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Category: Mathematics

  • [Solved] Prof Double R

    ✓ Verified Academic Solution Available

    Executive Solution Overview

    [>Algebra homework help](https://www.sweetstudy.com/fields/mathematics-algebra) COMPLETE THE ATTACH ASSIGNMENT BELOW – [\ \ IMG_2424DDE6-0A18-4233-AF5D-0126F7DE6E49.jpg](https://www.sweetstudy.com/files/img-2424dde6-0a18-4233-af5d-0126f7de6e49-jpg "IMG_2424DDE6-0A18-4233-AF5D-0126F7DE6E49.jpg")

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    Assignment Prompt & Instructions

    [>Algebra homework help](https://www.sweetstudy.com/fields/mathematics-algebra)

    COMPLETE THE ATTACH ASSIGNMENT BELOW

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  • [Solved] Math Unit VII

    ✓ Verified Academic Solution Available

    Executive Solution Overview

    [>Algebra homework help](https://www.sweetstudy.com/fields/mathematics-algebra) See attached **files (2)** – ## UnitVIIJournal.docx – ## UnitVIIStudyGuide.pdf **## UnitVIIJournal.docx** Unit VII Journal Watch [_Video 4: Embracing Challenges_](https://mediaplayer.pearsoncmg.com/assets/mindset_4?cente…

    Instant Solution Download

    $6.99

    Immediate access to the full model answer, formatted citations, and rubric breakdown.

    Need a Fresh Custom Paper?

    Have this question answered from scratch according to your specific instructions and deadline.

    Order on TutorsGallery →

    Assignment Prompt & Instructions

    [>Algebra homework help](https://www.sweetstudy.com/fields/mathematics-algebra)

    See attached

    **files (2)**

    – ## UnitVIIJournal.docx

    – ## UnitVIIStudyGuide.pdf

    **## UnitVIIJournal.docx**

    Unit VII Journal

    Watch
    [_Video 4: Embracing Challenges_](https://mediaplayer.pearsoncmg.com/assets/mindset_4?centerwin=yes). Reflect on your time in this course. What challenges have you faced? What strategies or mindsets did you implement to overcome these challenges? How could you improve your strategy and mindset so that they are more effective?

    [https://mediaplayer.pearsoncmg.com/assets/mindset_4?centerwin=yes](https://mediaplayer.pearsoncmg.com/assets/mindset_4?centerwin=yes)

    Your journal entry must be at least 200 words in length. No references or citations are necessary.

    **## UnitVIIStudyGuide.pdf**

    MAT 1302, College Algebra 1

    Course Learning Outcomes for Unit VII

    Upon completion of this unit, students should be able to:

    3. Utilize algebraic principles to graph systems.
    3.1 Investigate whether an ordered pair is a solution of a linear system in two variables.
    3.2 Solve linear and nonlinear systems by the substitution and addition method.
    3.3 Solve applications involving systems of linear equations in two variables.

    6. Solve linear systems with two variables.

    6.1 Graph linear and nonlinear inequalities in two variables.
    6.2 Graph linear and nonlinear systems of inequalities.

    Required Unit Resources

    Chapter 5: Systems of Equations and Inequalities, Sections 5.1, 5.4, 5.5

    Unit Lesson

    This unit lesson provides an overview of concepts that you will learn in Unit VII as well as links to required
    lesson videos. For additional instruction and examples, please refer to Sections 5.1, 5.4, and 5.5 in your
    textbook. It is recommended to use the Unit VII Homework Videos Note-Taking Guide as you work through
    the videos.

    Section 5.1: Systems of Linear Equations in Two Variables

    Assume that you are remodeling your home. You want to buy paint for each room and new carpet for each
    bedroom. You have a fixed budget of $3,000. If you know how much the carpet per square foot and paint per
    gallon costs, then you can create a system of equations to help you figure out how much paint and carpet you
    can afford. This scenario describes a system of linear equations in two variables where the variables
    represent the amount of paint and carpet. In this section, we will solve systems of linear equations in two
    variables.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Solutions to a System of Equations

    • Solving Systems of Linear Equations Part I

    • Solving Systems of Linear Equations Part II

    • Applications of Systems of Linear Equations

    Section 5.4: Systems of Nonlinear Equations in Two Variables

    We can expand our knowledge of systems of equations in two variables by looking at nonlinear systems. A
    nonlinear system is a system that contains at least one nonlinear equation. Examples of nonlinear equations
    are quadratic, cubic, and square-root equations.

    UNIT VII STUDY GUIDE

    Systems of Equations and Inequalities

    [https://online.columbiasouthern.edu/bbcswebdav/xid-146144996_1](https://online.columbiasouthern.edu/bbcswebdav/xid-146144996_1)

    [https://www.youtube.com/watch?v=I47hRZ3NkUQ](https://www.youtube.com/watch?v=I47hRZ3NkUQ)

    [https://www.youtube.com/watch?v=FawvUHimJHk](https://www.youtube.com/watch?v=FawvUHimJHk)

    [https://www.youtube.com/watch?v=4pKmdBGbU9g](https://www.youtube.com/watch?v=4pKmdBGbU9g)

    [https://www.youtube.com/watch?v=CnY0y2fjn-8](https://www.youtube.com/watch?v=CnY0y2fjn-8)

    MAT 1302, College Algebra 2

    UNIT x STUDY GUIDE

    Title

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Systems of Nonlinear Equations Part I

    • Systems of Nonlinear Equations Part II

    Section 5.5: Systems of Inequalities

    In Section 5.1, we learned that the point of intersection between two lines is a solution to the system of linear
    equations. In Section 5.4, we learned that there could be multiple solutions when two nonlinear equations or a
    nonlinear and linear equation intersect. In this section, we will examine linear and nonlinear inequalities and
    find the set of all solutions that fits the conditions given by the inequality sign.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Graphing Inequalities

    • MyMathLab Graphing Tool for Inequalities

    • Graphing Systems of Inequalities, Part I

    • MyMathLab Graphing Tool for Systems of Inequalities

    • Graphing Systems of Inequalities Part II

    Additional Help Available

    If you find yourself needing additional assistance with course material, please know that the Math Center
    is available and ready to help. Click the Math Center Request form to get connected with the Math
    Center’s tutors.

