College Algebra & Trigonometry - Standalone book
1st Edition
ISBN: 9780078035623
Author: Julie Miller, Donna Gerken
Publisher: McGraw-Hill Education
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Chapter 9.5, Problem 45PE
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Chapter 9 Solutions
College Algebra & Trigonometry - Standalone book
Ch. 9.1 - For Exercises R.1-R.4, solve the equation. R.1...Ch. 9.1 - Prob. R.2PECh. 9.1 - For Exercises R.1-R.4, solve the equation. R.3...Ch. 9.1 - Prob. R.4PECh. 9.1 - Graph the equation and identify the x and y-...Ch. 9.1 - Prob. R.6PECh. 9.1 - Prob. 1PECh. 9.1 - Prob. 2PECh. 9.1 - Prob. 3PECh. 9.1 - Prob. 4PE
Ch. 9.1 - A system of equations that has no solution is...Ch. 9.1 - A system of linear equations in two variables may...Ch. 9.1 - For Exercises 7-10, determine if the ordered pair...Ch. 9.1 - Prob. 8PECh. 9.1 - For Exercises 7-10, determine if the ordered pair...Ch. 9.1 - Prob. 10PECh. 9.1 - For Exercises 11-14, a system of equations is...Ch. 9.1 - For Exercises 11-14, a system of equations is...Ch. 9.1 - Prob. 13PECh. 9.1 - Prob. 14PECh. 9.1 - For Exercises 15-20, solve the system of equations...Ch. 9.1 - Prob. 16PECh. 9.1 - For Exercises 15-20, solve the system of equations...Ch. 9.1 - Prob. 18PECh. 9.1 - For Exercises 15-20, solve the system of equations...Ch. 9.1 - Prob. 20PECh. 9.1 - For Exercises 21-28, solve the system of equations...Ch. 9.1 - Prob. 22PECh. 9.1 - For Exercises 21-28, solve the system of equations...Ch. 9.1 - Prob. 24PECh. 9.1 - For Exercises 21-28, solve the system of equations...Ch. 9.1 - Prob. 26PECh. 9.1 - For Exercises 21-28, solve the system of equations...Ch. 9.1 - Prob. 28PECh. 9.1 - For Exercises 2934, solve the system by using any...Ch. 9.1 - Prob. 30PECh. 9.1 - For Exercises 2934, solve the system by using any...Ch. 9.1 - Prob. 32PECh. 9.1 - Prob. 33PECh. 9.1 - Prob. 34PECh. 9.1 - For Exercises 3536, Write the general solution....Ch. 9.1 - For Exercises 3536, Write the general solution....Ch. 9.1 - Prob. 37PECh. 9.1 - Prob. 38PECh. 9.1 - For Exercises 3750, solve the system using any...Ch. 9.1 - Prob. 40PECh. 9.1 - Prob. 41PECh. 9.1 - Prob. 42PECh. 9.1 - Prob. 43PECh. 9.1 - Prob. 44PECh. 9.1 - Prob. 45PECh. 9.1 - Prob. 46PECh. 9.1 - Prob. 47PECh. 9.1 - Prob. 48PECh. 9.1 - Prob. 49PECh. 9.1 - Prob. 50PECh. 9.1 - One antifreeze solution is 36% alcohol and another...Ch. 9.1 - Prob. 52PECh. 9.1 - A radiator has 16 L of a 36% antifreeze solution....Ch. 9.1 - Prob. 54PECh. 9.1 - Michelle borrows a total of $5000 in student loans...Ch. 