Basic College Mathematics (6th Edition) (What's New in Developmental Math)
6th Edition
ISBN: 9780134840420
Author: Elayn Martin-Gay
Publisher: PEARSON
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Chapter 9.1, Problem 64E
To determine
The average number of goals per game in 2013
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Consider the problem of minimising the Euclidean distance from the point (-4,5) in the plane to the set
of points (x, y) that have integer coordinates and satisfy the inequality:
x2
y²
+ ≤1.
4 9
(a) Use an exhaustive search to solve this problem.
(b) Use a local search method to solve this problem. First, define the search space and the neighbourhood.
Then, attempt to find the minimum starting from the initial point
(x, y) = (2,0).
The neighbourhood of a point should contain at least two distinct points but must not encompass
the entire feasible search space. Will your local search method find the global optimum?
Consider the relation ✓ on R² defined by
u ≤ v
u₁ + v₂+ 3u1 v² < u₂ + v³ + 3u²v₁
(u³ + v2 + 3u1v = u₂+ v³ + 3u²v₁ and u₂ < v2)
u = v
for any u, vЄR² with u = = (u1, u2), v = = (V1, V2).
or
우우
or
1. Prove that the relation ✓ is translation invariant. Hint: Use the formula of (a + b)³ for a, b = R.
2. Is the relation ✓ scale invariant? Justify your answer.
3. Is the relation ✓ reflexive? Justify your answer.
4. Is the relation ✓ transitive? Justify your answer.
5. Is the relation ✓ antisymmetric? Justify your answer.
6. Is the relation ✓ total? Justify your answer.
7. Is the relation ✓ continuous at zero? Justify your answer.
Let X = [−1, 1] C R and consider the functions ₤1, f2 : X → R to be minimised, where f₁(x) = x + x² and
f2(x) = x-x² for all x Є X. Solve the tradeoff model minøx µƒ₁(x)+ƒ2(x), for all values of µ ≥ 0. Show your
working.
Chapter 9 Solutions
Basic College Mathematics (6th Edition) (What's New in Developmental Math)
Ch. 9.1 - Use the pictograph shown in Example 1 to answer...Ch. 9.1 - Use the pictograph shown in Example 2 to answer...Ch. 9.1 - Prob. 3PCh. 9.1 - Prob. 4PCh. 9.1 - Prob. 5PCh. 9.1 - Prob. 6PCh. 9.1 - Prob. 7PCh. 9.1 - Prob. 8PCh. 9.1 - Prob. 9PCh. 9.1 - Prob. 1VRV
Ch. 9.1 - Fill in each blank with one of the choices...Ch. 9.1 - Fill in each blank with one of the choices...Ch. 9.1 - Fill in each blank with one of the choices...Ch. 9.1 - Prob. 1ECh. 9.1 - Prob. 2ECh. 9.1 - Prob. 3ECh. 9.1 - Prob. 4ECh. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - Prob. 7ECh. 9.1 - Prob. 8ECh. 9.1 - The following pictograph shows the average number...Ch. 9.1 - The following pictograph shows the average number...Ch. 9.1 - The following pictograph shows the average number...Ch. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - The National Weather Service has exacting...Ch. 9.1 - The National Weather Service has exacting...Ch. 9.1 - The National Weather Service has exacting...Ch. 9.1 - The National Weather Service has exacting...Ch. 9.1 - Prob. 23ECh. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - Prob. 26ECh. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - Use the information given to draw a vertical bar...Ch. 9.1 - Use the information given to draw a vertical bar...Ch. 9.1 - Use the information given to draw a vertical bar...Ch. 9.1 - Prob. 32ECh. 9.1 - Prob. 33ECh. 9.1 - Prob. 34ECh. 9.1 - Prob. 35ECh. 9.1 - Prob. 36ECh. 9.1 - Prob. 37ECh. 9.1 - Prob. 38ECh. 9.1 - Prob. 39ECh. 9.1 - Prob. 40ECh. 9.1 - Prob. 41ECh. 9.1 - Prob. 42ECh. 9.1 - Prob. 43ECh. 9.1 - Prob. 44ECh. 9.1 - Prob. 45ECh. 9.1 - Prob. 46ECh. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Prob. 49ECh. 9.1 - Prob. 50ECh. 9.1 - Prob. 51ECh. 9.1 - Prob. 52ECh. 9.1 - The following list shows the golf scores for an...Ch. 9.1 - Prob. 54ECh. 9.1 - Prob. 55ECh. 9.1 - Prob. 56ECh. 9.1 - Prob. 57ECh. 9.1 - Prob. 58ECh. 9.1 - Prob. 59ECh. 9.1 - Prob. 60ECh. 9.1 - Prob. 61ECh. 9.1 - Prob. 62ECh. 9.1 - Prob. 63ECh. 9.1 - Prob. 64ECh. 9.1 - Prob. 65ECh. 9.1 - Prob. 66ECh. 9.1 - Prob. 67ECh. 9.1 - Prob. 68ECh. 9.1 - Prob. 69ECh. 9.1 - Prob. 70ECh. 9.1 - Prob. 71ECh. 9.1 - Prob. 72ECh. 9.1 - Prob. 73ECh. 9.1 - Prob. 74ECh. 9.1 - Prob. 75ECh. 9.1 - Prob. 76ECh. 9.1 - Prob. 77ECh. 9.1 - Prob. 78ECh. 9.1 - Prob. 79ECh. 9.1 - Prob. 80ECh. 9.1 - Prob. 81ECh. 9.1 - Prob. 82ECh. 9.1 - Prob. 83ECh. 9.1 - Prob. 84ECh. 9.1 - Prob. 85ECh. 9.1 - Prob. 86ECh. 9.2 - Prob. 1PCh. 9.2 - Prob. 2PCh. 9.2 - Prob. 3PCh. 9.2 - Prob. 4PCh. 9.2 - Prob. 1VRVCh. 9.2 - Prob. 2VRVCh. 9.2 - Prob. 3VRVCh. 9.2 - Prob. 4VRVCh. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - The following circle graph shows the percent of...Ch. 9.2 - The total amount of land from the continents is...Ch. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Prob. 16ECh. 9.2 - Prob. 17ECh. 9.2 - The following circle graph shows the percent of...Ch. 9.2 - If this library has 125,600 books, find how many...Ch. 9.2 - If this library has 125,600 books, find how many...Ch. 9.2 - If this library has 125,600 books, find how many...Ch. 9.2 - Prob. 22ECh. 9.2 - Prob. 23ECh. 9.2 - Prob. 24ECh. 9.2 - Prob. 25ECh. 9.2 - Prob. 26ECh. 9.2 - Prob. 27ECh. 9.2 - Objective B Fill in each table. Round to the...Ch. 9.2 - Write the prime factorization of each number. See...Ch. 9.2 - Write the prime factorization of each number. See...Ch. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.2 - Prob. 36ECh. 9.2 - These oceans together make up 264,489,800 square...Ch. 9.2 - These oceans together make up 264,489,800 square...Ch. 9.2 - These oceans together make up 264,489,800 square...Ch. 9.2 - Prob. 40ECh. 9.2 - Prob. 41ECh. 9.2 - Prob. 42ECh. 9.2 - Prob. 43ECh. 9.2 - Prob. 44ECh. 9.2 - The following circle graph summarizes the results...Ch. 9.2 - Prob. 46ECh. 9.2 - Can the data below be represented by a circle...Ch. 9.2 - Prob. 48ECh. 9.3 - Prob. 1PCh. 9.3 - Prob. 2PCh. 9.3 - Prob. 3PCh. 9.3 - Find the median of the list of numbers: 5, 11, 14,...Ch. 9.3 - Find the median of the list of scores:
36, 91,...Ch. 9.3 - Find the mode of the list of numbers:
