Intermediate Algebra
Intermediate Algebra
10th Edition
ISBN: 9781305191495
Author: Jerome E. Kaufmann; Karen L. Schwitters
Publisher: Cengage Learning US
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Concept explainers

Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Chapter 9.1, Problem 7CQ
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Chapter 9 Solutions

Intermediate Algebra

Ch. 9.1 - For Problems 110, answer true or false. A function...Ch. 9.1 - Prob. 2CQCh. 9.1 - Prob. 3CQCh. 9.1 - Prob. 4CQCh. 9.1 - Prob. 5CQCh. 9.1 - Prob. 6CQCh. 9.1 - Prob. 7CQCh. 9.1 - Prob. 8CQCh. 9.1 - Prob. 9CQCh. 9.1 - Prob. 10CQ
Ch. 9.1 - Prob. 1PSCh. 9.1 - Prob. 2PSCh. 9.1 - Prob. 3PSCh. 9.1 - Prob. 4PSCh. 9.1 - Prob. 5PSCh. 9.1 - Prob. 6PSCh. 9.1 - Prob. 7PSCh. 9.1 - Prob. 8PSCh. 9.1 - Prob. 9PSCh. 9.1 - Prob. 10PSCh. 9.1 - Prob. 11PSCh. 9.1 - Prob. 12PSCh. 9.1 - Prob. 13PSCh. 9.1 - Prob. 14PSCh. 9.1 - Prob. 15PSCh. 9.1 - Prob. 16PSCh. 9.1 - Prob. 17PSCh. 9.1 - Prob. 18PSCh. 9.1 - Prob. 19PSCh. 9.1 - Prob. 20PSCh. 9.1 - Prob. 21PSCh. 9.1 - Prob. 22PSCh. 9.1 - Prob. 23PSCh. 9.1 - Prob. 24PSCh. 9.1 - Prob. 25PSCh. 9.1 - Prob. 26PSCh. 9.1 - Prob. 27PSCh. 9.1 - Prob. 28PSCh. 9.1 - Prob. 29PSCh. 9.1 - Prob. 30PSCh. 9.1 - Prob. 31PSCh. 9.1 - Prob. 32PSCh. 9.1 - Prob. 33PSCh. 9.1 - Prob. 34PSCh. 9.1 - Prob. 35PSCh. 9.1 - Prob. 36PSCh. 9.1 - Prob. 37PSCh. 9.1 - Prob. 38PSCh. 9.1 - Prob. 39PSCh. 9.1 - Prob. 40PSCh. 9.1 - Prob. 41PSCh. 9.1 - Prob. 42PSCh. 9.1 - Prob. 43PSCh. 9.1 - Prob. 44PSCh. 9.1 - Prob. 45PSCh. 9.1 - Prob. 46PSCh. 9.1 - Prob. 47PSCh. 9.1 - Prob. 48PSCh. 9.1 - Prob. 49PSCh. 9.1 - Prob. 50PSCh. 9.1 - Prob. 51PSCh. 9.1 - Prob. 52PSCh. 9.1 - Prob. 53PSCh. 9.1 - Prob. 54PSCh. 9.1 - Prob. 55PSCh. 9.1 - Prob. 56PSCh. 9.1 - If f(x)=3|x|1 and g(x)=|x|+1, find f(2), f(3),...Ch. 9.1 - Prob. 58PSCh. 9.1 - Prob. 59PSCh. 9.1 - Prob. 60PSCh. 9.1 - Prob. 61PSCh. 9.1 - Prob. 62PSCh. 9.1 - Prob. 63PSCh. 9.1 - Prob. 64PSCh. 9.1 - Prob. 65PSCh. 9.1 - Prob. 66PSCh. 9.1 - The height of a projectile fired vertically into...Ch. 9.1 - Prob. 68PSCh. 9.1 - Acar rental agency 50 per day plus 0.32 a mile....Ch. 9.1 - Prob. 70PSCh. 9.1 - The