    Learning Activities (Nongraded)

    Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit
    them. If you have questions, contact your instructor for further guidance and information.

    Open your study plan in MyMathLab to see your progress and do supplemental practice exercises. The study
    plan will update each time you take an assessment. The study plan is for extra practice.

    For assistance with course content, you may contact your instructor or a math specialist. Click the Student
    Resources link to find contact information for the Math Center.

    [https://www.youtube.com/watch?v=_gswZLpq-Uc](https://www.youtube.com/watch?v=_gswZLpq-Uc)

    [https://www.youtube.com/watch?v=a_ZX_2H6hJs](https://www.youtube.com/watch?v=a_ZX_2H6hJs)

    [https://www.youtube.com/watch?v=ddg1m37BeU4](https://www.youtube.com/watch?v=ddg1m37BeU4)

    [https://www.youtube.com/watch?v=ev0GYvAaPiE](https://www.youtube.com/watch?v=ev0GYvAaPiE)

    [https://www.youtube.com/watch?v=XnKRfTafoIU](https://www.youtube.com/watch?v=XnKRfTafoIU)

    [https://www.youtube.com/watch?v=gKBZgzwEsJg](https://www.youtube.com/watch?v=gKBZgzwEsJg)

    [https://www.youtube.com/watch?v=wnRjLUYlma8](https://www.youtube.com/watch?v=wnRjLUYlma8)

    [https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/](https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/)

    **## UnitVIIStudyGuide.pdf**

    MAT 1302, College Algebra 1

    Course Learning Outcomes for Unit VII

    Upon completion of this unit, students should be able to:

    3. Utilize algebraic principles to graph systems.
    3.1 Investigate whether an ordered pair is a solution of a linear system in two variables.
    3.2 Solve linear and nonlinear systems by the substitution and addition method.
    3.3 Solve applications involving systems of linear equations in two variables.

    6. Solve linear systems with two variables.

    6.1 Graph linear and nonlinear inequalities in two variables.
    6.2 Graph linear and nonlinear systems of inequalities.

    Required Unit Resources

    Chapter 5: Systems of Equations and Inequalities, Sections 5.1, 5.4, 5.5

    Unit Lesson

    This unit lesson provides an overview of concepts that you will learn in Unit VII as well as links to required
    lesson videos. For additional instruction and examples, please refer to Sections 5.1, 5.4, and 5.5 in your
    textbook. It is recommended to use the Unit VII Homework Videos Note-Taking Guide as you work through
    the videos.

    Section 5.1: Systems of Linear Equations in Two Variables

    Assume that you are remodeling your home. You want to buy paint for each room and new carpet for each
    bedroom. You have a fixed budget of $3,000. If you know how much the carpet per square foot and paint per
    gallon costs, then you can create a system of equations to help you figure out how much paint and carpet you
    can afford. This scenario describes a system of linear equations in two variables where the variables
    represent the amount of paint and carpet. In this section, we will solve systems of linear equations in two
    variables.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Solutions to a System of Equations

    • Solving Systems of Linear Equations Part I

    • Solving Systems of Linear Equations Part II

    • Applications of Systems of Linear Equations

    Section 5.4: Systems of Nonlinear Equations in Two Variables

    We can expand our knowledge of systems of equations in two variables by looking at nonlinear systems. A
    nonlinear system is a system that contains at least one nonlinear equation. Examples of nonlinear equations
    are quadratic, cubic, and square-root equations.

    UNIT VII STUDY GUIDE

    Systems of Equations and Inequalities

    [https://online.columbiasouthern.edu/bbcswebdav/xid-146144996_1](https://online.columbiasouthern.edu/bbcswebdav/xid-146144996_1)

    [https://www.youtube.com/watch?v=I47hRZ3NkUQ](https://www.youtube.com/watch?v=I47hRZ3NkUQ)

    [https://www.youtube.com/watch?v=FawvUHimJHk](https://www.youtube.com/watch?v=FawvUHimJHk)

    [https://www.youtube.com/watch?v=4pKmdBGbU9g](https://www.youtube.com/watch?v=4pKmdBGbU9g)

    [https://www.youtube.com/watch?v=CnY0y2fjn-8](https://www.youtube.com/watch?v=CnY0y2fjn-8)

    MAT 1302, College Algebra 2

    UNIT x STUDY GUIDE

    Title

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Systems of Nonlinear Equations Part I

    • Systems of Nonlinear Equations Part II

    Section 5.5: Systems of Inequalities

    In Section 5.1, we learned that the point of intersection between two lines is a solution to the system of linear
    equations. In Section 5.4, we learned that there could be multiple solutions when two nonlinear equations or a
    nonlinear and linear equation intersect. In this section, we will examine linear and nonlinear inequalities and
    find the set of all solutions that fits the conditions given by the inequality sign.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Graphing Inequalities

    • MyMathLab Graphing Tool for Inequalities

    • Graphing Systems of Inequalities, Part I

    • MyMathLab Graphing Tool for Systems of Inequalities

    • Graphing Systems of Inequalities Part II

    Additional Help Available

    If you find yourself needing additional assistance with course material, please know that the Math Center
    is available and ready to help. Click the Math Center Request form to get connected with the Math
    Center’s tutors.

    Learning Activities (Nongraded)

    Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit
    them. If you have questions, contact your instructor for further guidance and information.

    Open your study plan in MyMathLab to see your progress and do supplemental practice exercises. The study
    plan will update each time you take an assessment. The study plan is for extra practice.

    For assistance with course content, you may contact your instructor or a math specialist. Click the Student
    Resources link to find contact information for the Math Center.

