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Tag: Mathematics

  • [Solved] Conduct Hypothesis Testing using Bootstrap Methods, Resampling Techniques, and Confidence Intervals

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    ## **Background** Conduct hypothesis testing using bootstrap methods, implement resampling techniques, and compute confidence intervals. The assignment will incorporate a project developed in R, a report presenting the results. It will also incorporate a research review on the current state of Boots…

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    ## **Background**
    Conduct hypothesis testing using bootstrap methods, implement resampling techniques, and compute confidence intervals. The assignment will incorporate a project developed in R, a report presenting the results. It will also incorporate a research review on the current state of Bootstrapping techniques utilization in Data Science.
    ## **Instructions**
    Using this dataset contains physicochemical properties and quality ratings of red and white variants of the Portuguese "Vinho Verde" wine. Features include fixed acidity, volatile acidity, citric acid, residual sugar, chlorides, free sulfur dioxide, total sulfur dioxide, density, pH, sulphates, alcohol content, and a final quality rating from 0 (very bad) to 10 (very excellent).
    **Source**: The UCI Machine Learning Repository – Wine Quality Dataset ( [https://archive.ics.uci.edu/ml/datasets/wine+quality](https://archive.ics.uci.edu/ml/datasets/wine+quality))
    1. Setup and Data Preparation
    1. Install and load necessary R packages: tidyverse for data manipulation and visualization, boot for bootstrap analysis.
    2. Download the Wine Quality Dataset.
    3. Read the data into R using read.csv() and perform initial data exploration with functions like summary() and head().
    2. Exploratory Data Analysis (EDA)
    1. Visualize the distribution of wine quality ratings for both red and white wine samples.
    2. Explore relationships between physicochemical properties and wine quality using scatter plots and correlation analysis.
    3. Formulate a Hypothesis
    1. Example hypothesis: "The average alcohol content of high-quality wine (rating >= 7) is significantly higher than that of lower-quality wine (rating < 7)."
    4. Bootstrap Resampling for Hypothesis Testing
    1. Implement bootstrap resampling to estimate the difference in mean alcohol content between high-quality and low-quality wines.
    2. Draw many resamples with replacement from the observed dataset, compute the mean alcohol content for high-quality and low-quality wines in each resample, and calculate the difference.
    5. Compute Confidence Intervals
    1. Use the bootstrap samples to compute a 95% confidence interval for the mean difference in alcohol content.
    2. Interpret the confidence interval in the context of the hypothesis.
    6. Perform Hypothesis Testing
    1. Determine whether the observed difference in means is statistically significant based on the bootstrap confidence interval.
    2. Discuss the p-value interpretation and whether the null hypothesis can be rejected.
    7. Report Writing
    1. Introduction: Briefly introduce the project, dataset, and hypothesis.
    2. Methods: Describe the bootstrap resampling technique, hypothesis testing approach, and confidence interval computation.
    3. Results: Present the findings from the bootstrap analysis, including visualizations of the confidence interval and the conclusion regarding the hypothesis.
    4. Discussion: Interpret the results, discuss potential limitations of the study, and suggest future research directions.
    5. References: Cite all sources and R packages used.
    **Submit:**
    – **R Script (.R file)**: Containing all the code used for data preparation, EDA, bootstrap analysis, hypothesis testing, and confidence interval computation.
    – **Report (.docx):** A comprehensive report detailing the project's objective, methodology, results, and conclusions.
    **Length**: This assignment must be 5-8 pages (excluding the title and reference page).
    **References:** Include 3 scholarly resources.

  • [Solved] VVS

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    In-depth study guidance and analytical solution covering VVS.

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    Full assignment prompt and step-by-step guidance are included in the downloadable solution file.

  • [Solved] math helpppp

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  • [Solved] Dimensional Analysis

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    Dimensional Analysis is a multi-step conversion process to convert one unit into another. You will use dimensional analysis to create a presentation this week. **Scenario**: A mother has been given a prescription for her child. She fills the prescription at her local pharmacy. When she gets home, sh…

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    Assignment Prompt & Instructions

    Dimensional Analysis is a multi-step conversion process to convert one unit into another. You will use dimensional analysis to create a presentation this week.
    **Scenario**:  A mother has been given a prescription for her child. She fills the prescription at her local pharmacy. When she gets home, she reads the prescription instructions and doesn’t know how to administer the prescription with the tools that she has at home.  She calls you.
    Create a presentation with voice narration (voice over):
    – Your instructor will provide you with the prescription instructions. Please reach out on Monday of Week 5 if you have not received the prescription instructions you are supposed to use for this presentation.
    – Use the provided template and use dimensional analysis to complete the conversion needed in the prescription instructions given by your instructor.
    – Make sure to explain every step in your process and speak to the conclusion questions thoroughly.
    – Summarize what you would tell the mother after you complete your calculations.
    – Describe another situation or professional field in which dimensional analysis would take place.
    – What did you learn after completing this presentation?
    Your presentation should be done in **PowerPoint** with audio narration (voice over) and should be 3 – 5 minutes in length.
    #### Grading
    \
    Math_105_Week_5_Presentation_Template.pptx](https://www.sweetstudy.com/files/math-105-week-5-presentation-template-pptx "Math_105_Week_5_Presentation_Template.pptx")