9.1 - Prob. 56PECh. 9.1 - Prob. 57PECh. 9.1 - A total of $6000 is invested for 5 yr with a total...Ch. 9.1 - Monique and Tara each make an ice cream sundae....Ch. 9.1 - Prob. 60PECh. 9.1 - Prob. 61PECh. 9.1 - The average of an electrician's hourly wage and a...Ch. 9.1 - A moving sidewalk in an airport moves people...Ch. 9.1 - Prob. 64PECh. 9.1 - Prob. 65PECh. 9.1 - Prob. 66PECh. 9.1 - A cleaning company charges $100 for each office it...Ch. 9.1 - Prob. 68PECh. 9.1 - For Exercises 6970, refer to Figure 9-1 and the...Ch. 9.1 - Prob. 70PECh. 9.1 - Prob. 71PECh. 9.1 - Prob. 72PECh. 9.1 - Prob. 73PECh. 9.1 - Prob. 74PECh. 9.1 - Two angles are complementary. The measure of one...Ch. 9.1 - Prob. 76PECh. 9.1 - For Exercises 7778, find the measure of angles x...Ch. 9.1 - Prob. 78PECh. 9.1 - Prob. 79PECh. 9.1 - Prob. 80PECh. 9.1 - Prob. 81PECh. 9.1 - Prob. 82PECh. 9.1 - Prob. 83PECh. 9.1 - Prob. 84PECh. 9.1 - Prob. 85PECh. 9.1 - Prob. 86PECh. 9.1 - Prob. 87PECh. 9.1 - Prob. 88PECh. 9.1 - Prob. 89PECh. 9.1 - Prob. 90PECh. 9.1 - Prob. 91PECh. 9.1 - Prob. 92PECh. 9.1 - Prob. 93PECh. 9.1 - Prob. 94PECh. 9.1 - Prob. 95PECh. 9.1 - Prob. 96PECh. 9.1 - Prob. 97PECh. 9.1 - Prob. 98PECh. 9.1 - Prob. 99PECh. 9.2 - How much interest will Roxanne have to pay if she...Ch. 9.2 - Prob. R.2PECh. 9.2 - Prob. R.3PECh. 9.2 - Prob. 1PECh. 9.2 - Prob. 2PECh. 9.2 - Prob. 3PECh. 9.2 - Prob. 4PECh. 9.2 - For Exercises 5-8, determine if the ordered triple...Ch. 9.2 - Prob. 6PECh. 9.2 - Prob. 7PECh. 9.2 - Prob. 8PECh. 9.2 - For Exercises 9-32, solve the system. If a system...Ch. 9.2 - Prob. 10PECh. 9.2 - For Exercises 9-32, solve the system. If a system...Ch. 9.2 - Prob. 12PECh. 9.2 - For Exercises 9-32, solve the system. If a system...Ch. 9.2 - Prob. 14PECh. 9.2 - For Exercises 9-32, solve the system. If a system...Ch. 9.2 - Prob. 16PECh. 9.2 - For Exercises 9-32, solve the system. If a system...Ch. 9.2 - Prob. 18PECh. 9.2 - For Exercises 9-32, solve the system. If a system...Ch. 9.2 - Prob. 20PECh. 9.2 - For Exercises 9-32, solve the system. If a system...Ch. 9.2 - Prob. 22PECh. 9.2 - Prob. 23PECh. 9.2 - Prob. 24PECh. 9.2 - For Exercises 9-32, solve the system. If a system...Ch. 9.2 - Prob. 26PECh. 9.2 - Prob. 27PECh. 9.2 - Prob. 28PECh. 9.2 - Prob. 29PECh. 9.2 - Prob. 30PECh. 9.2 - Prob. 31PECh. 9.2 - Prob. 32PECh. 9.2 - Prob. 33PECh. 9.2 - Prob. 34PECh. 9.2 - Prob. 35PECh. 9.2 - Prob. 36PECh. 9.2 - Prob. 37PECh. 9.2 - Prob. 38PECh. 9.2 - Devon invested $8000 in three different mutual...Ch. 9.2 - Prob. 40PECh. 9.2 - A basketball player