    [https://www.youtube.com/watch?v=_gswZLpq-Uc](https://www.youtube.com/watch?v=_gswZLpq-Uc)

    [https://www.youtube.com/watch?v=a_ZX_2H6hJs](https://www.youtube.com/watch?v=a_ZX_2H6hJs)

    [https://www.youtube.com/watch?v=ddg1m37BeU4](https://www.youtube.com/watch?v=ddg1m37BeU4)

    [https://www.youtube.com/watch?v=ev0GYvAaPiE](https://www.youtube.com/watch?v=ev0GYvAaPiE)

    [https://www.youtube.com/watch?v=XnKRfTafoIU](https://www.youtube.com/watch?v=XnKRfTafoIU)

    [https://www.youtube.com/watch?v=gKBZgzwEsJg](https://www.youtube.com/watch?v=gKBZgzwEsJg)

    [https://www.youtube.com/watch?v=wnRjLUYlma8](https://www.youtube.com/watch?v=wnRjLUYlma8)

    [https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/](https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/)

    **## UnitVIIJournal.docx**

    Unit VII Journal

    Watch
    [_Video 4: Embracing Challenges_](https://mediaplayer.pearsoncmg.com/assets/mindset_4?centerwin=yes). Reflect on your time in this course. What challenges have you faced? What strategies or mindsets did you implement to overcome these challenges? How could you improve your strategy and mindset so that they are more effective?

    [https://mediaplayer.pearsoncmg.com/assets/mindset_4?centerwin=yes](https://mediaplayer.pearsoncmg.com/assets/mindset_4?centerwin=yes)

    Your journal entry must be at least 200 words in length. No references or citations are necessary.

    **## UnitVIIStudyGuide.pdf**

    MAT 1302, College Algebra 1

    Course Learning Outcomes for Unit VII

    Upon completion of this unit, students should be able to:

    3. Utilize algebraic principles to graph systems.
    3.1 Investigate whether an ordered pair is a solution of a linear system in two variables.
    3.2 Solve linear and nonlinear systems by the substitution and addition method.
    3.3 Solve applications involving systems of linear equations in two variables.

    6. Solve linear systems with two variables.

    6.1 Graph linear and nonlinear inequalities in two variables.
    6.2 Graph linear and nonlinear systems of inequalities.

    Required Unit Resources

    Chapter 5: Systems of Equations and Inequalities, Sections 5.1, 5.4, 5.5

    Unit Lesson

    This unit lesson provides an overview of concepts that you will learn in Unit VII as well as links to required
    lesson videos. For additional instruction and examples, please refer to Sections 5.1, 5.4, and 5.5 in your
    textbook. It is recommended to use the Unit VII Homework Videos Note-Taking Guide as you work through
    the videos.

    Section 5.1: Systems of Linear Equations in Two Variables

    Assume that you are remodeling your home. You want to buy paint for each room and new carpet for each
    bedroom. You have a fixed budget of $3,000. If you know how much the carpet per square foot and paint per
    gallon costs, then you can create a system of equations to help you figure out how much paint and carpet you
    can afford. This scenario describes a system of linear equations in two variables where the variables
    represent the amount of paint and carpet. In this section, we will solve systems of linear equations in two
    variables.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Solutions to a System of Equations

    • Solving Systems of Linear Equations Part I

    • Solving Systems of Linear Equations Part II

    • Applications of Systems of Linear Equations

    Section 5.4: Systems of Nonlinear Equations in Two Variables

    We can expand our knowledge of systems of equations in two variables by looking at nonlinear systems. A
    nonlinear system is a system that contains at least one nonlinear equation. Examples of nonlinear equations
    are quadratic, cubic, and square-root equations.

    UNIT VII STUDY GUIDE

    Systems of Equations and Inequalities

    [https://online.columbiasouthern.edu/bbcswebdav/xid-146144996_1](https://online.columbiasouthern.edu/bbcswebdav/xid-146144996_1)

    [https://www.youtube.com/watch?v=I47hRZ3NkUQ](https://www.youtube.com/watch?v=I47hRZ3NkUQ)

    [https://www.youtube.com/watch?v=FawvUHimJHk](https://www.youtube.com/watch?v=FawvUHimJHk)

    [https://www.youtube.com/watch?v=4pKmdBGbU9g](https://www.youtube.com/watch?v=4pKmdBGbU9g)

    [https://www.youtube.com/watch?v=CnY0y2fjn-8](https://www.youtube.com/watch?v=CnY0y2fjn-8)

    MAT 1302, College Algebra 2

    UNIT x STUDY GUIDE

    Title

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Systems of Nonlinear Equations Part I

    • Systems of Nonlinear Equations Part II

    Section 5.5: Systems of Inequalities

    In Section 5.1, we learned that the point of intersection between two lines is a solution to the system of linear
    equations. In Section 5.4, we learned that there could be multiple solutions when two nonlinear equations or a
    nonlinear and linear equation intersect. In this section, we will examine linear and nonlinear inequalities and
    find the set of all solutions that fits the conditions given by the inequality sign.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Graphing Inequalities

    • MyMathLab Graphing Tool for Inequalities

    • Graphing Systems of Inequalities, Part I

    • MyMathLab Graphing Tool for Systems of Inequalities

    • Graphing Systems of Inequalities Part II

    Additional Help Available

    If you find yourself needing additional assistance with course material, please know that the Math Center
    is available and ready to help. Click the Math Center Request form to get connected with the Math
    Center’s tutors.

    Learning Activities (Nongraded)

    Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit
    them. If you have questions, contact your instructor for further guidance and information.

    Open your study plan in MyMathLab to see your progress and do supplemental practice exercises. The study
    plan will update each time you take an assessment. The study plan is for extra practice.

    For assistance with course content, you may contact your instructor or a math specialist. Click the Student
    Resources link to find contact information for the Math Center.

    [https://www.youtube.com/watch?v=_gswZLpq-Uc](https://www.youtube.com/watch?v=_gswZLpq-Uc)

    [https://www.youtube.com/watch?v=a_ZX_2H6hJs](https://www.youtube.com/watch?v=a_ZX_2H6hJs)

    [https://www.youtube.com/watch?v=ddg1m37BeU4](https://www.youtube.com/watch?v=ddg1m37BeU4)

    [https://www.youtube.com/watch?v=ev0GYvAaPiE](https://www.youtube.com/watch?v=ev0GYvAaPiE)

    [https://www.youtube.com/watch?v=XnKRfTafoIU](https://www.youtube.com/watch?v=XnKRfTafoIU)

    [https://www.youtube.com/watch?v=gKBZgzwEsJg](https://www.youtube.com/watch?v=gKBZgzwEsJg)

    [https://www.youtube.com/watch?v=wnRjLUYlma8](https://www.youtube.com/watch?v=wnRjLUYlma8)

    [https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/](https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/)

    **## UnitVIIJournal.docx**

    Unit VII Journal

    Watch
    [_Video 4: Embracing Challenges_](https://mediaplayer.pearsoncmg.com/assets/mindset_4?centerwin=yes). Reflect on your time in this course. What challenges have you faced? What strategies or mindsets did you implement to overcome these challenges? How could you improve your strategy and mindset so that they are more effective?