14, 10, 10,...Ch. 9.3 - Prob. 7PCh. 9.3 - Prob. 8PCh. 9.3 - Prob. 9PCh. 9.3 - Prob. 1VRVCh. 9.3 - Prob. 2VRVCh. 9.3 - Prob. 3VRVCh. 9.3 - Prob. 4VRVCh. 9.3 - Prob. 5VRVCh. 9.3 - Prob. 6VRVCh. 9.3 - Use the choices below to fill in each blank. Some...Ch. 9.3 - Mixed Practice For each set of numbers, find the...Ch. 9.3 - Mixed Practice For each set of numbers, find the...Ch. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - The 10 tallest buildings in the world, completed...Ch. 9.3 - The 10 tallest buildings in the world, completed...Ch. 9.3 - Prob. 13ECh. 9.3 - The 10 tallest buildings in the world, completed...Ch. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - In a mathematics class, the following test scores...Ch. 9.3 - In a mathematics class, the following test scores...Ch. 9.3 - The following pulse rates were recorded for a...Ch. 9.3 - Prob. 26ECh. 9.3 - Prob. 27ECh. 9.3 - Prob. 28ECh. 9.3 - Prob. 29ECh. 9.3 - Prob. 30ECh. 9.3 - Prob. 31ECh. 9.3 - Prob. 32ECh. 9.3 - Prob. 33ECh. 9.3 - Prob. 34ECh. 9.3 - Find the range for each data set. See Example...Ch. 9.3 - Find the range for each data set. See Example...Ch. 9.3 - Find the range for each data set. See Example...Ch. 9.3 - Prob. 38ECh. 9.3 - Prob. 39ECh. 9.3 - Prob. 40ECh. 9.3 - Prob. 41ECh. 9.3 - Prob. 42ECh. 9.3 - Prob. 43ECh. 9.3 - Prob. 44ECh. 9.3 - Prob. 45ECh. 9.3 - Use each graph of data items to find the a. mean,...Ch. 9.3 - Use each graph of data items to find the a. mean,...Ch. 9.3 - Use each graph of data items to find the a. mean,...Ch. 9.3 - Prob. 49ECh. 9.3 - Prob. 50ECh. 9.3 - Prob. 51ECh. 9.3 - Prob. 52ECh. 9.3 - Prob. 53ECh. 9.3 - Prob. 54ECh. 9.3 - Prob. 55ECh. 9.3 - Prob. 56ECh. 9.3 - Write each fraction in simplest form. See Section...Ch. 9.3 - Write a list of numbers for which you feel the...Ch. 9.4 - Prob. 1PCh. 9.4 - Prob. 2PCh. 9.4 - Prob. 3PCh. 9.4 - Prob. 4PCh. 9.4 - Prob. 5PCh. 9.4 - Prob. 1VRVCh. 9.4 - Prob. 2VRVCh. 9.4 - Prob. 3VRVCh. 9.4 - Use the choices below to fill in each blank....Ch. 9.4 - Use the choices below to fill in each blank....Ch. 9.4 - Use the choices below to fill in each blank....Ch. 9.4 - Prob. 1ECh. 9.4 - Prob. 2ECh. 9.4 - Prob. 3ECh. 9.4 - Prob. 4ECh. 9.4 - Prob. 5ECh. 9.4 - Prob. 6ECh. 9.4 - Draw a tree diagram for each experiment. Then use...Ch. 9.4 - Prob. 8ECh. 9.4 - Draw a tree diagram for each experiment. Then use...Ch. 9.4 - Prob. 10ECh. 9.4 - If a single die is tossed once, find the...Ch. 9.4 - If a single die is tossed once, find the...Ch. 9.4 - If a single die is tossed once, find the...Ch. 9.4 - Prob. 14ECh. 9.4 - Prob. 15ECh. 9.4 - Prob. 16ECh. 9.4 - Prob. 17ECh. 9.4 - If a single die is tossed once, find the...Ch. 9.4 - Prob. 19ECh. 9.4 - Prob. 20ECh. 9.4 - Prob. 21ECh. 9.4 - Prob. 22ECh. 9.4 - Suppose the spinner shown is spun once. Find the...Ch. 9.4 - Suppose the spinner shown is spun once. Find the...Ch. 9.4 - If a single choice is made from the bag of marbles...Ch. 9.4 - Prob. 26ECh. 9.4 - Prob. 27ECh. 9.4 - Prob. 28ECh. 9.4 - Prob. 29ECh. 9.4 - Prob. 30ECh. 9.4 - Prob. 31ECh. 9.4 - Prob. 32ECh. 9.4 - Prob. 33ECh. 9.4 - Prob. 34ECh. 9.4 - Perform each indicated operation.