equation I(r)=500r expresses the amount of...Ch. 9.1 - Prob. 72PSCh. 9.1 - Prob. 73PSCh. 9.1 - Prob. 74PSCh. 9.1 - Prob. 75PSCh. 9.1 - Prob. 76PSCh. 9.1 - Prob. 77PSCh. 9.2 - For Problems 110, answer true or false. The...Ch. 9.2 - Prob. 2CQCh. 9.2 - For problems 110, answer true or false. The graph...Ch. 9.2 - Prob. 4CQCh. 9.2 - Prob. 5CQCh. 9.2 - Prob. 6CQCh. 9.2 - Prob. 7CQCh. 9.2 - Prob. 8CQCh. 9.2 - Prob. 9CQCh. 9.2 - Prob. 10CQCh. 9.2 - Prob. 1PSCh. 9.2 - Prob. 2PSCh. 9.2 - Prob. 3PSCh. 9.2 - Prob. 4PSCh. 9.2 - Prob. 5PSCh. 9.2 - Prob. 6PSCh. 9.2 - Prob. 7PSCh. 9.2 - Prob. 8PSCh. 9.2 - Prob. 9PSCh. 9.2 - Prob. 10PSCh. 9.2 - Prob. 11PSCh. 9.2 - Prob. 12PSCh. 9.2 - Prob. 13PSCh. 9.2 - Prob. 14PSCh. 9.2 - Prob. 15PSCh. 9.2 - Prob. 16PSCh. 9.2 - Prob. 17PSCh. 9.2 - Prob. 18PSCh. 9.2 - Prob. 19PSCh. 9.2 - Prob. 20PSCh. 9.2 - Prob. 21PSCh. 9.2 - Prob. 22PSCh. 9.2 - Prob. 23PSCh. 9.2 - Prob. 24PSCh. 9.2 - Prob. 25PSCh. 9.2 - Prob. 26PSCh. 9.2 - Prob. 27PSCh. 9.2 - Prob. 28PSCh. 9.2 - Prob. 29PSCh. 9.2 - Prob. 30PSCh. 9.2 - Prob. 31PSCh. 9.2 - Prob. 32PSCh. 9.2 - Prob. 33PSCh. 9.2 - Prob. 34PSCh. 9.2 - To solve Problems 3544, use linear functions....Ch. 9.2 - Prob. 36PSCh. 9.2 - Prob. 37PSCh. 9.2 - Prob. 38PSCh. 9.2 - Prob. 39PSCh. 9.2 - To solve Problems 3544, use linear functions....Ch. 9.2 - Prob. 41PSCh. 9.2 - Prob. 42PSCh. 9.2 - Prob. 43PSCh. 9.2 - Prob. 44PSCh. 9.2 - Prob. 45PSCh. 9.2 - Prob. 46PSCh. 9.2 - Prob. 47PSCh. 9.2 - Prob. 48PSCh. 9.2 - Prob. 49PSCh. 9.2 - Prob. 50PSCh. 9.2 - Prob. 51PSCh. 9.2 - A specialty bicycle manufacturer has determined...Ch. 9.2 - Prob. 53PSCh. 9.2 - Prob. 54PSCh. 9.2 - Prob. 55PSCh. 9.2 - Prob. 56PSCh. 9.2 - Thoughts Into Words Suppose that Bianca walks at a...Ch. 9.2 - Use a graphing calculator to check your graphs for...Ch. 9.2 - Prob. 59.1PSCh. 9.2 - Prob. 59.2PSCh. 9.2 - Prob. 59.3PSCh. 9.2 - Prob. 59.4PSCh. 9.2 - Prob. 59.5PSCh. 9.2 - Prob. 60PSCh. 9.2 - Prob. 61PSCh. 9.3 - Prob. 1CQCh. 9.3 - Prob. 2CQCh. 9.3 - Prob. 3CQCh. 9.3 - Prob. 4CQCh. 9.3 - Prob. 5CQCh. 9.3 - Prob. 6CQCh. 9.3 - Prob. 7CQCh. 9.3 - Prob. 8CQCh. 9.3 - Prob. 9CQCh. 9.3 - Prob. 10CQCh. 9.3 - For Problems 16, match the