scored 26 points in one game....Ch. 9.2 - Prob. 42PECh. 9.2 - Prob. 43PECh. 9.2 - Prob. 44PECh. 9.2 - Prob. 45PECh. 9.2 - Prob. 46PECh. 9.2 - The measure of the largest angle in a triangle is...Ch. 9.2 - Prob. 48PECh. 9.2 - a. Show that the points (l, 0), (3, 10), and (-2,...Ch. 9.2 - Prob. 50PECh. 9.2 - For Exercises 51-52, find an equation of the form...Ch. 9.2 - For Exercises 51-52, find an equation of the form...Ch. 9.2 - Prob. 53PECh. 9.2 - Prob. 54PECh. 9.2 - Prob. 55PECh. 9.2 - Many statistics courses cover a topic called...Ch. 9.2 - Prob. 57PECh. 9.2 - Prob. 58PECh. 9.2 - Prob. 59PECh. 9.2 - Prob. 60PECh. 9.2 - Prob. 61PECh. 9.2 - Prob. 62PECh. 9.2 - Prob. 63PECh. 9.2 - Prob. 64PECh. 9.2 - Prob. 65PECh. 9.2 - Prob. 66PECh. 9.2 - Prob. 67PECh. 9.2 - Prob. 68PECh. 9.3 - Prob. R.1PECh. 9.3 - Prob. R.2PECh. 9.3 - Prob. R.3PECh. 9.3 - Prob. R.4PECh. 9.3 - Prob. R.5PECh. 9.3 - Prob. 1PECh. 9.3 - Prob. 2PECh. 9.3 - Prob. 3PECh. 9.3 - Prob. 4PECh. 9.3 - Prob. 5PECh. 9.3 - Prob. 6PECh. 9.3 - Prob. 7PECh. 9.3 - Prob. 8PECh. 9.3 - Prob. 9PECh. 9.3 - Prob. 10PECh. 9.3 - Prob. 11PECh. 9.3 - Prob. 12PECh. 9.3 - Prob. 13PECh. 9.3 - Prob. 14PECh. 9.3 - Prob. 15PECh. 9.3 - Prob. 16PECh. 9.3 - Prob. 17PECh. 9.3 - Prob. 18PECh. 9.3 - Prob. 19PECh. 9.3 - Prob. 20PECh. 9.3 - Prob. 21PECh. 9.3 - Prob. 22PECh. 9.3 - Prob. 23PECh. 9.3 - Prob. 24PECh. 9.3 - Prob. 25PECh. 9.3 - Prob. 26PECh. 9.3 - Prob. 27PECh. 9.3 - Prob. 28PECh. 9.3 - Prob. 29PECh. 9.3 - Prob. 30PECh. 9.3 - Prob. 31PECh. 9.3 - Prob. 32PECh. 9.3 - Prob. 33PECh. 9.3 - Prob. 34PECh. 9.3 - Prob. 35PECh. 9.3 - Prob. 36PECh. 9.3 - Prob. 37PECh. 9.3 - Prob. 38PECh. 9.3 - Prob. 39PECh. 9.3 - Prob. 40PECh. 9.3 - Prob. 41PECh. 9.3 - Prob. 42PECh. 9.3 - Prob. 43PECh. 9.3 - Prob. 44PECh. 9.3 - Prob. 45PECh. 9.3 - Prob. 46PECh. 9.3 - Prob. 47PECh. 9.3 - Prob. 48PECh. 9.3 - Prob. 49PECh. 9.3 - Prob. 50PECh. 9.3 - Prob. 51PECh. 9.3 - Prob. 52PECh. 9.3 - Prob. 53PECh. 9.3 - Prob. 54PECh. 9.3 - Prob. 55PECh. 9.3 - Prob. 56PECh. 9.4 - For Exercises R.1-R.3, graph the equation. R.1....Ch. 9.4 - Prob. R.2PECh. 9.4 - Prob. R.3PECh. 9.4 - Prob. R.4PECh. 9.4 - Prob. R.5PECh. 9.4 - Prob. 1PECh. 9.4 - Prob. 2PECh. 9.4 - For Exercises 3-14, a. Graph the equations in the...Ch. 9.4 - Prob. 4PECh. 9.4 - Prob. 5PECh. 9.4 - Prob. 6PECh. 9.4 - For Exercises 3-14, a. Graph the equations in the...Ch. 9.4 - Prob. 8PECh. 9.4 - Prob. 9PECh. 9.4 - Prob. 10PECh. 9.4 - For Exercises 3-14, a. Graph the equations in the...Ch. 9.4 - Prob. 12PECh. 9.4 - For Exercises 3-14, a. Graph the equations in the...Ch. 