COLL ALG & TRIG ALEKS 360 ACCESS CARD
1st Edition
ISBN: 9781265934590
Author: Miller
Publisher: MCG CUSTOM
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Chapter 10, Problem 32RE
To determine
The matrix for
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2. A microwave manufacturing firm has determined that their profit function is P(x)=-0.0014x+0.3x²+6x-355 , where is the number of microwaves sold annually. a. Graph the profit function using a calculator. b. Determine a reasonable viewing window for the function. c. Approximate all of the zeros of the function using the CALC menu of your calculator. d. What must be the range of microwaves sold in order for the firm to profit?
A clothing manufacturer's profitability
can be modeled by p (x)=-x4 + 40x² - 144, where .x
is the number of items sold in thousands and p (x) is
the company's profit in thousands of dollars.
a. Sketch the function on your calculator and describe the end behavior.
b. Determine the zeros of the function.
c. Between what two values should the company sell
in order to be profitable?
d. Explain why only two of the zeros are considered
in part c.
CCSS REASONING The number of subscribers
using pagers in the United States can be modeled by
f(x) = 0.015x4 -0.44x³ +3.46x² - 2.7x+9.68
where x is the number of years after 1990 and f(x) is
the number of subscribers in millions.
a. Graph the function.
b. Describe the end behavior of the graph.
c. What does the end behavior suggest about the
number of pager subscribers?
d. Will this trend continue indefinitely? Explain your
reasoning.
Chapter 10 Solutions
COLL ALG & TRIG ALEKS 360 ACCESS CARD
Ch. 10.1 - Solve the equation and check the solution....Ch. 10.1 - Prob. R.2PECh. 10.1 - Prob. R.3PECh. 10.1 - Prob. R.4PECh. 10.1 - Prob. 1PECh. 10.1 - Prob. 2PECh. 10.1 - Explain the meaning of the notation R2R3.Ch. 10.1 - Prob. 4PECh. 10.1 - Prob. 5PECh. 10.1 - Prob. 6PE
Ch. 10.1 - Prob. 7PECh. 10.1 - Explain the meaning of the notation 4R2+R3R3.Ch. 10.1 - Prob. 9PECh. 10.1 - Prob. 10PECh. 10.1 - For Exercises 9-14, write the augmented matrix for...Ch. 10.1 - Prob. 12PECh. 10.1 - Prob. 13PECh. 10.1 - Prob. 14PECh. 10.1 - Prob. 15PECh. 10.1 - Prob. 16PECh. 10.1 - For Exercises 15-20, write a system of linear...Ch. 10.1 - Prob. 18PECh. 10.1 - Prob. 19PECh. 10.1 - Prob. 20PECh. 10.1 - Prob. 21PECh. 10.1 - Prob. 22PECh. 10.1 - For Exercises 21-26, perform the elementary row...Ch. 10.1 - Prob. 24PECh. 10.1 - Prob. 25PECh. 10.1 - Prob. 26PECh. 10.1 - Prob. 27PECh. 10.1 - Prob. 28PECh. 10.1 - Prob. 29PECh. 10.1 - Prob. 30PECh. 10.1 - Prob. 31PECh. 10.1 - Prob. 32PECh. 10.1 - Prob. 33PECh. 10.1 - Prob. 34PECh. 10.1 - For Exercises 33-36, determine if the matrix is in...Ch. 10.1 - Prob. 36PECh. 10.1 - Prob. 37PECh. 10.1 - Prob. 38PECh. 10.1 - Prob. 39PECh. 10.1 - Prob. 40PECh. 10.1 - For Exercises 41-60, solve the system by using...Ch. 10.1 - Prob. 42PECh. 10.1 - For Exercises 41-60, solve the system by using...Ch. 10.1 - Prob. 44PECh. 10.1 - Prob. 45PECh. 10.1 - Prob. 46PECh. 10.1 - For Exercises 41-60, solve the system by using...Ch. 10.1 - Prob. 48PECh. 10.1 - For Exercises 41-60, solve the system by using...Ch. 10.1 - Prob. 50PECh. 10.1 - For Exercises 41-60, solve the system by using...Ch. 10.1 - Prob. 52PECh. 10.1 - Prob. 53PECh. 10.1 - Prob. 54PECh. 10.1 - Prob. 55PECh. 10.1 - Prob. 56PECh. 10.1 - Prob. 57PECh. 10.1 - Prob. 58PECh. 10.1 - Prob. 59PECh. 10.1 - Prob. 60PECh. 10.1 - Prob. 61PECh. 10.1 - Prob. 62PECh. 10.1 - For Exercises 61-64, set up a system of linear...Ch. 10.1 - Prob. 64PECh. 10.1 - Prob. 65PECh. 10.1 - Prob. 66PECh. 10.1 - Prob. 67PECh. 10.1 - Prob. 68PECh. 10.1 - Prob. 69PECh. 10.1 - Prob. 70PECh. 10.1 - Prob. 71PECh. 10.1 - Prob. 72PECh. 10.1 - Prob. 73PECh. 10.1 - Prob. 74PECh. 10.1 - Prob. 75PECh. 10.1 - Prob. 76PECh. 10.2 - Prob. R.1PECh. 10.2 - Prob. R.2PECh. 10.2 - Prob. R.3PECh. 10.2 - Prob. R.4PECh. 10.2 - Prob. 1PECh. 10.2 - Prob. 2PECh. 10.2 - Prob. 3PECh. 10.2 - Prob. 4PECh. 10.2 - Prob. 5PECh. 10.2 - Prob. 6PECh. 10.2 - Prob. 7PECh. 10.2 - Prob. 8PECh. 10.2 - Prob. 9PECh. 10.2 - Prob. 10PECh. 10.2 - Prob. 11PECh. 10.2 - Prob. 12PECh. 10.2 - Prob. 13PECh. 10.2 - Prob. 14PECh. 10.2 - Prob. 15PECh. 10.2 - Prob. 16PECh. 10.2 - Prob. 17PECh. 10.2 - Prob. 18PECh. 10.2 - Prob. 19PECh. 10.2 - Prob. 20PECh. 10.2 - Prob. 21PECh. 10.2 - Prob. 22PECh. 10.2 - Prob. 23PECh. 10.2 - Prob. 24PECh. 10.2 - For Exercises 19-38, solve the system by using...Ch. 10.2 - For Exercises 19-38, solve the system by using...Ch. 10.2 - Prob. 27PECh. 10.2 - Prob. 28PECh. 10.2 - Prob. 29PECh. 10.2 - Prob. 30PECh. 10.2 - For Exercises 19-38, solve the system by using...Ch. 10.2 - Prob. 32PECh. 10.2 - Prob. 33PECh. 10.2 - Prob. 34PECh. 10.2 - Prob. 35PECh. 10.2 - Prob. 36PECh. 10.2 - Prob. 37PECh. 10.2 - Prob. 38PECh. 10.2 - Prob. 39PECh. 10.2 - Prob. 40PECh. 10.2 - Prob. 41PECh. 10.2 - Prob. 42PECh. 10.2 - Prob. 43PECh. 10.2 - Prob. 44PECh. 10.2 - Prob. 45PECh. 10.2 - Prob. 46PECh. 10.2 - Prob. 47PECh. 10.2 - Prob. 48PECh. 10.2 - Prob. 49PECh. 10.2 - A concession stand at a city park sells...Ch. 10.2 - Prob. 51PECh. 10.2 - Prob. 52PECh. 10.2 - Prob. 53PECh. 10.2 - Prob. 54PECh. 10.2 - Prob. 55PECh. 10.2 - Prob. 