Nature of Mathematics (MindTap Course List)
13th Edition
ISBN: 9781133947257
Author: karl J. smith
Publisher: Cengage Learning
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Chapter 17.3, Problem 2PS
To determine
To explain:
The arithmetic mean and the geometric mean.
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5. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.AE.003.
y
y= ex²
0
Video Example
x
EXAMPLE 3
(a) Use the Midpoint Rule with n = 10 to approximate the integral
कर
L'ex²
dx.
(b) Give an upper bound for the error involved in this approximation.
SOLUTION
8+2
1
L'ex² d
(a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.)
dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)]
0.1 [0.0025 +0.0225
+
+ e0.0625 + 0.1225
e0.3025 + e0.4225
+ e0.2025
+
+ e0.5625 €0.7225 +0.9025]
The figure illustrates this approximation.
(b) Since f(x) = ex², we have f'(x)
=
0 ≤ f'(x) =
< 6e.
ASK YOUR TEACHER
and f'(x) =
Also, since 0 ≤ x ≤ 1 we have x² ≤
and so
Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final
answer to five decimal places.)
6e(1)3
e
24(
=
≈
1. Consider the following preference ballots:
Number of voters
Rankings 6 5 4 2
1st choice A DCB
DC
2nd choice B B D
3rd choice DCBD
4th choice CA
AAA
For each of the four voting systems we have studied, determine who would win the election
in each case. (Remember: For plurality with runoff, all but the top two vote-getters are
simultaneously eliminated at the end of round 1.)
Practice
k Help
ises
A
96
Anewer The probability that you get a sum of at least 10 is
Determine the number of ways that the specified event can occur when
two number cubes are rolled.
1. Getting a sum of 9 or 10
3. Getting a sum less than 5
2. Getting a sum of 6 or 7
4. Getting a sum that is odd
Tell whether you would use the addition principle or the multiplication
principle to determine the total number of possible outcomes for the
situation described.
5. Rolling three number cubes
6. Getting a sum of 10 or 12 after rolling three number cubes
A set of playing cards contains four groups of cards designated by color
(black, red, yellow, and green) with cards numbered from 1 to 14 in each
group. Determine the number of ways that the specified event can occur
when a card is drawn from the set.
7. Drawing a 13 or 14
9. Drawing a number less than 4
8. Drawing a yellow or green card
10. Drawing a black, red, or green car
The spinner is divided into equal parts.
Find the specified…
Chapter 17 Solutions
Nature of Mathematics (MindTap Course List)
Ch. 17.1 - Prob. 1PSCh. 17.1 - Prob. 2PSCh. 17.1 - Prob. 3PSCh. 17.1 - Prob. 4PSCh. 17.1 - Prob. 5PSCh. 17.1 - Prob. 6PSCh. 17.1 - Prob. 7PSCh. 17.1 - Prob. 8PSCh. 17.1 - Prob. 9PSCh. 17.1 - Prob. 10PS
Ch. 17.1 - Prob. 11PSCh. 17.1 - Prob. 12PSCh. 17.1 - Prob. 13PSCh. 17.1 - Prob. 14PSCh. 17.1 - In voting among three candidates, the outcomes are...Ch. 17.1 - Prob. 16PSCh. 17.1 - Prob. 17PSCh. 17.1 - Prob. 18PSCh. 17.1 - Prob. 19PSCh. 17.1 - In voting among four candidates, the outcomes are...Ch. 17.1 - Prob. 21PSCh. 17.1 - In voting among four candidates, the outcomes are...Ch. 17.1 - In voting among four candidates, the outcomes are...Ch. 17.1 - Prob. 24PSCh. 17.1 - a.How many different ways can a voter rank 3...Ch. 17.1 - Prob. 26PSCh. 17.1 - How many different ways can a voter rank n...Ch. 17.1 - Prob. 28PSCh. 17.1 - Prob. 29PSCh. 17.1 - Prob. 30PSCh. 17.1 - In voting method among three candidates, the...Ch. 17.1 - Prob. 32PSCh. 17.1 - Prob. 33PSCh. 17.1 - Prob. 34PSCh. 17.1 - Twelve board members are voting on after-meeting...Ch. 17.1 - Prob. 36PSCh. 