9.4 - Prob. 14PECh. 9.4 - Prob. 15PECh. 9.4 - Prob. 16PECh. 9.4 - For Exercises 15-22, solve the system by using the...Ch. 9.4 - Prob. 18PECh. 9.4 - Prob. 19PECh. 9.4 - Prob. 20PECh. 9.4 - Prob. 21PECh. 9.4 - Prob. 22PECh. 9.4 - Prob. 23PECh. 9.4 - Prob. 24PECh. 9.4 - Prob. 25PECh. 9.4 - Prob. 26PECh. 9.4 - Prob. 27PECh. 9.4 - Prob. 28PECh. 9.4 - Prob. 29PECh. 9.4 - Prob. 30PECh. 9.4 - Prob. 31PECh. 9.4 - Prob. 32PECh. 9.4 - Prob. 33PECh. 9.4 - Prob. 34PECh. 9.4 - Prob. 35PECh. 9.4 - Prob. 36PECh. 9.4 - Find two numbers whose sum is 12 and whose product...Ch. 9.4 - Prob. 38PECh. 9.4 - Prob. 39PECh. 9.4 - Prob. 40PECh. 9.4 - Prob. 41PECh. 9.4 - Prob. 42PECh. 9.4 - Prob. 43PECh. 9.4 - Prob. 44PECh. 9.4 - Prob. 45PECh. 9.4 - Prob. 46PECh. 9.4 - Prob. 47PECh. 9.4 - Prob. 48PECh. 9.4 - Prob. 49PECh. 9.4 - Prob. 50PECh. 9.4 - Prob. 51PECh. 9.4 - Prob. 52PECh. 9.4 - Prob. 53PECh. 9.4 - Prob. 54PECh. 9.4 - Prob. 55PECh. 9.4 - Prob. 56PECh. 9.4 - Prob. 57PECh. 9.4 - Prob. 58PECh. 9.4 - Prob. 59PECh. 9.4 - Prob. 60PECh. 9.4 - Prob. 61PECh. 9.4 - Prob. 62PECh. 9.4 - Prob. 63PECh. 9.4 - Prob. 64PECh. 9.4 - Prob. 65PECh. 9.4 - Prob. 66PECh. 9.4 - Prob. 67PECh. 9.4 - Prob. 68PECh. 9.4 - Prob. 69PECh. 9.4 - Prob. 70PECh. 9.4 - Prob. 71PECh. 9.4 - Prob. 72PECh. 9.4 - Prob. 73PECh. 9.4 - Prob. 74PECh. 9.4 - Prob. 75PECh. 9.4 - Prob. 76PECh. 9.4 - Prob. 77PECh. 9.4 - Prob. 78PECh. 9.4 - Prob. 79PECh. 9.4 - Prob. 80PECh. 9.5 - Use the graph to solve the equation and...Ch. 9.5 - Prob. 1PECh. 9.5 - Prob. 2PECh. 9.5 - Prob. 3PECh. 9.5 - Prob. 4PECh. 9.5 - Prob. 5PECh. 9.5 - Prob. 6PECh. 9.5 - Prob. 7PECh. 9.5 - Prob. 8PECh. 9.5 - Prob. 9PECh. 9.5 - Prob. 10PECh. 9.5 - Prob. 11PECh. 9.5 - Prob. 12PECh. 9.5 - Prob. 13PECh. 9.5 - Prob. 14PECh. 9.5 - Prob. 15PECh. 9.5 - Prob. 16PECh. 9.5 - Prob. 17PECh. 9.5 - Prob. 18PECh. 9.5 - Prob. 19PECh. 9.5 - Prob. 20PECh. 9.5 - Prob. 21PECh. 9.5 - Prob. 22PECh. 9.5 - Prob. 23PECh. 9.5 - Prob. 24PECh. 9.5 - Prob. 25PECh. 9.5 - Prob. 26PECh. 9.5 - Prob. 27PECh. 9.5 - Prob. 28PECh. 9.5 - Prob. 29PECh. 9.5 - Prob. 30PECh. 9.5 - Prob. 31PECh. 9.5 - Prob. 32PECh. 9.5 - Prob. 33PECh. 9.5 - Prob. 34PECh. 9.5 - Prob. 35PECh. 9.5 - Prob. 36PECh. 9.5 - Prob. 37PECh. 9.5 - Prob. 38PECh. 9.5 - Prob. 39PECh. 9.5 - Prob. 40PECh. 9.5 - Prob. 41PECh. 9.5 - Prob. 42PECh. 9.5 - Prob. 43PECh. 9.5 - Prob. 44PECh. 9.5 - Prob. 45PECh. 9.5 - Prob. 46PECh. 9.5 - Prob. 47PECh. 9.5 - Prob. 48PECh. 9.5 - Prob. 49PECh. 9.5 - Prob. 50PECh. 9.5 - Prob. 51PECh. 9.5 - Prob. 52PECh. 9.5 - Prob. 53PECh. 9.5 - For Exercises 