56PECh. 10.2 - Prob. 57PECh. 10.2 - Prob. 58PECh. 10.2 - Prob. 59PECh. 10.2 - Prob. 60PECh. 10.2 - Prob. 61PECh. 10.2 - Prob. 62PECh. 10.2 - Prob. 63PECh. 10.2 - Prob. 64PECh. 10.2 - Prob. 65PECh. 10.2 - Prob. 66PECh. 10.3 - Identify the additive inverse of 9.Ch. 10.3 - Prob. R.2PECh. 10.3 - Prob. R.3PECh. 10.3 - Prob. 1PECh. 10.3 - A matrix with the same number of rows and columns...Ch. 10.3 - What are the requirements for two matrices to be...Ch. 10.3 - An mn matrix whose elements are all zero is called...Ch. 10.3 - Prob. 5PECh. 10.3 - Prob. 6PECh. 10.3 - True or false: Matrix multiplication is a...Ch. 10.3 - Prob. 8PECh. 10.3 - Prob. 9PECh. 10.3 - Prob. 10PECh. 10.3 - For Exercises 11-16, Give the order of the matrix....Ch. 10.3 - Prob. 12PECh. 10.3 - Prob. 13PECh. 10.3 - Prob. 14PECh. 10.3 - Prob. 15PECh. 10.3 - Prob. 16PECh. 10.3 - Prob. 17PECh. 10.3 - Prob. 18PECh. 10.3 - Prob. 19PECh. 10.3 - Prob. 20PECh. 10.3 - Prob. 21PECh. 10.3 - Prob. 22PECh. 10.3 - Given A=[2xz-5] and B=[y410-5], for what values of...Ch. 10.3 - Prob. 24PECh. 10.3 - Given B=[4693567], find the additive inverse of B.Ch. 10.3 - Prob. 26PECh. 10.3 - For Exercises 27-32, add or subtract the given...Ch. 10.3 - Prob. 28PECh. 10.3 - For Exercises 27-32, add or subtract the given...Ch. 10.3 - Prob. 30PECh. 10.3 - For Exercises 27-32, add or subtract the given...Ch. 10.3 - Prob. 32PECh. 10.3 - Prob. 33PECh. 10.3 - Prob. 34PECh. 10.3 - For Exercises 35-42, use A=[24-91312] and...Ch. 10.3 - Prob. 36PECh. 10.3 - For Exercises 35-42, use A=[24-91312] and...Ch. 10.3 - Prob. 38PECh. 10.3 - For Exercises 35-42, use A=[24-91312] and...Ch. 10.3 - Prob. 40PECh. 10.3 - Prob. 41PECh. 10.3 - Prob. 42PECh. 10.3 - Prob. 43PECh. 10.3 - Prob. 44PECh. 10.3 - Prob. 45PECh. 10.3 - Prob. 46PECh. 10.3 - Prob. 47PECh. 10.3 - Prob. 48PECh. 10.3 - Prob. 49PECh. 10.3 - Prob. 50PECh. 10.3 - Given that E is a 51 matrix arid F is a 15 matrix,...Ch. 10.3 - Prob. 52PECh. 10.3 - For Exercises 53-64, (See Examples 6-7) a. Find AB...Ch. 10.3 - Prob. 54PECh. 10.3 - For Exercises 53-64, (See Examples 6-7) a. Find AB...Ch. 10.3 - Prob. 56PECh. 10.3 - For Exercises 53-64, (See Examples 6-7) a. Find AB...Ch. 10.3 - Prob. 58PECh. 10.3 - For Exercises 53-64, (See Examples 6-7) a. Find AB...Ch. 10.3 - For Exercises 53-64, (See Examples 6-7) a. Find AB...Ch. 10.3 - For Exercises 53-64, (See Examples 6-7) a. Find AB...Ch. 10.3 - For Exercises 53-64, (See Examples 6-7) a. Find AB...Ch. 10.3 - Prob. 65PECh. 10.3 - Prob. 66PECh. 10.3 - Prob. 67PECh. 10.3 - Prob. 68PECh. 10.3 - Prob. 69PECh. 10.3 - In matrix C, a coffee shop records