  • [Solved] math practice help

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  • [Solved] Unit III J Math

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    see attached – ## TheUnitIIIJournal.docx – ## UnitIIIStudyGuide.pdf **## TheUnitIIIJournal.docx** The Unit III Journal entry is a reflection of scientific notation, a concept covered in Unit III as well as personal time management strategies. Be sure to complete _both_ parts A and B. Part A: In this…

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    Assignment Prompt & Instructions

    see attached

    – ## TheUnitIIIJournal.docx

    – ## UnitIIIStudyGuide.pdf

    **## TheUnitIIIJournal.docx**

    The Unit III Journal entry is a reflection of scientific notation, a concept covered in Unit III as well as personal time management strategies. Be sure to complete
    _both_ parts A and B.

    Part A: In this unit, we cover the concept of scientific notation. In your own words, explain what scientific notation is, where it could be used in the real world, and what benefit there is to using it in those particular fields.

    Part B: You may have noticed that learning mathematics can take a little more time than other subjects. In the same way that scientific notation can potentially help save time in calculations, there are different approaches to better managing your time when it comes to this course.

    · Share your routine or schedule for completing each unit. What are some time management strategies you are currently utilizing to help complete the assignments and tasks in this course?

    · Next, explain a new technique that you can adopt to help you improve your understanding and completion of each lesson. If you do not readily know of one, try doing a quick web search for ideas.

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

    **## UnitIIIStudyGuide.pdf**

    MAT 1301, Liberal Arts Math 1

    Course Learning Outcomes for Unit III

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

    3. Perform computations with real numbers.
    3.1 Identify rational and irrational numbers.
    3.2 Perform operations using exponents, radicals, and scientific notation.
    3.3 Compute future terms of arithmetic and geometric sequences.

    Required Unit Resources

    Chapter 6: Number Theory and the Real Number System: Understanding the Numbers All Around Us,

    Sections 6.4–6.6

    Unit Lesson

    Chapter 6: Number Theory and the Real Number System: Understanding the Numbers All Around Us

    Unit I introduced counting numbers, integers, and whole numbers. In this unit, we will learn about other types
    of numbers that make up the real number system. Specifically, we will learn about rational and irrational
    numbers.

    Rational numbers are numbers that can be expressed as fractions. Whole numbers, integers, and some
    decimals are rational numbers. You have probably used rational numbers when shopping or cooking.

    Irrational numbers are numbers that cannot be expressed as a fraction. The decimal expansion of an
    irrational number does not end and does not repeat.

    An example of an irrational number is pi where pi is approximately equal to 3.141592654. This number goes
    on forever without a repeating pattern. The number pi is utilized in anything that has a curvature. For
    example, the construction of a football involves a calculation with pi.

    As you learn more about rational and irrational numbers, you will learn how to compute radicals, perform
    operations with exponents, and use scientific notation, and you will be introduced to number patterns known
    as sequences.

    To complete the unit, read the unit lesson, and begin your unit assignments in MyLab Math. Do not forget to
    use the reference sheet and note-taking guide located in this lesson.

    Also, please be aware that you will need a scientific calculator to perform some of the calculations in this unit.
    Please email your professor if you need assistance with your calculator.

    Section 6.4: The Real Number System

    Mathematicians have categorized numbers into different sets. As shown previously, some sets of numbers
    have different rules when performing computations. For example, integer operations are dependent on the
    sign of the number, and fraction operations require that we manipulate the denominator when adding or
    subtracting. In this section, we will expand our knowledge of rational numbers and learn about another group
    of numbers called irrational numbers.

    UNIT III STUDY GUIDE

    The Real Number System Continued

    MAT 1301, Liberal Arts Math 2

    UNIT x STUDY GUIDE

    Title

    Click the link to view the Section 6.4: The Real Number System lesson.

    Section 6.5: Exponents and Scientific Notation

    Exponential and scientific notation is used to identify very small and very large numbers. For example, these
    notations will help us to express a number that is 100 digits long. Exponents and scientific notation will also
    aid in performing calculations with very small and very large numbers.

    Click the link to view the Section 6.5: Exponents and Scientific Notation lesson.

    Section 6.6: Sequences

    As children, we were taught to recognize patterns. We might have been given three shapes and been asked
    to provide the fourth shape based upon a recognizable pattern. As adults, we can recognize patterns or
    trends in things such as utility bills or gas prices. For example, we may expect an increase in our cable bill if
    that bill increased in previous years. In this section, we will learn how to recognize patterns in number
    sequences and predict the next number in a given sequence.