Ch. 9.4 - Prob. 36ECh. 9.4 - Prob. 37ECh. 9.4 - Prob. 38ECh. 9.4 - Prob. 39ECh. 9.4 - Prob. 40ECh. 9.4 - Prob. 41ECh. 9.4 - Prob. 42ECh. 9.4 - Prob. 43ECh. 9.4 - Prob. 44ECh. 9.4 - Prob. 45ECh. 9.4 - Prob. 46ECh. 9.4 - Prob. 47ECh. 9.4 - Prob. 48ECh. 9.4 - Prob. 49ECh. 9.4 - Prob. 50ECh. 9.4 - Prob. 51ECh. 9.4 - Prob. 52ECh. 9.4 - Prob. 53ECh. 9.4 - Prob. 54ECh. 9 - Prob. 1IRCh. 9 - Prob. 2IRCh. 9 - Prob. 3IRCh. 9 - Prob. 4IRCh. 9 - Prob. 5IRCh. 9 - Prob. 6IRCh. 9 - Prob. 7IRCh. 9 - Prob. 8IRCh. 9 - Prob. 9IRCh. 9 - Prob. 10IRCh. 9 - Prob. 11IRCh. 9 - Prob. 12IRCh. 9 - Prob. 13IRCh. 9 - Prob. 14IRCh. 9 - Prob. 15IRCh. 9 - The following circle graph shows the types of milk...Ch. 9 - Prob. 17IRCh. 9 - Prob. 18IRCh. 9 - Prob. 19IRCh. 9 - Prob. 20IRCh. 9 - Prob. 21IRCh. 9 - Prob. 22IRCh. 9 - Prob. 1VCCh. 9 - Prob. 2VCCh. 9 - Fill in each blank with one of the words or...Ch. 9 - Fill in each blank with one of the words or...Ch. 9 - Prob. 5VCCh. 9 - Prob. 6VCCh. 9 - Prob. 7VCCh. 9 - Prob. 8VCCh. 9 - Prob. 9VCCh. 9 - Prob. 10VCCh. 9 - Prob. 11VCCh. 9 - Prob. 12VCCh. 9 - Fill in each blank with one of the words or...Ch. 9 - Fill in each blank with one of the words or...Ch. 9 - The following pictograph shows the number of new...Ch. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RECh. 9 - The following bar graph shows the percent of...Ch. 9 - The following bar graph shows the percent of...Ch. 9 - The following line graph shows the total number of...Ch. 9 - The following line graph shows the total number of...Ch. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - The following histogram shows the hours worked per...Ch. 9 - The following histogram shows the hours worked per...Ch. 9 - The following histogram shows the hours worked per...Ch. 9 - Prob. 21RECh. 9 - Prob. 22RECh. 9 - Prob. 23RECh. 9 - Prob. 24RECh. 9 - Prob. 25RECh. 9 - The following circle graph shows a family’s $4000...Ch. 9 - The following circle graph shows a family’s $4000...Ch. 9 - The following circle graph shows a family’s $4000...Ch. 9 - Prob. 29RECh. 9 - The following circle graph shows a family’s $4000...Ch. 9 - Prob. 31RECh. 9 - Prob. 32RECh. 9 - In 2016, there were approximately 117 buildings...Ch. 9 - In 2016, there were approximately 117 buildings...Ch. 9 - Find the mean, median, and any mode(s) for each...Ch. 9 - Prob. 36RECh. 9 - Prob. 37RECh. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - Find the range for each data set.
1, 1, 1, 8, 8
Ch. 9 - Find the range for each data set.
70, 75, 95, 60,...Ch. 9 - Find the range for each data set.
80, 87, 97, 99,...Ch. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Prob. 47RECh. 9 - Prob. 48RECh. 9 - Prob. 49RECh. 9 - Prob. 50RECh. 9 - Prob. 51RECh. 9 - Prob. 52RECh. 9 - Prob. 53RECh. 9 - Draw a tree diagram for each experiment. Then use...Ch. 9 - Draw a tree diagram for each experiment. Then use...Ch. 9 - Draw a tree diagram for each experiment. Then use...Ch. 9 - Prob. 57RECh. 9 - Prob. 58RECh. 9 - Prob. 59RECh. 9 - Prob. 60RECh. 9 - Prob. 61RECh. 9 - Prob. 62RECh. 9 - Prob. 63RECh. 9 - Find the probability of each event.
Rolling an...Ch. 9 - Find the probability of each event.