function with its graph...Ch. 9.3 - For Problems 16, match the function with its graph...Ch. 9.3 - Prob. 3PSCh. 9.3 - Prob. 4PSCh. 9.3 - For Problems 16, match the function with its graph...Ch. 9.3 - Prob. 6PSCh. 9.3 - Prob. 7PSCh. 9.3 - Prob. 8PSCh. 9.3 - Prob. 9PSCh. 9.3 - Prob. 10PSCh. 9.3 - Prob. 11PSCh. 9.3 - Prob. 12PSCh. 9.3 - Prob. 13PSCh. 9.3 - Prob. 14PSCh. 9.3 - Prob. 15PSCh. 9.3 - Prob. 16PSCh. 9.3 - Prob. 17PSCh. 9.3 - Prob. 18PSCh. 9.3 - Prob. 19PSCh. 9.3 - Prob. 20PSCh. 9.3 - Prob. 21PSCh. 9.3 - Prob. 22PSCh. 9.3 - Prob. 23PSCh. 9.3 - Prob. 24PSCh. 9.3 - Prob. 25PSCh. 9.3 - Prob. 26PSCh. 9.3 - Prob. 27PSCh. 9.3 - Prob. 28PSCh. 9.3 - Prob. 29PSCh. 9.3 - Prob. 30PSCh. 9.3 - Prob. 31PSCh. 9.3 - Prob. 32PSCh. 9.3 - Prob. 33PSCh. 9.3 - Prob. 34PSCh. 9.3 - Prob. 35PSCh. 9.3 - Prob. 36PSCh. 9.3 - Prob. 37PSCh. 9.3 - Prob. 38PSCh. 9.3 - Prob. 39PSCh. 9.3 - Prob. 40PSCh. 9.3 - Prob. 41PSCh. 9.3 - Prob. 42PSCh. 9.3 - Prob. 43PSCh. 9.3 - Prob. 44PSCh. 9.3 - Prob. 45PSCh. 9.3 - Prob. 46PSCh. 9.3 - Prob. 47PSCh. 9.3 - Prob. 48PSCh. 9.3 - Prob. 49PSCh. 9.3 - Prob. 50PSCh. 9.3 - Prob. 51PSCh. 9.3 - Prob. 52PSCh. 9.3 - Prob. 53PSCh. 9.3 - Prob. 54PSCh. 9.3 - Prob. 55PSCh. 9.3 - Prob. 56PSCh. 9.3 - Prob. 57PSCh. 9.3 - Prob. 58PSCh. 9.3 - Prob. 59PSCh. 9.3 - Prob. 60PSCh. 9.3 - Prob. 61PSCh. 9.3 - Prob. 62.1PSCh. 9.3 - Prob. 62.2PSCh. 9.3 - Prob. 62.3PSCh. 9.3 - Use the definition of absolute value to help you...Ch. 9.3 - Prob. 62.5PSCh. 9.3 - Prob. 63PSCh. 9.3 - Prob. 64PSCh. 9.3 - Prob. 65PSCh. 9.3 - Prob. 66PSCh. 9.3 - Prob. 67PSCh. 9.3 - Prob. 68.1PSCh. 9.3 - Prob. 68.2PSCh. 9.3 - Prob. 68.3PSCh. 9.3 - Prob. 68.4PSCh. 9.3 - Prob. 68.5PSCh. 9.3 - Prob. 68.6PSCh. 9.3 - Prob. 68.7PSCh. 9.3 - For each of the following, answer the question on...Ch. 9.3 - Prob. 68.9PSCh. 9.3 - Prob. 69PSCh. 9.3 - Prob. 70PSCh. 9.4 - Prob. 1CQCh. 9.4 - Prob. 2CQCh. 9.4 - Prob. 3CQCh. 9.4 - Prob. 4CQCh. 9.4 - Prob. 5CQCh. 9.4 - Prob. 6CQCh. 9.4 - Prob. 7CQCh. 9.4 - Prob. 8CQCh. 9.4 - Prob. 9CQCh. 9.4 - Prob. 10CQCh. 9.4 - Prob. 1PSCh. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - Prob. 3PSCh. 9.4 - Prob. 4PSCh. 9.4 - Prob. 5PSCh. 9.4 - Prob. 6PSCh. 9.4 - Prob. 7PSCh. 9.4 - Prob. 8PSCh. 9.4 - Prob. 9PSCh. 9.4 - Prob. 10PSCh. 9.4 - Prob. 11PSCh. 9.4 - Prob. 12PSCh. 9.4 - Prob. 13PSCh. 9.4 - For Problems 118, determine (fg)(x).and (gf)(x)...Ch. 9.4 - Prob. 15PSCh. 9.4 - Prob. 16PSCh. 9.4 - Prob. 17PSCh. 9.4 - Prob. 18PSCh. 9.4 - Prob. 19PSCh. 9.4 - Prob. 20PSCh. 9.4 - Prob. 21PSCh. 9.4 - For Problems 1926, show that (fg)(x)=x and...Ch. 9.4 - Prob. 23PSCh. 9.4 - Prob. 24PSCh. 9.4 - Prob. 25PSCh. 9.4 - Prob. 26PSCh. 9.4 - Prob. 27PSCh. 9.4 - Prob. 28PSCh. 9.4 - Prob. 29PSCh. 9.4 - Prob. 30PSCh. 9.4 - Prob. 31PSCh. 9.4 - Prob. 32PSCh. 9.4 - Prob. 33PSCh. 9.4 - Prob. 34PSCh. 9.4 - Prob. 35PSCh. 9.4 - Prob. 36PSCh. 9.4 - Prob. 37PSCh. 9.4 - Prob. 38PSCh. 9.4 - Prob. 39.1PSCh. 9.4 - Prob. 39.2PSCh. 9.4 - Prob. 39.3PSCh. 9.4 - Prob. 39.4PSCh. 9.4 - Prob. 39.5PSCh. 9.5 - Prob. 1CQCh. 9.5 - Prob. 2CQCh. 9.5 - Prob. 3CQCh. 9.5 - Prob. 4CQCh. 9.5 - Prob. 5CQCh. 9.5 - Prob. 6CQCh. 9.5 - Prob. 7CQCh. 9.5 - Prob. 8CQCh. 9.5 - Prob. 9CQCh. 9.5 - Prob. 10CQCh. 9.5 - Prob. 1PSCh. 9.5 - Prob. 2PSCh. 9.5 - Prob. 3PSCh. 9.5 - Prob. 4PSCh. 9.5 - Prob. 5PSCh. 9.5 - Prob. 6PSCh. 9.5 - Prob. 7PSCh. 9.5 - Prob. 8PSCh. 9.5 - Prob. 9PSCh. 9.5 - Prob. 10PSCh. 9.5 - Prob. 11PSCh. 9.5 - Prob. 12PSCh. 9.5 - Prob. 13PSCh. 9.5 - Prob. 14PSCh. 9.5 - Prob. 15PSCh. 9.5 - Prob. 16PSCh. 9.5 - Prob. 17PSCh. 9.5 - Prob. 18PSCh. 9.5 - Prob. 19PSCh. 9.5 - Prob. 20PSCh. 9.5 - Prob. 21PSCh. 9.5 - Prob. 22PSCh. 9.5 - Prob. 23PSCh. 9.5 - Prob. 24PSCh. 9.5 - Prob. 25PSCh. 9.5 - Prob. 26PSCh. 9.5 - Prob. 27PSCh. 9.5 - Prob. 28PSCh. 9.5 - Prob. 29PSCh. 9.5 - Prob. 30PSCh. 9.5 - Prob. 31PSCh. 9.5 - Prob. 32PSCh. 9.5 - Prob. 33PSCh. 9.5 - Prob. 34PSCh. 9.5 - Prob. 35PSCh. 9.5 - Prob. 36PSCh. 9.5 - Prob. 37PSCh. 9.5 - Prob. 38PSCh. 9.5 - Prob. 39PSCh. 9.5 - Prob. 40PSCh. 9.5 - Prob. 41PSCh. 9.5 - Prob. 42PSCh. 9.5 - Prob. 43PSCh. 9.5 - Prob. 44PSCh. 9.5 - Prob. 45PSCh. 9.5 - Prob. 46PSCh. 9.5 - Prob. 47PSCh. 9.5 - Prob. 48PSCh. 9.5 - Prob. 49PSCh. 9.5 - Prob. 50PSCh. 9.5 - Prob. 51PSCh. 9.5 - Prob. 52PSCh. 9.5 - Prob. 53PSCh. 9.5 - Prob. 54PSCh. 9.5 - Prob. 55PSCh. 9.5 - Prob. 56PSCh. 9.6 - Prob. 1CQCh. 9.6 - Prob. 2CQCh. 