    [https://mediaplayer.pearsoncmg.com/assets/mindset_4?centerwin=yes](https://mediaplayer.pearsoncmg.com/assets/mindset_4?centerwin=yes)

    Your journal entry must be at least 200 words in length. No references or citations are necessary.

    **## UnitVIIStudyGuide.pdf**

    MAT 1302, College Algebra 1

    Course Learning Outcomes for Unit VII

    Upon completion of this unit, students should be able to:

    3. Utilize algebraic principles to graph systems.
    3.1 Investigate whether an ordered pair is a solution of a linear system in two variables.
    3.2 Solve linear and nonlinear systems by the substitution and addition method.
    3.3 Solve applications involving systems of linear equations in two variables.

    6. Solve linear systems with two variables.

    6.1 Graph linear and nonlinear inequalities in two variables.
    6.2 Graph linear and nonlinear systems of inequalities.

    Required Unit Resources

    Chapter 5: Systems of Equations and Inequalities, Sections 5.1, 5.4, 5.5

    Unit Lesson

    This unit lesson provides an overview of concepts that you will learn in Unit VII as well as links to required
    lesson videos. For additional instruction and examples, please refer to Sections 5.1, 5.4, and 5.5 in your
    textbook. It is recommended to use the Unit VII Homework Videos Note-Taking Guide as you work through
    the videos.

    Section 5.1: Systems of Linear Equations in Two Variables

    Assume that you are remodeling your home. You want to buy paint for each room and new carpet for each
    bedroom. You have a fixed budget of $3,000. If you know how much the carpet per square foot and paint per
    gallon costs, then you can create a system of equations to help you figure out how much paint and carpet you
    can afford. This scenario describes a system of linear equations in two variables where the variables
    represent the amount of paint and carpet. In this section, we will solve systems of linear equations in two
    variables.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Solutions to a System of Equations

    • Solving Systems of Linear Equations Part I

    • Solving Systems of Linear Equations Part II

    • Applications of Systems of Linear Equations

    Section 5.4: Systems of Nonlinear Equations in Two Variables

    We can expand our knowledge of systems of equations in two variables by looking at nonlinear systems. A
    nonlinear system is a system that contains at least one nonlinear equation. Examples of nonlinear equations
    are quadratic, cubic, and square-root equations.

    UNIT VII STUDY GUIDE

    Systems of Equations and Inequalities

    [https://online.columbiasouthern.edu/bbcswebdav/xid-146144996_1](https://online.columbiasouthern.edu/bbcswebdav/xid-146144996_1)

    [https://www.youtube.com/watch?v=I47hRZ3NkUQ](https://www.youtube.com/watch?v=I47hRZ3NkUQ)

    [https://www.youtube.com/watch?v=FawvUHimJHk](https://www.youtube.com/watch?v=FawvUHimJHk)

    [https://www.youtube.com/watch?v=4pKmdBGbU9g](https://www.youtube.com/watch?v=4pKmdBGbU9g)

    [https://www.youtube.com/watch?v=CnY0y2fjn-8](https://www.youtube.com/watch?v=CnY0y2fjn-8)

    MAT 1302, College Algebra 2

    UNIT x STUDY GUIDE

    Title

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Systems of Nonlinear Equations Part I

    • Systems of Nonlinear Equations Part II

    Section 5.5: Systems of Inequalities

    In Section 5.1, we learned that the point of intersection between two lines is a solution to the system of linear
    equations. In Section 5.4, we learned that there could be multiple solutions when two nonlinear equations or a
    nonlinear and linear equation intersect. In this section, we will examine linear and nonlinear inequalities and
    find the set of all solutions that fits the conditions given by the inequality sign.

    The following videos can be viewed here as well as in your homework assignment. Please click the titles
    below to view the videos. A transcript and closed captioning are available once you access the videos.

    • Graphing Inequalities

    • MyMathLab Graphing Tool for Inequalities

    • Graphing Systems of Inequalities, Part I

    • MyMathLab Graphing Tool for Systems of Inequalities

    • Graphing Systems of Inequalities Part II

    Additional Help Available

    If you find yourself needing additional assistance with course material, please know that the Math Center
    is available and ready to help. Click the Math Center Request form to get connected with the Math
    Center’s tutors.

    Learning Activities (Nongraded)

    Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit
    them. If you have questions, contact your instructor for further guidance and information.

    Open your study plan in MyMathLab to see your progress and do supplemental practice exercises. The study
    plan will update each time you take an assessment. The study plan is for extra practice.

    For assistance with course content, you may contact your instructor or a math specialist. Click the Student
    Resources link to find contact information for the Math Center.