Rolling a...Ch. 9 - Find the mean, median, and any mode(s) for each...Ch. 9 - Prob. 67RECh. 9 - Prob. 68RECh. 9 - Prob. 69RECh. 9 - Prob. 70RECh. 9 - Prob. 71RECh. 9 - Prob. 72RECh. 9 - Prob. 73RECh. 9 - Prob. 74RECh. 9 - For each graph, calculate parts a.–d. Round the...Ch. 9 - How many bushels of oranges did Orchard 1...Ch. 9 - Which orchard above produced the most...Ch. 9 - Prob. 3GRTCh. 9 - Prob. 4GRTCh. 9 - Prob. 5GRTCh. 9 - Prob. 6GRTCh. 9 - Prob. 7GRTCh. 9 - Prob. 8GRTCh. 9 - Prob. 9GRTCh. 9 - Prob. 10GRTCh. 9 - Prob. 11GRTCh. 9 - For Exercises 11 through 13, use the data sets and...Ch. 9 - For Exercises 11 through 13, use the data sets and...Ch. 9 - MATCHING Exercises 14 through 17 are Matching...Ch. 9 - Prob. 15GRTCh. 9 - Prob. 16GRTCh. 9 - Prob. 17GRTCh. 9 - Prob. 1TCh. 9 - Prob. 2TCh. 9 - Prob. 3TCh. 9 - Prob. 4TCh. 9 - Prob. 5TCh. 9 - The bar graph shows the normal monthly...Ch. 9 - Use the information in the table to draw a bar...Ch. 9 - The following line graph shows the annual...Ch. 9 - The following line graph shows the annual...Ch. 9 - Prob. 10TCh. 9 - Prob. 11TCh. 9 - Prob. 12TCh. 9 - Prob. 13TCh. 9 - Prob. 14TCh. 9 - A professor measures the heights of the students...Ch. 9 - A professor measures the heights of the students...Ch. 9 - The history test scores of 25 students are shown...Ch. 9 - Prob. 18TCh. 9 - Prob. 19TCh. 9 - Prob. 20TCh. 9 - Prob. 21TCh. 9 - Prob. 22TCh. 9 - Prob. 23TCh. 9 - Prob. 24TCh. 9 - Prob. 25TCh. 9 - Prob. 26TCh. 9 - Prob. 27TCh. 9 - Suppose that the numbers 1 to 10 are each written...Ch. 9 - Prob. 29TCh. 9 - Prob. 1CRCh. 9 - Prob. 2CRCh. 9 - Prob. 3CRCh. 9 - Prob. 4CRCh. 9 - Prob. 5CRCh. 9 - Prob. 6CRCh. 9 - The formula for finding the area of a triangle is...Ch. 9 - Find the perimeter of a rectangle with length ...Ch. 9 - Write the ratio of $15 to $10 as a fraction in...Ch. 9 - Prob. 10CRCh. 9 - Prob. 11CRCh. 9 - Prob. 12CRCh. 9 - Prob. 13CRCh. 9 - Prob. 14CRCh. 9 - Prob. 15CRCh. 9 - Prob. 16CRCh. 9 - Prob. 17CRCh. 9 - Prob. 18CRCh. 9 - Prob. 19CRCh. 9 - Prob. 20CRCh. 9 - Prob. 21CRCh. 9 - Prob. 22CRCh. 9 - Prob. 23CRCh. 9 - Prob. 24CRCh. 9 - Prob. 25CRCh. 9 - Prob. 26CRCh. 9 - Prob. 27CRCh. 9 - Prob. 28CRCh. 9 - Prob. 29CRCh. 9 - Prob. 30CRCh. 9 - Prob. 31CRCh. 9 - Prob. 32CRCh. 9 - Prob. 33CRCh. 9 - Prob. 34CRCh. 9 - Prob. 35CRCh. 9 - Prob. 36CRCh. 9 - Prob. 37CRCh. 9 - Prob. 38CRCh. 9 - Prob. 39CRCh. 9 - Prob. 40CRCh. 9 - Prob. 41CRCh. 9 - Prob. 42CRCh. 9 - Prob. 43CRCh. 9 - Prob. 44CRCh. 9 - Prob. 45CRCh. 9 - Prob. 46CRCh. 9 - Prob. 47CRCh. 9 - Prob. 48CRCh. 9 - Prob. 49CRCh. 9 - Prob. 50CR
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