9.6 - Prob. 3CQCh. 9.6 - Prob. 4CQCh. 9.6 - Prob. 5CQCh. 9.6 - Prob. 6CQCh. 9.6 - Prob. 7CQCh. 9.6 - Prob. 8CQCh. 9.6 - Prob. 9CQCh. 9.6 - Prob. 10CQCh. 9.6 - Prob. 1PSCh. 9.6 - Prob. 2PSCh. 9.6 - Prob. 3PSCh. 9.6 - Prob. 4PSCh. 9.6 - Prob. 5PSCh. 9.6 - For Problems 110, translate each statement of...Ch. 9.6 - Prob. 7PSCh. 9.6 - Prob. 8PSCh. 9.6 - For Problems 110, translate each statement of...Ch. 9.6 - For Problems 110, translate each statement of...Ch. 9.6 - Prob. 11PSCh. 9.6 - Prob. 12PSCh. 9.6 - Prob. 13PSCh. 9.6 - Prob. 14PSCh. 9.6 - Prob. 15PSCh. 9.6 - Prob. 16PSCh. 9.6 - Prob. 17PSCh. 9.6 - Prob. 18PSCh. 9.6 - Prob. 19PSCh. 9.6 - Prob. 20PSCh. 9.6 - Prob. 21PSCh. 9.6 - Prob. 22PSCh. 9.6 - Prob. 23PSCh. 9.6 - Prob. 24PSCh. 9.6 - Prob. 25PSCh. 9.6 - Prob. 26PSCh. 9.6 - Prob. 27PSCh. 9.6 - Prob. 28PSCh. 9.6 - Prob. 29PSCh. 9.6 - Prob. 30PSCh. 9.6 - Prob. 31PSCh. 9.6 - Prob. 32PSCh. 9.6 - Prob. 33PSCh. 9.6 - Prob. 34PSCh. 9.6 - Prob. 35PSCh. 9.6 - Prob. 36PSCh. 9.6 - Solve each of the following problems. Objective...Ch. 9.6 - Prob. 38PSCh. 9.6 - Prob. 39PSCh. 9.6 - Prob. 40PSCh. 9.6 - Prob. 41PSCh. 9.6 - Prob. 42PSCh. 9.6 - Prob. 43PSCh. 9.6 - Prob. 44PSCh. 9.6 - Prob. 45PSCh. 9.6 - Prob. 46PSCh. 9.S - Specify the domain and range of the relation and...Ch. 9.S - Prob. 2SCh. 9.S - Prob. 3SCh. 9.S - Prob. 4SCh. 9.S - Prob. 5SCh. 9.S - Prob. 6SCh. 9.S - Prob. 7SCh. 9.S - Suppose the cost function for producing a...Ch. 9.S - Graph f(x)=|x3|+1.Ch. 9.S - Prob. 10SCh. 9.S - Prob. 11SCh. 9.S - Prob. 12SCh. 9.S - Prob. 13SCh. 9.S - Prob. 14SCh. 9.S - Prob. 15SCh. 9.S - Prob. 16SCh. 9.S - Prob. 17SCh. 9.S - Prob. 18SCh. 9.S - Prob. 19SCh. 9.S - Prob. 20SCh. 9.S - Prob. 21SCh. 9.CR - For Problems 14, determine if the following...Ch. 9.CR - Prob. 2CRCh. 9.CR - Prob. 3CRCh. 9.CR - Prob. 4CRCh. 9.CR - Prob. 5CRCh. 9.CR - Prob. 6CRCh. 9.CR - Prob. 7CRCh. 9.CR - Prob. 8CRCh. 9.CR - Prob. 9CRCh. 9.CR - For Problems 710, specify the domain of each...Ch. 9.CR - Prob. 11CRCh. 9.CR - Prob. 12CRCh. 9.CR - Prob. 13CRCh. 9.CR - Prob. 14CRCh. 9.CR - For Problems 1522, graph each of the functions....Ch. 9.CR - For Problems 1522, graph each of the