    [https://www.youtube.com/watch?v=_gswZLpq-Uc](https://www.youtube.com/watch?v=_gswZLpq-Uc)

    [https://www.youtube.com/watch?v=a_ZX_2H6hJs](https://www.youtube.com/watch?v=a_ZX_2H6hJs)

    [https://www.youtube.com/watch?v=ddg1m37BeU4](https://www.youtube.com/watch?v=ddg1m37BeU4)

    [https://www.youtube.com/watch?v=ev0GYvAaPiE](https://www.youtube.com/watch?v=ev0GYvAaPiE)

    [https://www.youtube.com/watch?v=XnKRfTafoIU](https://www.youtube.com/watch?v=XnKRfTafoIU)

    [https://www.youtube.com/watch?v=gKBZgzwEsJg](https://www.youtube.com/watch?v=gKBZgzwEsJg)

    [https://www.youtube.com/watch?v=wnRjLUYlma8](https://www.youtube.com/watch?v=wnRjLUYlma8)

    [https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/](https://mycsu.columbiasouthern.edu/student/forms/courses/math-center-request/)

  • [Solved] STATISTICS

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    [>Statistics homework help](https://www.sweetstudy.com/fields/mathematics-statistics) – [\ \ IMG_0811.png](https://www.sweetstudy.com/files/img-0811-png-10510365 "IMG_0811.png") – [\ \ IMG_0814.png](https://www.sweetstudy.com/files/img-0814-png-10510367 "IMG_0814.png") – [\ \ IMG_0813.png](…

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    [>Statistics homework help](https://www.sweetstudy.com/fields/mathematics-statistics)

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  • [Solved] Statistics Project

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    [>Statistics homework help](https://www.sweetstudy.com/fields/mathematics-statistics) Walkthrough recorded Spring 2025: [**https://arizona.box.com/s/ii2mhua71jusvwdwlnuhr63kzhuk09c8**](https://arizona.box.com/s/ii2mhua71jusvwdwlnuhr63kzhuk09c8) **Final Project** **For this project, we are going to p…

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    [>Statistics homework help](https://www.sweetstudy.com/fields/mathematics-statistics)

    Walkthrough recorded Spring 2025:

    [**https://arizona.box.com/s/ii2mhua71jusvwdwlnuhr63kzhuk09c8**](https://arizona.box.com/s/ii2mhua71jusvwdwlnuhr63kzhuk09c8)

    **Final Project**

    **For this project, we are going to pretend that you are doing an experiment on a topic of your choice. For demonstration purposes, I'm going to do an analysis on the topic of how much 30 people agree with me about COVID-19 vaccinations and how two different approaches (Approch A and Approch B) affect that agreement. I want you to think of a topic that you are interested and this final project will include an analysis of the data in light of these randomly selected results.**

    **Step 1:**

    Create your randomized data in Excel

    You can create random numbers that are in the range of data points you would expect from your measurements in your experiments. For example, if you had a Likert scale measure then you would create numbers between 0 and 10 or 1 and 5 etc.

    In a Word Document (or equivalent) Describe what your Experiment is about just like I did.

    in Excel use =rand() then create 3 column and 30 rows

    Insert a category row above this with labels that correspond to what your data is showing. EX My three columns are Agreement, Approach A and, Approach B.

    **Step 2:**

    Convert these columns into binomial (dichotomous) data. In my experiment, I'm interested in agreement so I will convert the percentage of the agreement into a dichotomous Agree or Disagree category.

    In excel, you can use this function

    =if(A2 > 0.5, "Agree","Disagree")

    And right corner drag across three columns and then down to the 30 participants.

    a.) Look at the pattern of Agreement and Disagreement and find the longest string of dichotomous variables you have discovered and calculate how likely that would be… Don't forget to multiply by the number of potential occurrences.

    EX:

    0.5^(largest string) so a string of 7 heads in a row is .5^7*90 …. ~0.78125 or ~78% should we be surprised to see this string of Heads in a row? Write a sentence or two about this result.

    b.) What is the likelihood of getting at least this many Agreements in this random sample? (I created three new columns and counted the agreements by modifying our if statement to read out 1 if agreement and 0 if disagreement and then count the number of agreements.

    EX = _If(A2>0.5,1,0))_

    BINOMDIST(num_successes, num_trials, prob_success, cumulative)

    EX:

    _=binomdist(42,90,.5,True)_

    For the probability of at least that many occurrences (Culmilitve percentage).

    _=binomdist(42,90,.5,False)_

    Probablity of getting exact percentage.

    Is the result you got probable or not? Write a sentence or two about the likelihood that you would get this result.

    If you were interviewing people for your study and you got this number of disagreements (or agreements) in a row should you be surprised?

    **Step 3:**

    Let's say that Approach A increases agreement by 10% and Approach B Decreases agreement 20%

    Note you can choose these effects for your own project but having an increase and decrease should be a good start.

    Change the data to reflect these calculations.

    in Excel

    _=B2*1.10_

    in new column and drag down

    _=C2*0.8_

    in another new column and drag down

    **Step 4:**

    Create a new column with the average of each of the three rows.

    In Excel you can use =average(highlight first row) in a new column then apply to the column by dragging the formula (bottom right corner of box when it turns into a black **+** and drag down)

    Now let's look at histograms for the averages vs. the random numbers

    a.) What should we expect to see? Which one is closer to a normal distribution? Write a paragraph explaining your findings.

    a. Insert Graph Histogram in Sheets for each column

    EX

    Please paste your histograms in the word file to demonstrate your work.

    **What do we expect to see in a distribution?**

    Most data will fall into a normal curve because this kind of data is usually measuring something that is a result of many different independent factors.

    Even though each factor by itself might have a non-normal distribution, i.e. for a single die the distribution is completely flat, the combination of multiple independent factors will more often than not create a normal distribution (bell curve).

    Does it have Skew?

    =skew(Highlight)

    in Excel

    Are there Floor or Ceiling effects?

    NOTE: For statistical analysis to work correctly the distribution has to be normal so translating the numbers into a different scale i.e. Log, Exponential etc. can turn a skew into an appropriate scale that shows a normal distribution.

    **Step 5:**

    Translation of scale to create a normal distribution

    ![Log data vs. normal data](https://www.sweetstudy.com/questions/statistics-project-20964155)

    It may seem strange but changing the scale doesn't affect the statistics but for the stats to work the data have to be on a normalized distribution.

    if we apply a logarithmic translation to a normal graph we should get non-normal distribution as a result but if you saw a logarithmic histogram (terrorist damage, earthquake energy etc.) you would be able to do this to reverse the process so we could do statistical analysis on the results.

    We can test this by creating another column that takes the natural log of our average column and then taking a look at the histogram to evaluate it's normality.

    _=ln(highlight first-row point then drag down)_

    and insert chart histogram of this column

    in new column in Sheets/Excel

    a.) Should we apply this transformation to our data before moving on? Why or why not? Take a couple of sentences to explain.

    b.) What is the Skew of each kind of data?