the cost to...Ch. 10.3 - A street vendor at a parade sells fresh lemonade,...Ch. 10.3 - Prob. 72PECh. 10.3 - Prob. 73PECh. 10.3 - Prob. 74PECh. 10.3 - The labor costs per hour for an electrician,...Ch. 10.3 - Prob. 76PECh. 10.3 - Prob. 77PECh. 10.3 - Prob. 78PECh. 10.3 - a. Write a matrix A that represents the...Ch. 10.3 - a. Write a matrix A that represents the...Ch. 10.3 - a. Write a matrix A that represents the...Ch. 10.3 - Prob. 82PECh. 10.3 - Prob. 83PECh. 10.3 - Prob. 84PECh. 10.3 - For Exercises 85-86, use the following gray scale....Ch. 10.3 - Prob. 86PECh. 10.3 - Prob. 87PECh. 10.3 - Prob. 88PECh. 10.3 - Prob. 89PECh. 10.3 - Prob. 90PECh. 10.3 - Prob. 91PECh. 10.3 - Prob. 92PECh. 10.3 - Prob. 93PECh. 10.3 - Prob. 94PECh. 10.3 - Prob. 95PECh. 10.3 - Prob. 96PECh. 10.3 - Prob. 97PECh. 10.3 - Prob. 98PECh. 10.3 - Prob. 99PECh. 10.3 - Prob. 100PECh. 10.3 - Prob. 101PECh. 10.3 - Prob. 102PECh. 10.3 - Prob. 103PECh. 10.3 - Prob. 104PECh. 10.4 - Prob. R.1PECh. 10.4 - Prob. R.2PECh. 10.4 - Prob. R.3PECh. 10.4 - Prob. R.4PECh. 10.4 - Prob. 1PECh. 10.4 - Prob. 2PECh. 10.4 - Prob. 3PECh. 10.4 - A matrix that does not have an inverse is called a...Ch. 10.4 - Prob. 5PECh. 10.4 - Prob. 6PECh. 10.4 - Prob. 7PECh. 10.4 - Prob. 8PECh. 10.4 - Prob. 9PECh. 10.4 - Prob. 10PECh. 10.4 - Prob. 11PECh. 10.4 - Prob. 12PECh. 10.4 - Prob. 13PECh. 10.4 - Prob. 14PECh. 10.4 - Prob. 15PECh. 10.4 - Prob. 16PECh. 10.4 - Prob. 17PECh. 10.4 - Prob. 18PECh. 10.4 - Prob. 19PECh. 10.4 - Prob. 20PECh. 10.4 - Prob. 21PECh. 10.4 - Prob. 22PECh. 10.4 - Prob. 23PECh. 10.4 - Prob. 24PECh. 10.4 - Prob. 25PECh. 10.4 - Prob. 26PECh. 10.4 - Prob. 27PECh. 10.4 - Prob. 28PECh. 10.4 - Prob. 29PECh. 10.4 - Prob. 30PECh. 10.4 - For Exercises 19-34, determine the inverse of the...Ch. 10.4 - Prob. 32PECh. 10.4 - Prob. 33PECh. 10.4 - Prob. 34PECh. 10.4 - Prob. 35PECh. 10.4 - Prob. 36PECh. 10.4 - Prob. 37PECh. 10.4 - Prob. 38PECh. 10.4 - Prob. 39PECh. 10.4 - Prob. 40PECh. 10.4 - Prob. 41PECh. 10.4 - Prob. 42PECh. 10.4 - Prob. 43PECh. 10.4 - Prob. 44PECh. 10.4 - Prob. 45PECh. 10.4 - Prob. 46PECh. 10.4 - Prob. 47PECh. 10.4 - Prob. 48PECh. 10.4 - For Exercises 39-50, solve the system by using the...Ch. 10.4 - For Exercises 39-50, solve the system by using the...Ch. 10.4 - Prob. 51PECh. 10.4 - Prob. 52PECh. 10.4 - Prob. 53PECh. 10.4 - Prob. 54PECh. 10.4 - Prob. 55PECh. 10.4 - Prob. 56PECh. 10.4 - Prob. 57PECh. 10.4 - Prob. 58PECh. 10.4 - Prob. 59PECh. 10.4 - Prob. 60PECh. 10.4 - Prob. 61PECh. 10.4 - Prob. 62PECh. 10.4 - Prob. 63PECh. 10.4 - Prob. 64PECh. 10.4 - Prob. 65PECh. 10.4 - Prob. 66PECh. 10.4 - Prob. 