17.1 - Prob. 37PSCh. 17.1 - Prob. 38PSCh. 17.1 - Prob. 39PSCh. 17.1 - Twelve people serve on a board and are considering...Ch. 17.1 - Twelve people serve on a board and are considering...Ch. 17.1 - Twelve people serve on a board and are considering...Ch. 17.1 - Twelve people serve on a board and are considering...Ch. 17.1 - Prob. 44PSCh. 17.1 - Prob. 45PSCh. 17.1 - Prob. 46PSCh. 17.1 - Seventeen people serve on a board and are...Ch. 17.1 - Seventeen people serve on a board and are...Ch. 17.1 - Prob. 49PSCh. 17.1 - Prob. 50PSCh. 17.1 - Prob. 51PSCh. 17.1 - Prob. 52PSCh. 17.1 - Prob. 53PSCh. 17.1 - Suppose your college transcripts show the...Ch. 17.1 - Prob. 55PSCh. 17.1 - Prob. 56PSCh. 17.1 - Prob. 57PSCh. 17.1 - Prob. 58PSCh. 17.1 - Prob. 59PSCh. 17.1 - Prob. 60PSCh. 17.2 - Prob. 1PSCh. 17.2 - Prob. 2PSCh. 17.2 - Prob. 3PSCh. 17.2 - Prob. 4PSCh. 17.2 - Prob. 5PSCh. 17.2 - Prob. 6PSCh. 17.2 - Prob. 7PSCh. 17.2 - Prob. 8PSCh. 17.2 - Prob. 9PSCh. 17.2 - Prob. 10PSCh. 17.2 - Prob. 11PSCh. 17.2 - Prob. 12PSCh. 17.2 - An election with three candidates has the...Ch. 17.2 - Prob. 14PSCh. 17.2 - Consider the following voting situation:...Ch. 17.2 - Consider the following voting situation:...Ch. 17.2 - Prob. 17PSCh. 17.2 - The philosophy department is selecting a...Ch. 17.2 - The Adobe School District is hiring a vice...Ch. 17.2 - The seniors at Weseltown High School are voting...Ch. 17.2 - The seniors at Weseltown High School are voting...Ch. 17.2 - Prob. 22PSCh. 17.2 - Prob. 23PSCh. 17.2 - Prob. 24PSCh. 17.2 - The seniors at Weseltown High School are voting...Ch. 17.2 - The seniors at Weseltown High School are voting...Ch. 17.2 - The seniors at Weseltown High School are voting...Ch. 17.2 - The seniors at Weseltown High School are voting...Ch. 17.2 - Prob. 29PSCh. 17.2 - A focus group of 33 people for ABCTV were asked to...Ch. 17.2 - Prob. 31PSCh. 17.2 - Prob. 32PSCh. 17.2 - Prob. 33PSCh. 17.2 - Prob. 34PSCh. 17.2 - Prob. 35PSCh. 17.2 - Prob. 36PSCh. 17.2 - Prob. 37PSCh. 17.2 - Prob. 38PSCh. 17.2 - HISTORICAL QUEST In 1993 the 101st International...Ch. 17.2 - The U.S. president is elected with a vote of the...Ch. 17.2 - HISTORICAL QUEST Article 7 of the French...Ch. 17.2 - A group of fun-loving people have decided to play...Ch. 17.2 - A group of fun-loving people have decided to play...Ch. 17.2 - Prob. 44PSCh. 17.2 - Prob. 45PSCh. 17.2 - The fraternity is electing a national president,...Ch. 17.2 - The fraternity is electing a national president,...Ch. 17.2 - The fraternity is electing a national president,...Ch. 17.2 - Prob. 49PSCh. 17.2 - Consider an election with three candidates with...Ch. 17.2 - Consider an election with four candidates with the...Ch. 17.2 - Prob. 52PSCh. 17.2 - Consider an election with four candidates with the...Ch. 17.2 - Prob. 54PSCh. 17.2 - Consider an election with three candidates with...Ch. 17.2 - Prob. 56PSCh. 17.2 - Prob. 57PSCh. 17.2 - Prob. 58PSCh. 17.2 - Prob. 59PSCh. 17.2 - The Game of WIN Construct a set of nonstandard...Ch. 17.3 - Prob. 1PSCh. 17.3 - Prob. 2PSCh. 17.3 - Prob. 3PSCh. 17.3 - IN YOUR OWN WORDS What is the quota rule? Does...Ch. 17.3 - Prob. 5PSCh. 17.3 - Prob. 6PSCh. 17.3 - Prob. 7PSCh. 17.3 - Prob. 8PSCh. 17.3 - Prob. 9PSCh. 17.3 - Prob. 10PSCh. 17.3 - Modified quotas are given in Problems 714. Round...Ch. 17.3 - Prob. 12PSCh. 17.3 - Prob. 13PSCh. 17.3 - Prob. 14PSCh. 17.3 - Find the standard divisor to two decimal places...Ch. 17.3 - Prob. 16PSCh. 17.3 - Prob. 17PSCh. 17.3 - Prob. 18PSCh. 17.3 - Prob. 19PSCh. 17.3 - Prob. 20PSCh. 17.3 - Prob. 21PSCh. 17.3 - Prob. 22PSCh. 17.3 - For the given