    _=skew(highlight column)_

    in Sheets/Excel

    **Step 6:**

    Find the Mean, Median and Mode of your data. What do these measurements tell us about your data?

    =Average( _highlight data_) is the function for Mean

    Graph these means Please (Highlight means and insert bar chart)

    EXTRA CREDIT: Add SEM error bars.

    =Median( _highlight data_) is the function for Median

    =Mode( _highlight data_) is the function of Mode

    Note: for our data there likely isn't a mode but you can check your function on the dichotomous variables to see if it works.

    a.) When should you use medians vs. means? Which is best for Skewed distributions? Write a couple of sentences explaining why.

    b.) Getting modes for this type of data are inappropriate but we saw these in the histograms. If you were getting people to vote would you use plurality votes or rank-order voting write a couple of sentences as to why?

    _**Step 7:**_

    **Do a T-test between your data and another measurement of your choice and explain this difference/non-difference.**

    =ttest( _highlight data of first group, highlight data of second group, 2,1_)  is a function for a 2 tail paired t-test.

    or

    t.test(Data$ApprochA,Data$Agreement,paired=TRUE)

    t.test(Data$ApprochB,Data$Agreement,paired=TRUE)

    is there a significant difference between the People who Agree or Disagree?

    t.test(Data$Agreement~Data$DoAgree)

    a.) Does that result make sense? Explain in a couple of sentences.

    Would it be more appropriate to do an ANOVA?

    In R:

    one.way <- aov(Score ~ Group, data = Data)

    summary(one.way)

    In Sheets using a spreadsheet:

    [anova.xls](https://d2l.arizona.edu/content/enforced/1726113-218-2261-7W1BASV314101103201203/anova.xls?ou=1726113)

    Converting F to P-value. [https://www.socscistatistics.com/pvalues/fdistribution.aspx](https://www.socscistatistics.com/pvalues/fdistribution.aspx)

    b.) Explain why ANOVA is used vs. T-tests. What is an F ratio?

    **Step 8:**

    **Correlate the three first columns with each other**

    _In Excel_

    _=Correl(Highlight first group, highlight the second group)_

    a.) Which columns have the highest/lowest correlations? Is this result surprising (expected by random chance)?

    Extra Credit: Provide a Scatterplot with a trendline showing this relationship.

    **Step 9:**

    What do you do if your data has non-linear relationships?

    First, we have to create non-linear data.

    In a new column us the first column (EX Agreement) to apply a sin wave pattern.

    In excel:

    _=sin(row()/10)+A2_

    In a new column using the equation above to add a non-linear relationship to your data create Then drag down

    In R:

    _Data$Sin <- sin(seq(1,30,1)/10)_

    _Data$SinAndAgg <- Data$Sin+Data$Agreement_

    Check out the added pattern

    _plot(Data$SinAndAgg)_

    _lines(Data$Sin)_

    Now let's take that out again by taking the residuals

    Do a regression analysis to find out if other measurements could be used to predict your own. Explain the results.

    **Regression**

    As mentioned above correlations can be used to make predictions based on many different forms of data. If you are trying to predict something using correlated data it's called regression. For example, let's see if there is a relationship between Agreement and Agreement and Sin.

    _AggResid <- lm(SinAndAgg ~ Sin, data=Data)_

    _summary(AggResid)_

    a.) Was there a relationship between our combined factor Sin and Aggression and the Sin component?

    _Data$AggResid <- resid(AggResid)_

    _plot(Data$AggResid)_

    _abline(h=0)_

    b.) Let's look at what variance is leftover.

    How does this relate to the original Agreement data?

    plot(Data$AggResid~Data$Agreement)

    c.) Now let's see if there is a relationship between our combined factor Sin and Aggression and the Aggression component?

    _SinResid <- lm(SinAndAgg ~ Agreement, data=Data)_

    _summary(SinResid)_

    d.) Now, what is leftover?

    _Data$SinResid <- resid(SinResid)_

    _plot(Data$SinResid)_

    _abline(h=0)_

    e.) How does this relate to the original Sin data?

    _plot(Data$SinResid~Data$Sin)_

    **Step 10:**

    **Do an Exploratory Factor Analysis to see how our measures relate to each other.**

    It's not always clear what we should include in our models of what's going on. For example, we might ask the questions are both math and reading scores required in an analysis of our country data? Statisticians can help researchers narrow down what they think is important by doing an Exploratory Factor Analysis to see if we can combine/eliminate variables because they are redundant. We can often find that variables that were distinct factors are really related and can be combined into a single **Latent** variable (i.e. component 1, 2 of IQ etc.).

    or if you want to look at inflation data this has my data I've gathered. [https://docs.google.com/spreadsheets/d/1_zX6yhNj5SbrqvepUmMk06Xiu21j9WVoCXi0bka-1rk/edit?usp=sharing](https://docs.google.com/spreadsheets/d/1_zX6yhNj5SbrqvepUmMk06Xiu21j9WVoCXi0bka-1rk/edit?usp=sharing)

    Upload data to R

    pc <-read.csv(file.choose())

    _princomp(pc, cor=TRUE)_

    _**AgreementsApprochRelated <-princomp(pc, cor=TRUE)**_

    _**summary(AgreementsApprochRelated)**_

    _**plot(AgreementsApprochRelated)**_

    **this is a kind of scree plot as describes here** [**https://en.wikipedia.org/wiki/Scree_plot#:~:text=In%20multivariate%20statistics%2C%20a%20scree,principal%20component%20analysis%20(PCA).**](https://en.wikipedia.org/wiki/Scree_plot#:~:text=In%20multivariate%20statistics%2C%20a%20scree,principal%20component%20analysis%20(PCA).)

