Ch. 11.3 - Prob. 10ECh. 11.3 - Prob. 11ECh. 11.3 - Prob. 12ECh. 11.3 - In Exercises 13-16, write out all winning...Ch. 11.3 - Prob. 14ECh. 11.3 - In Exercises 13-16, write out all winning...Ch. 11.3 - Prob. 16ECh. 11.3 - Prob. 17ECh. 11.3 - Prob. 18ECh. 11.3 - Prob. 19ECh. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Prob. 32ECh. 11.3 - In Exercises 29-34, determine the Banzhaf power...Ch. 11.3 - Prob. 34ECh. 11.3 - The system [3:1,1,1,1,1] is an example of a one...Ch. 11.3 - Prob. 36ECh. 11.3 - Consider the system [14:15,2,3,3,5] in which A is...Ch. 11.3 - Prob. 38ECh. 11.3 - Calculating power in the electoral college. After...Ch. 11.3 - Prob. 40ECh. 11.3 - Prob. 41ECh. 11.3 - Prob. 42ECh. 11.3 - Prob. 43ECh. 11.3 - In Example 5, we analyzed the voting power of the...Ch. 11.3 - In Example 5, we analyzed the voting power of the...Ch. 11.3 - Prob. 46ECh. 11.3 - Prob. 47ECh. 11.3 - Prob. 48ECh. 11.3 - Prob. 49ECh. 11.3 - Prob. 50ECh. 11.3 - A dummy in a weighted voting system is a voter...Ch. 11.3 - Prob. 52ECh. 11.3 - Prob. 53ECh. 11.3 - Prob. 54ECh. 11.3 - In Exercises 55 and 56, devise a voting system...Ch. 11.3 - Prob. 56ECh. 11.4 - In Exercises 1 4, use tree diagrams to find all...Ch. 11.4 - Prob. 2ECh. 11.4 - In Exercises 1 4, use tree diagrams to find all...Ch. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - In Exercises 1116, determine the Shapley-Shubik...Ch. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - The system [3:1,1,1,1,1] is an example of a one...Ch. 11.4 - Measuring power on a jury. We can consider a...Ch. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Prob. 21ECh. 11.4 - Measuring power on a theater guild. The Theater...Ch. 11.4 - Measuring power on a state committee. The college...Ch. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - A new social media company, Chirp, has an...Ch. 11.4 - Prob. 27ECh. 11.4 - Measuring power among states. Repeat Exercise 27...Ch. 11.4 - Explain the difference between the Banzhaf index...Ch. 11.4 - Prob. 30ECh. 11.4 - Prob. 31ECh. 11.4 - Prob. 32ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.CR - Prob. 1CRCh. 11.CR - Prob. 2CRCh. 11.CR - Prob. 3CRCh. 11.CR - Prob. 4CRCh. 11.CR - Prob. 5CRCh. 11.CR - Prob. 6CRCh. 11.CR - Prob. 7CRCh. 11.CR - Prob. 8CRCh. 11.CR - Prob. 9CRCh. 11.CR - Prob. 10CRCh. 11.CR - Prob. 11CRCh. 11.CR - Prob. 12CRCh. 11.CR - Prob. 13CRCh. 11.CR - Prob. 14CRCh. 11.CR - Prob. 15CRCh. 11.CR - Prob. 16CRCh. 11.CR - Prob. 17CRCh. 11.CR - Prob. 18CRCh. 11.CT - Prob. 1CTCh. 11.CT - Prob. 2CTCh. 11.CT - Prob. 3CTCh. 11.CT - Prob. 4CTCh. 11.CT - Prob. 5CTCh. 11.CT - Prob. 6CTCh. 11.CT - Prob. 7CTCh. 11.CT - Prob. 8CTCh. 11.CT - Prob. 9CTCh. 11.CT - Determine the Banzhaf power index for each voter...Ch. 11.CT - Prob. 11CTCh. 11.CT - Prob. 12CTCh. 11.CT - Prob. 13CTCh. 11.CT - Prob. 14CTCh. 11.CT - Prob. 15CTCh. 11.CT - Prob. 16CT
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