67PECh. 10.4 - Prob. 68PECh. 10.4 - Prob. 69PECh. 10.4 - Prob. 70PECh. 10.4 - Prob. 71PECh. 10.4 - For Exercises 72-73, use a graphing calculator and...Ch. 10.4 - Prob. 73PECh. 10.5 - For Exercises R1-R.2, simplify the exponential...Ch. 10.5 - Prob. R.2PECh. 10.5 - Prob. R.3PECh. 10.5 - Prob. 1PECh. 10.5 - Prob. 2PECh. 10.5 - Prob. 3PECh. 10.5 - Prob. 4PECh. 10.5 - Prob. 5PECh. 10.5 - Prob. 6PECh. 10.5 - For Exercises 7-16, evaluate the determinant of...Ch. 10.5 - Prob. 8PECh. 10.5 - Prob. 9PECh. 10.5 - Prob. 10PECh. 10.5 - For Exercises 7-16, evaluate the determinant of...Ch. 10.5 - Prob. 12PECh. 10.5 - Prob. 13PECh. 10.5 - Prob. 14PECh. 10.5 - Prob. 15PECh. 10.5 - Prob. 16PECh. 10.5 - Prob. 17PECh. 10.5 - Prob. 18PECh. 10.5 - Prob. 19PECh. 10.5 - Prob. 20PECh. 10.5 - Prob. 21PECh. 10.5 - Prob. 22PECh. 10.5 - Prob. 23PECh. 10.5 - Prob. 24PECh. 10.5 - Prob. 25PECh. 10.5 - Prob. 26PECh. 10.5 - Prob. 27PECh. 10.5 - Prob. 28PECh. 10.5 - Prob. 29PECh. 10.5 - Prob. 30PECh. 10.5 - Prob. 31PECh. 10.5 - Prob. 32PECh. 10.5 - For Exercises 33-48, solve the system if possible...Ch. 10.5 - Prob. 34PECh. 10.5 - For Exercises 33-48, solve the system if possible...Ch. 10.5 - Prob. 36PECh. 10.5 - Prob. 37PECh. 10.5 - Prob. 38PECh. 10.5 - For Exercises 33-48, solve the system if possible...Ch. 10.5 - Prob. 40PECh. 10.5 - Prob. 41PECh. 10.5 - Prob. 42PECh. 10.5 - Prob. 43PECh. 10.5 - Prob. 44PECh. 10.5 - Prob. 45PECh. 10.5 - Prob. 46PECh. 10.5 - Prob. 47PECh. 10.5 - Prob. 48PECh. 10.5 - Prob. 49PECh. 10.5 - Prob. 50PECh. 10.5 - Prob. 51PECh. 10.5 - Prob. 52PECh. 10.5 - Prob. 53PECh. 10.5 - Prob. 54PECh. 10.5 - Prob. 55PECh. 10.5 - Prob. 56PECh. 10.5 - Prob. 57PECh. 10.5 - Prob. 58PECh. 10.5 - Prob. 59PECh. 10.5 - Given a square matrix A, elementary row operations...Ch. 10.5 - Prob. 61PECh. 10.5 - Prob. 62PECh. 10.5 - Prob. 63PECh. 10.5 - Prob. 64PECh. 10.5 - Prob. 65PECh. 10.5 - Prob. 66PECh. 10.5 - Prob. 67PECh. 10.5 - Prob. 68PECh. 10.5 - Prob. 69PECh. 10.5 - Prob. 70PECh. 10.5 - Prob. 71PECh. 10.5 - Prob. 72PECh. 10.5 - Prob. 73PECh. 10.5 - Prob. 74PECh. 10.5 - Prob. 75PECh. 10.5 - Prob. 76PECh. 10.5 - Prob. 77PECh. 10.5 - Prob. 78PECh. 10.5 - Prob. 79PECh. 10.5 - Prob. 80PECh. 10.5 - Prob. 81PECh. 10.5 - Prob. 82PECh. 10 - For Exercises 1-4, solve the system of equations...Ch. 10 - For Exercises 1-4, solve the system of equations...Ch. 10 - For Exercises 1-4, solve the system of equations...Ch. 10 - Prob. 4PRECh. 10 - For Exercises 5-8, Evaluate the determinant of the...Ch. 10 - Prob. 6PRECh. 10 - For Exercises 5-8, Evaluate the determinant of the...Ch. 10 - For Exercises 5-8, Evaluate the determinant of the...Ch. 10 - Prob. 1RECh. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Prob. 8RECh. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Prob. 12RECh. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Prob. 20RECh. 10 - Prob. 21RECh. 10 - Prob. 22RECh. 10 - Prob. 23RECh. 10 - Prob. 24RECh. 10 - Prob. 25RECh. 10 - Prob. 26RECh. 10 - Prob. 27RECh. 10 - Prob. 28RECh. 10 - Prob. 29RECh. 10 - Prob. 30RECh. 10 - Prob. 31RECh. 10 - Prob. 32RECh. 10 - Prob. 33RECh. 10 - Prob. 34RECh. 10 - Prob. 35RECh. 10 - Prob. 36RECh. 10 - Prob. 37RECh. 10 - Prob. 38RECh. 10 - Prob. 39RECh. 10 - Prob. 40RECh. 10 - Prob. 41RECh. 10 - Prob. 42RECh. 10 - Prob. 43RECh. 10 - Prob. 44RECh. 10 - Prob. 45RECh. 10 - Prob. 46RECh. 10 - Prob. 47RECh. 10 - Prob. 48RECh. 10 - Prob. 49RECh. 10 - Prob. 50RECh. 10 - Prob. 51RECh. 10 - Prob. 52RECh. 10 - Prob. 53RECh. 10 - Prob. 54RECh. 10 - Prob. 55RECh. 10 - Prob. 56RECh. 10 - Prob. 57RECh. 10 - Prob. 58RECh. 10 - Prob. 59RECh. 10 - Prob. 60RECh. 10 - Prob. 61RECh. 10 - Prob. 62RECh. 10 - Prob. 63RECh. 10 - Prob. 64RECh. 10 - Prob. 65RECh. 10 - Prob. 66RECh. 10 - Prob. 67RECh. 10 - Prob. 68RECh. 10 - Prob. 69RECh. 10 - Prob. 70RECh. 10 - Prob. 71RECh. 10 - Prob. 72RECh. 10 - Prob. 73RECh. 10 - Prob. 74RECh. 10 - Prob. 75RECh. 10 - Prob. 76RECh. 10 - Prob. 77RECh. 10 - Prob. 78RECh. 10 - Prob. 1TCh. 10 - Prob. 2TCh. 10 - Prob. 3TCh. 10 - Prob. 4TCh. 10 - Prob. 5TCh. 10 - Prob. 6TCh. 10 - Prob. 7TCh. 10 - Prob. 8TCh. 10 - Prob. 9TCh. 10 - Prob. 10TCh. 10 - Prob. 11TCh. 10 - Prob. 12TCh. 10 - For Exercises 13-16, solve the system by using...Ch. 10 - Prob. 14TCh. 10 - Prob. 15TCh. 10 - Prob. 16TCh. 10 - Prob. 17TCh. 10 - Prob. 18TCh. 10 - Prob. 19TCh. 10 - Prob. 20TCh. 10 - Prob. 21TCh. 10 - Prob. 22TCh. 10 - Prob. 23TCh. 10 - Prob. 24TCh. 10 - Prob. 25TCh. 10 - Prob. 26TCh. 10 - Prob. 27TCh. 10 - Prob. 28TCh. 10 - Prob. 29TCh. 10 - Prob. 30TCh. 10 - Prob. 31TCh. 10 - Prob. 32TCh. 10 - Prob. 1CRECh. 10 - Prob. 2CRECh. 10 - Prob. 3CRECh. 10 - Prob. 4CRECh. 10 - Prob. 5CRECh. 10 - Prob. 6CRECh. 10 - Prob. 7CRECh. 10 - Prob. 8CRECh. 10 - Prob. 9CRECh. 10 - Prob. 10CRECh. 10 - Prob. 11CRECh. 10 - Prob. 12CRECh. 10 - Prob. 13CRECh. 10 - Prob. 14CRECh. 10 - Prob. 15CRECh. 10 - Prob. 16CRECh. 10 - Prob. 17CRECh. 10 - Prob. 18CRECh. 10 - Prob. 19CRECh. 10 - Prob. 20CRECh. 10 - Prob. 21CRECh. 10 - Prob. 22CRECh. 10 - Prob. 23CRECh. 10 - Prob. 24CRECh. 10 - Prob. 25CRECh. 10 - Prob. 26CRECh. 10 - Prob. 27CRECh. 10 - Prob. 28CRECh. 10 - Prob. 29CRECh. 10 - Prob. 30CRE
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