    _**biplot(AgreementsApprochRelated)**_

    **are there any clusters/groups?**

    **loadings(AgreementsApprochRelated)**

    **gives a numerical table that shows you component loadings of each factor.**

    [**This link shows how to understand factor analysis with graphs.**](http://youtu.be/kAR93XfsrEs)

    **a.) Paste a bi-plot/loadings of your factor analysis and Tell us if you could combine any of the factors we are given? How many unique factors are in our dataset? What would you call them? i.e. how many groups do you see now and what did those measures have in common?**

  • [Solved] Mathematics Math homework assistant

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    Mathematics Math homework assistant

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    Mathematics Math homework assistant

  • [Solved] math in everyday life

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    work assignments **files (1)** – combinepdf241.pdf **combinepdf241.pdf** This file is too large to display. [View in new window](https://www.sweetstudy.com/files/combinepdf241-pdf) **combinepdf241.pdf** This file is too large to display. [View in new window](https://www.sweetstudy.com/files/combinep…

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    work assignments

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    – combinepdf241.pdf

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  • [Solved] Home work

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    [>Statistics homework help](https://www.sweetstudy.com/fields/mathematics-statistics) **files (1)** – ## DLV12.docx **## DLV12.docx** **Competencies** 1. Describe the data using the measures of central tendency and measures of variability. 2. Apply the normal distribution, standard normal distribu…

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    [>Statistics homework help](https://www.sweetstudy.com/fields/mathematics-statistics)

    **files (1)**

    – ## DLV12.docx

    **## DLV12.docx**

    **Competencies**

    1. Describe the data using the measures of central tendency and measures of variability.

    2. Apply the normal distribution, standard normal distribution, and central limit theorem.

    3. Develop a confidence interval for a population parameter.

    4. Evaluate hypothesis tests for population parameters from one population.

    5. Evaluate hypothesis tests for population parameters from two populations.

    6. Determine the linear correlation and regression equation between two variables to make predictions for the dependent variable.

    **Project Deliverable tie to Competency**

    In the final assignment, you will demonstrate your understanding of all the competencies from the course, from using descriptive statistics to provide an overview of a data set, analyzing a distribution, making estimates using a confidence interval, conducting hypothesis test using one or more samples, and using regression analysis to make predictions.

    **Scenario**

    Your success in your prior position has opened new opportunities for you and you have accepted a new position at a local hospital where you will be able to apply your statistical knowledge and skills to help make evidence-based decisions to improve the care and well-being of patients.

    As you settle into your new role, you are tasked to do a comprehensive analysis of patient data that will help all practitioners better understand the population they work with. The data set includes the following variables (including units of measurement, where applicable):

    >Patient ID Number

    >Age (in years)

    >Intake Temperature (Degrees Fahrenheit)

    >Length of Stay (Days)

    >Pain Score (On a scale of 1 to 10)

    >Department

    Download the Excel Workbook provided below. Ensure that you use the data provided in the Workbook to make all calculations.

    **Instructions**

    The Excel Workbook contains eight tabs. The first tab contains the instructions. The second tab, labeled "data", contains the raw data that will be used for your calculations. The next six tabs contain questions for you to answer. Ensure that you are completely answering all questions with explanations, and your work is shown in Excel when needed.

    **Submission Requirements**

    · You must submit the Workbook with the completed calculations, answers, and analysis.

    **## DLV12.docx**

    **Competencies**

    1. Describe the data using the measures of central tendency and measures of variability.

    2. Apply the normal distribution, standard normal distribution, and central limit theorem.

    3. Develop a confidence interval for a population parameter.

    4. Evaluate hypothesis tests for population parameters from one population.

    5. Evaluate hypothesis tests for population parameters from two populations.

    6. Determine the linear correlation and regression equation between two variables to make predictions for the dependent variable.

    **Project Deliverable tie to Competency**

    In the final assignment, you will demonstrate your understanding of all the competencies from the course, from using descriptive statistics to provide an overview of a data set, analyzing a distribution, making estimates using a confidence interval, conducting hypothesis test using one or more samples, and using regression analysis to make predictions.

    **Scenario**

    Your success in your prior position has opened new opportunities for you and you have accepted a new position at a local hospital where you will be able to apply your statistical knowledge and skills to help make evidence-based decisions to improve the care and well-being of patients.

    As you settle into your new role, you are tasked to do a comprehensive analysis of patient data that will help all practitioners better understand the population they work with. The data set includes the following variables (including units of measurement, where applicable):

    >Patient ID Number

    >Age (in years)

    >Intake Temperature (Degrees Fahrenheit)

    >Length of Stay (Days)

    >Pain Score (On a scale of 1 to 10)

    >Department

    Download the Excel Workbook provided below. Ensure that you use the data provided in the Workbook to make all calculations.

    **Instructions**

    The Excel Workbook contains eight tabs. The first tab contains the instructions. The second tab, labeled "data", contains the raw data that will be used for your calculations. The next six tabs contain questions for you to answer. Ensure that you are completely answering all questions with explanations, and your work is shown in Excel when needed.

    **Submission Requirements**

    · You must submit the Workbook with the completed calculations, answers, and analysis.

  • [Solved] Math exercice first Bac –need solution

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    Hello, I have a math exercise from First Bac level. Can someone solve it step by step please? **files (2)** – ## math_exam_variant_1.pdf – ## math_exam_variant_2.pdf **## math_exam_variant_1.pdf** Exercice 1 Soit la fonction numérique f définie par : f(x) = (x^3 – 4x) / (3x^2 – 3x + 5) 1) C…

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    Hello,

    I have a math exercise from First Bac level.

    Can someone solve it step by step please?