functions....Ch. 9.CR - Prob. 17CRCh. 9.CR - Prob. 18CRCh. 9.CR - Prob. 19CRCh. 9.CR - Prob. 20CRCh. 9.CR - Prob. 21CRCh. 9.CR - Prob. 22CRCh. 9.CR - Prob. 23CRCh. 9.CR - An outpatient operating room charges each patient...Ch. 9.CR - Prob. 25CRCh. 9.CR - Prob. 26CRCh. 9.CR - Prob. 27CRCh. 9.CR - Prob. 28CRCh. 9.CR - Prob. 29CRCh. 9.CR - Prob. 30CRCh. 9.CR - Prob. 31CRCh. 9.CR - Prob. 32CRCh. 9.CR - Prob. 33CRCh. 9.CR - Find the coordinates of the vertex and the...Ch. 9.CR - Find two numbers whose sum is 40 and whose product...Ch. 9.CR - Prob. 36CRCh. 9.CR - A garden has 60 yards of fencing and wants to...Ch. 9.CR - Suppose that 50 students are able to raise 250 for...Ch. 9.CR - Prob. 39CRCh. 9.CR - Prob. 40CRCh. 9.CR - Prob. 41CRCh. 9.CR - Prob. 42CRCh. 9.CR - Prob. 43CRCh. 9.CR - Prob. 44CRCh. 9.CR - Prob. 45CRCh. 9.CR - Prob. 46CRCh. 9.CR - Prob. 47CRCh. 9.CR - Prob. 48CRCh. 9.CR - For Problems 3956, graph the functions. f(x)=|x2|Ch. 9.CR - Prob. 50CRCh. 9.CR - Prob. 51CRCh. 9.CR - Prob. 52CRCh. 9.CR - Prob. 53CRCh. 9.CR - Prob. 54CRCh. 9.CR - Prob. 55CRCh. 9.CR - Prob. 56CRCh. 9.CR - Prob. 57CRCh. 9.CR - Prob. 58CRCh. 9.CR - Prob. 59CRCh. 9.CR - Prob. 60CRCh. 9.CR - Prob. 61CRCh. 9.CR - Prob. 62CRCh. 9.CR - Prob. 63CRCh. 9.CR - Prob. 64CRCh. 9.CR - Prob. 65CRCh. 9.CR - Prob. 66CRCh. 9.CR - Prob. 67CRCh. 9.CR - Prob. 68CRCh. 9.CR - Prob. 69CRCh. 9.CR - Prob. 70CRCh. 9.CR - Prob. 71CRCh. 9.CR - Prob. 72CRCh. 9.CR - Prob. 73CRCh. 9.CR - The surface area of a cube varies directly as the...Ch. 9.CR - Prob. 75CRCh. 9.CR - Prob. 76CRCh. 9.CR - Prob. 77CRCh. 9.CR - Prob. 78CRCh. 9.CT - Prob. 1CTCh. 9.CT - Prob. 2CTCh. 9.CT - Prob. 3CTCh. 9.CT - Prob. 4CTCh. 9.CT - Prob. 5CTCh. 9.CT - Prob. 6CTCh. 9.CT - Prob. 7CTCh. 9.CT - Prob. 8CTCh. 9.CT - Prob. 9CTCh. 9.CT - Prob. 10CTCh. 9.CT - Prob. 11CTCh. 9.CT - Prob. 12CTCh. 9.CT - Prob. 13CTCh. 9.CT - Prob. 14CTCh. 9.CT - Prob. 15CTCh. 9.CT - Prob. 16CTCh. 9.CT - Prob. 17CTCh. 9.CT - Prob. 18CTCh. 9.CT - Prob. 19CTCh. 9.CT - Prob. 20CTCh. 9.CT - Prob. 21CTCh. 9.CT - Prob. 22CTCh. 9.CT - Prob. 23CTCh. 9.CT - Prob. 24CTCh. 9.CT - Prob. 25CT
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