year, find the standard quotas for...Ch. 17.3 - For the given year, find the standard quotas for...Ch. 17.3 - For the given year, find the standard quotas for...Ch. 17.3 - For the given year, find the standard quotas for...Ch. 17.3 - For the given year, find the standard quotas for...Ch. 17.3 - For the given year, find the standard quotas for...Ch. 17.3 - Consider the populations given in Problems 2932....Ch. 17.3 - Consider the populations given in Problems 2932....Ch. 17.3 - Consider the populations given in Problems 29-32....Ch. 17.3 - Consider the populations given in Problems 29-32....Ch. 17.3 - Consider the populations given in Problems 33-36....Ch. 17.3 - Consider the populations given in Problem. a.Find...Ch. 17.3 - Prob. 35PSCh. 17.3 - Prob. 36PSCh. 17.3 - Prob. 37PSCh. 17.3 - Prob. 38PSCh. 17.3 - Prob. 39PSCh. 17.3 - Prob. 40PSCh. 17.3 - Consider the following apportionment problem for...Ch. 17.3 - Prob. 42PSCh. 17.3 - Prob. 43PSCh. 17.3 - Consider the following apportionment problem for...Ch. 17.3 - Prob. 45PSCh. 17.3 - Consider the following apportionment problem:...Ch. 17.3 - Prob. 47PSCh. 17.3 - Prob. 48PSCh. 17.3 - Prob. 49PSCh. 17.3 - Consider the following apportionment problem:...Ch. 17.3 - Consider the following apportionment problem:...Ch. 17.3 - Consider the following apportionment problem:...Ch. 17.3 - Consider the following apportionment problem:...Ch. 17.3 - Prob. 54PSCh. 17.3 - Prob. 55PSCh. 17.3 - Prob. 56PSCh. 17.3 - Consider the following apportionment problem:...Ch. 17.3 - Prob. 58PSCh. 17.3 - Consider the following apportionment problem:...Ch. 17.3 - Consider the following apportionment problem:...Ch. 17.4 - Prob. 1PSCh. 17.4 - Prob. 2PSCh. 17.4 - Prob. 3PSCh. 17.4 - Prob. 4PSCh. 17.4 - Prob. 5PSCh. 17.4 - Prob. 6PSCh. 17.4 - Prob. 7PSCh. 17.4 - Prob. 8PSCh. 17.4 - Prob. 9PSCh. 17.4 - Prob. 10PSCh. 17.4 - Prob. 11PSCh. 17.4 - Prob. 12PSCh. 17.4 - Prob. 13PSCh. 17.4 - Prob. 14PSCh. 17.4 - Prob. 15PSCh. 17.4 - Prob. 16PSCh. 17.4 - Prob. 17PSCh. 17.4 - Prob. 18PSCh. 17.4 - Prob. 19PSCh. 17.4 - Prob. 20PSCh. 17.4 - Prob. 21PSCh. 17.4 - Prob. 22PSCh. 17.4 - Prob. 23PSCh. 17.4 - Prob. 24PSCh. 17.4 - Prob. 25PSCh. 17.4 - In Problems 2326, apportion the indicated number...Ch. 17.4 - Prob. 27PSCh. 17.4 - Prob. 28PSCh. 17.4 - Prob. 29PSCh. 17.4 - Prob. 30PSCh. 17.4 - Prob. 31PSCh. 17.4 - Prob. 32PSCh. 17.4 - Prob. 33PSCh. 17.4 - Prob. 34PSCh. 17.4 - Prob. 35PSCh. 17.4 - Prob. 36PSCh. 17.4 - Prob. 37PSCh. 17.4 - Prob. 38PSCh. 17.4 - Prob. 39PSCh. 17.4 - Prob. 40PSCh. 17.4 - Prob. 41PSCh. 17.4 - Prob. 42PSCh. 17.4 - Prob. 43PSCh. 17.4 - Prob. 44PSCh. 17.4 - Prob. 45PSCh. 17.4 - Prob. 46PSCh. 17.4 - Prob. 47PSCh. 17.4 - Prob. 48PSCh. 17.4 - Prob. 49PSCh. 17.4 - Prob. 50PSCh. 17.4 - Prob. 51PSCh. 17.4 - Prob. 52PSCh. 17.4 - Prob. 53PSCh. 17.4 - In problems 54-56, suppose the annual salaries of...Ch. 17.4 - In problems 54-56, suppose the annual salaries of...Ch. 17.4 - Prob. 56PSCh. 17.4 - Prob. 57PSCh. 17.4 - An elderly rancher died and left her estate to her...Ch. 17.4 - Prob. 59PSCh. 17.4 - Prob. 60PSCh. 17.CR - Prob. 1CRCh. 17.CR - Prob. 2CRCh. 17.CR - Prob. 3CRCh. 17.CR - Prob. 4CRCh. 17.CR - Prob. 5CRCh. 17.CR - Prob. 6CRCh. 17.CR - Prob. 7CRCh. 17.CR - Prob. 8CRCh. 17.CR - Prob. 9CRCh. 17.CR - Prob. 10CRCh. 17.CR - Prob. 11CRCh. 17.CR - Prob. 12CRCh. 17.CR - Chemistry is taught at five high schools in the...Ch. 17.CR - Prob. 14CRCh. 17.CR - Prob. 15CRCh. 17.CR - Prob. 16CRCh. 17.CR - Prob. 17CRCh. 17.CR - Prob. 18CRCh. 17.CR - Prob. 19CRCh. 17.CR - Prob. 20CR
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