    **files (2)**

    – ## math_exam_variant_1.pdf

    – ## math_exam_variant_2.pdf

    **## math_exam_variant_1.pdf**

    Exercice 1
    Soit la fonction numérique f définie par :

    f(x) = (x^3 – 4x) / (3x^2 – 3x + 5)

    1) Calculer lim f(x) quand x → +∞

    2) Calculer lim f(x) quand x → −∞

    Exercice 2 : Calculer les limites suivantes

    1) lim (4x^3 + 2x^2 + 4) / (3x + 4) quand x → +∞

    2) lim √(x^2 + 4x + 10) / 2x quand x → +∞

    3) lim ( √(x + 4) − 3 ) / (x − 1) quand x → 1

    Exercice 3

    Résoudre dans R :

    cos(2x + π/5) = 1/2

    On pose : A(x) = sin²x − √2 sinx cosx + cos²x

    1) Calculer A(π/5) et A(π/7)

    2) Montrer que A(x) = 2 cos(2x + π/5) + 3

    3) Résoudre dans l’intervalle [-π , π] l’équation A(x) = 3

    **## math_exam_variant_2.pdf**

    Exercice 1
    Soit la fonction numérique f définie par :

    f(x) = (x^3 – 7x) / (4x^2 – 3x + 5)

    1) Calculer lim f(x) quand x → +∞

    2) Calculer lim f(x) quand x → −∞

    Exercice 2 : Calculer les limites suivantes

    1) lim (7x^3 + 2x^2 + 4) / (3x + 7) quand x → +∞

    2) lim √(x^2 + 7x + 10) / 3x quand x → +∞

    3) lim ( √(x + 7) − 4 ) / (x − 1) quand x → 1

    Exercice 3

    Résoudre dans R :

    cos(2x + π/5) = 1/2

    On pose : A(x) = sin²x − √2 sinx cosx + cos²x

    1) Calculer A(π/5) et A(π/7)

    2) Montrer que A(x) = 2 cos(2x + π/5) + 3

    3) Résoudre dans l’intervalle [-π , π] l’équation A(x) = 3

    **## math_exam_variant_2.pdf**

    Exercice 1
    Soit la fonction numérique f définie par :

    f(x) = (x^3 – 7x) / (4x^2 – 3x + 5)

    1) Calculer lim f(x) quand x → +∞

    2) Calculer lim f(x) quand x → −∞

    Exercice 2 : Calculer les limites suivantes

    1) lim (7x^3 + 2x^2 + 4) / (3x + 7) quand x → +∞

    2) lim √(x^2 + 7x + 10) / 3x quand x → +∞

    3) lim ( √(x + 7) − 4 ) / (x − 1) quand x → 1

    Exercice 3

    Résoudre dans R :

    cos(2x + π/5) = 1/2

    On pose : A(x) = sin²x − √2 sinx cosx + cos²x

    1) Calculer A(π/5) et A(π/7)

    2) Montrer que A(x) = 2 cos(2x + π/5) + 3

    3) Résoudre dans l’intervalle [-π , π] l’équation A(x) = 3

    **## math_exam_variant_1.pdf**

    Exercice 1
    Soit la fonction numérique f définie par :

    f(x) = (x^3 – 4x) / (3x^2 – 3x + 5)

    1) Calculer lim f(x) quand x → +∞

    2) Calculer lim f(x) quand x → −∞

    Exercice 2 : Calculer les limites suivantes

    1) lim (4x^3 + 2x^2 + 4) / (3x + 4) quand x → +∞

    2) lim √(x^2 + 4x + 10) / 2x quand x → +∞

    3) lim ( √(x + 4) − 3 ) / (x − 1) quand x → 1

    Exercice 3

    Résoudre dans R :

    cos(2x + π/5) = 1/2

    On pose : A(x) = sin²x − √2 sinx cosx + cos²x

    1) Calculer A(π/5) et A(π/7)

    2) Montrer que A(x) = 2 cos(2x + π/5) + 3

    3) Résoudre dans l’intervalle [-π , π] l’équation A(x) = 3

    **## math_exam_variant_2.pdf**

    Exercice 1
    Soit la fonction numérique f définie par :

    f(x) = (x^3 – 7x) / (4x^2 – 3x + 5)

    1) Calculer lim f(x) quand x → +∞

    2) Calculer lim f(x) quand x → −∞

    Exercice 2 : Calculer les limites suivantes

    1) lim (7x^3 + 2x^2 + 4) / (3x + 7) quand x → +∞

    2) lim √(x^2 + 7x + 10) / 3x quand x → +∞

    3) lim ( √(x + 7) − 4 ) / (x − 1) quand x → 1

    Exercice 3

    Résoudre dans R :

    cos(2x + π/5) = 1/2

    On pose : A(x) = sin²x − √2 sinx cosx + cos²x

    1) Calculer A(π/5) et A(π/7)

    2) Montrer que A(x) = 2 cos(2x + π/5) + 3

    3) Résoudre dans l’intervalle [-π , π] l’équation A(x) = 3

    **## math_exam_variant_1.pdf**

    Exercice 1
    Soit la fonction numérique f définie par :

    f(x) = (x^3 – 4x) / (3x^2 – 3x + 5)

    1) Calculer lim f(x) quand x → +∞

    2) Calculer lim f(x) quand x → −∞

    Exercice 2 : Calculer les limites suivantes

    1) lim (4x^3 + 2x^2 + 4) / (3x + 4) quand x → +∞

    2) lim √(x^2 + 4x + 10) / 2x quand x → +∞

    3) lim ( √(x + 4) − 3 ) / (x − 1) quand x → 1

    Exercice 3

    Résoudre dans R :

    cos(2x + π/5) = 1/2

    On pose : A(x) = sin²x − √2 sinx cosx + cos²x

    1) Calculer A(π/5) et A(π/7)

    2) Montrer que A(x) = 2 cos(2x + π/5) + 3

    3) Résoudre dans l’intervalle [-π , π] l’équation A(x) = 3

    **## math_exam_variant_2.pdf**

    Exercice 1
    Soit la fonction numérique f définie par :

    f(x) = (x^3 – 7x) / (4x^2 – 3x + 5)

    1) Calculer lim f(x) quand x → +∞

    2) Calculer lim f(x) quand x → −∞

    Exercice 2 : Calculer les limites suivantes

    1) lim (7x^3 + 2x^2 + 4) / (3x + 7) quand x → +∞

    2) lim √(x^2 + 7x + 10) / 3x quand x → +∞

    3) lim ( √(x + 7) − 4 ) / (x − 1) quand x → 1

    Exercice 3

    Résoudre dans R :

    cos(2x + π/5) = 1/2

    On pose : A(x) = sin²x − √2 sinx cosx + cos²x

    1) Calculer A(π/5) et A(π/7)

    2) Montrer que A(x) = 2 cos(2x + π/5) + 3

    3) Résoudre dans l’intervalle [-π , π] l’équation A(x) = 3

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