41-58, graph the solution set. If...Ch. 9.5 - For Exercises 41-58, graph the solution set. If...Ch. 9.5 - Prob. 56PECh. 9.5 - For Exercises 41-58, graph the solution set. If...Ch. 9.5 - For Exercises 41-58, graph the solution set. If...Ch. 9.5 - Prob. 59PECh. 9.5 - Prob. 60PECh. 9.5 - Prob. 61PECh. 9.5 - Prob. 62PECh. 9.5 - Prob. 63PECh. 9.5 - Prob. 64PECh. 9.5 - Prob. 65PECh. 9.5 - Prob. 66PECh. 9.5 - Prob. 67PECh. 9.5 - Prob. 68PECh. 9.5 - Prob. 69PECh. 9.5 - Prob. 70PECh. 9.5 - Prob. 71PECh. 9.5 - Prob. 72PECh. 9.5 - Prob. 73PECh. 9.5 - Prob. 74PECh. 9.5 - Prob. 75PECh. 9.5 - Explain how test points are used to determine the...Ch. 9.5 - Prob. 77PECh. 9.5 - Prob. 78PECh. 9.5 - Prob. 79PECh. 9.5 - Prob. 80PECh. 9.5 - Prob. 81PECh. 9.5 - Prob. 82PECh. 9.6 - A salesperson makes a base salary of $500 per week...Ch. 9.6 - A luxury car rental company charges $123 per day...Ch. 9.6 - The process that maximizes or minimizes a function...Ch. 9.6 - The function to be optimized in a linear...Ch. 9.6 - The region in the plane that represents the...Ch. 9.6 - The points of intersection of a feasible region...Ch. 9.6 - Prob. 5PECh. 9.6 - Prob. 6PECh. 9.6 - Prob. 7PECh. 9.6 - Prob. 8PECh. 9.6 - Prob. 9PECh. 9.6 - Prob. 10PECh. 9.6 - Prob. 11PECh. 9.6 - Prob. 12PECh. 9.6 - Prob. 13PECh. 9.6 - Prob. 14PECh. 9.6 - Prob. 15PECh. 9.6 - Prob. 16PECh. 9.6 - Prob. 17PECh. 9.6 - Prob. 18PECh. 9.6 - Prob. 19PECh. 9.6 - Prob. 20PECh. 9.6 - Prob. 21PECh. 9.6 - Guyton makes $24/hr tutoring chemistry and $20/hr...Ch. 9.6 - A plant nursery sells two sizes of oak trees to...Ch. 9.6 - A sporting goods store sells two types of exercise...Ch. 9.6 - Prob. 25PECh. 9.6 - A large department store needs at least 3600 labor...Ch. 9.6 - A manufacturer produces two models of a gas grill....Ch. 9.6 - Prob. 28PECh. 9.6 - A farmer has 1200 acres ofland and plans to plant...Ch. 9.6 - Prob. 30PECh. 9.6 - Prob. 31PECh. 9.6 - Prob. 32PECh. 9.6 - Prob. 33PECh. 9.6 - Prob. 34PECh. 9 - For Exercises 1-2, for parts (a) and (b), graph...Ch. 9 - For Exercises 1-2, for parts (a) and (b), graph...Ch. 9 - Prob. 3PRECh. 9 - Prob. 4PRECh. 9 - Prob. 1RECh. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - Prob. 18RECh. 9 - Emily receives an inheritance of $20,000 and...Ch. 9 - Prob. 20RECh. 9 - For Exercises 20-21, use a system of linear...Ch. 9 - Prob. 22RECh. 9 - Prob. 23RECh. 9 - Prob. 24RECh. 9 - Prob. 25RECh. 9 - Prob. 26RECh. 9 - Prob. 27RECh. 9 - Prob. 28RECh. 9 - Prob. 29RECh. 9 - Prob. 30RECh. 9 - Prob. 31RECh. 9 - Prob. 32RECh. 9 - Prob. 33RECh. 9 - Prob. 34RECh. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Prob. 37RECh. 9 - The sum of the squares of two negative numbers is...Ch. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 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 - Prob. 54RECh. 9 - Prob. 55RECh. 9 - Prob. 56RECh. 9 - Prob. 57RECh. 9 - A fitness instructor wants to mix two brands...Ch. 9 - Prob. 1TCh. 9 - Prob. 2TCh. 9 - Prob. 3TCh. 9 - Prob. 4TCh. 9 - Prob. 5TCh. 9 - Prob. 6TCh. 9 - Prob. 7TCh. 9 - Prob. 8TCh. 9 - Prob. 9TCh. 9 - Prob. 10TCh. 9 - Prob. 11TCh. 9 - Prob. 12TCh. 9 - Prob. 13TCh. 9 - Prob. 14TCh. 9 - Prob. 15TCh. 9 - Prob. 16TCh. 9 - Prob. 17TCh. 9 - Prob. 18TCh. 9 - Prob. 19TCh. 9 - Prob. 20TCh. 9 - Use a system of linear equations in three...Ch. 9 - Prob. 22TCh. 9 - Prob. 23TCh. 9 - Prob. 24TCh. 9 - Prob. 25TCh. 9 - Prob. 26TCh. 9 - Prob. 27TCh. 9 - Prob. 28TCh. 9 - Prob. 29TCh. 9 - Prob. 30TCh. 9 - Prob. 31TCh. 9 - Prob. 32TCh. 9 - Prob. 33TCh. 9 - Prob. 34TCh. 9 - Prob. 35TCh. 9 - Prob. 36TCh. 9 - A weight lifter wants to mix two types of protein...Ch. 9 - Prob. 1CRECh. 9 - Prob. 2CRECh. 9 - Prob. 3CRECh. 9 - Prob. 4CRECh. 9 - Prob. 5CRECh. 9 - Prob. 6CRECh. 9 - Prob. 7CRECh. 9 - Prob. 8CRECh. 9 - Prob. 9CRECh. 9 - Prob. 10CRECh. 9 - Prob. 11CRECh. 9 - Prob. 12CRECh. 9 - Prob. 13CRECh. 9 - Prob. 14CRECh. 9 - Prob. 15CRECh. 9 - Prob. 16CRECh. 9 - Prob. 17CRECh. 9 - Prob. 18CRECh. 9 - Prob. 19CRECh. 9 - Prob. 20CRECh. 9 - Prob. 21CRECh. 9 - Prob. 22CRE
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- Make up two polynomial functions, f(x) and g(x). • f(x) should be of degree 3 or higher. g(x) should be of degree 4 or higher. • Find f(3) in each of the three ways: substitution, remainder theorem (synthetic division), and long division. You should get the same answer three times for f(3). Find g(-2) once using your choice of the three methods.arrow_forwardere are many real-world situations that exhibit exponential and logarithmic nctions. • Describe two real world scenarios, one exponential and one logarithmic. Do not identify yet whether your scenarios are logarithmic or exponential.arrow_forwardstacie is a resident at a medical facility you work at. You are asked to chart the amount of solid food that she consumes.For the noon meal today, she ate 1/2 of a 3 ounce serving of meatloaf, 3/4 of her 3 ounce serving of mashed potatoes, and 1/3 of her 2 ounce serving of green beans. Show in decimal form how many ounces of solid food that Stacie consumedarrow_forward
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