    Click the link to view the Section 6.6: Sequences lesson.

    Looking Forward

    After you review Sections 6.4, 6.5, and 6.6 of the unit lesson, begin your Unit III Homework assignment in
    MyLab Math. You will be instructed to watch several instructional videos before you complete your homework
    problems. It is recommended that you print the following reference sheet and note-taking guide to use while
    you watch the unit homework videos and complete the unit homework assignment.

    • Unit III Reference Sheet

    • Unit III Note-Taking Guide

    Suggested Unit Resources

    In order to access the following resources, click the links below.

    The following videos can be viewed here as well as in your homework assignment within MyLab Math. Please
    click the titles below to view the videos. Transcripts and closed captioning will be available once you access
    the videos.

    • Rational and Irrational Numbers video

    • Computations With Radicals video

    • Operations With Exponents video

    • Scientific Notation video

    • Multiplying and Dividing Numbers in Scientific Notation, Part I video

    • Multiplying and Dividing Numbers in Scientific Notation, Part II video

    • Arithmetic and Geometric Sequences, Part I video

    • Arithmetic and Geometric Sequences, Part II video

    • Arithmetic and Geometric Sequences, Part III video

    • Arithmetic and Geometric Sequences, Part IV video

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517514_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517514_1)

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517515_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517515_1)

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517512_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517512_1)

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517513_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517513_1)

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517511_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517511_1)

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

    [https://www.youtube.com/watch?v=PX5x138J5Ao](https://www.youtube.com/watch?v=PX5x138J5Ao)

    [https://www.youtube.com/watch?v=z6FPlGM4_p0](https://www.youtube.com/watch?v=z6FPlGM4_p0)

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

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

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

    [https://www.youtube.com/watch?v=4QVX0qELqDY](https://www.youtube.com/watch?v=4QVX0qELqDY)

    [https://www.youtube.com/watch?v=-oZNZEUO1Y0](https://www.youtube.com/watch?v=-oZNZEUO1Y0)

    [https://www.youtube.com/watch?v=dUHk4xZlZhY](https://www.youtube.com/watch?v=dUHk4xZlZhY)

    [https://www.youtube.com/watch?v=-7l2VLOTBGY](https://www.youtube.com/watch?v=-7l2VLOTBGY)

    **## UnitIIIStudyGuide.pdf**

    MAT 1301, Liberal Arts Math 1

    Course Learning Outcomes for Unit III

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

    3. Perform computations with real numbers.
    3.1 Identify rational and irrational numbers.
    3.2 Perform operations using exponents, radicals, and scientific notation.
    3.3 Compute future terms of arithmetic and geometric sequences.

    Required Unit Resources

    Chapter 6: Number Theory and the Real Number System: Understanding the Numbers All Around Us,

    Sections 6.4–6.6

    Unit Lesson

    Chapter 6: Number Theory and the Real Number System: Understanding the Numbers All Around Us

    Unit I introduced counting numbers, integers, and whole numbers. In this unit, we will learn about other types
    of numbers that make up the real number system. Specifically, we will learn about rational and irrational
    numbers.

    Rational numbers are numbers that can be expressed as fractions. Whole numbers, integers, and some
    decimals are rational numbers. You have probably used rational numbers when shopping or cooking.

    Irrational numbers are numbers that cannot be expressed as a fraction. The decimal expansion of an
    irrational number does not end and does not repeat.

    An example of an irrational number is pi where pi is approximately equal to 3.141592654. This number goes
    on forever without a repeating pattern. The number pi is utilized in anything that has a curvature. For
    example, the construction of a football involves a calculation with pi.

    As you learn more about rational and irrational numbers, you will learn how to compute radicals, perform
    operations with exponents, and use scientific notation, and you will be introduced to number patterns known
    as sequences.

    To complete the unit, read the unit lesson, and begin your unit assignments in MyLab Math. Do not forget to
    use the reference sheet and note-taking guide located in this lesson.

    Also, please be aware that you will need a scientific calculator to perform some of the calculations in this unit.
    Please email your professor if you need assistance with your calculator.

    Section 6.4: The Real Number System

    Mathematicians have categorized numbers into different sets. As shown previously, some sets of numbers
    have different rules when performing computations. For example, integer operations are dependent on the
    sign of the number, and fraction operations require that we manipulate the denominator when adding or
    subtracting. In this section, we will expand our knowledge of rational numbers and learn about another group
    of numbers called irrational numbers.

    UNIT III STUDY GUIDE

    The Real Number System Continued

    MAT 1301, Liberal Arts Math 2

    UNIT x STUDY GUIDE

    Title

    Click the link to view the Section 6.4: The Real Number System lesson.

    Section 6.5: Exponents and Scientific Notation

    Exponential and scientific notation is used to identify very small and very large numbers. For example, these
    notations will help us to express a number that is 100 digits long. Exponents and scientific notation will also
    aid in performing calculations with very small and very large numbers.

    Click the link to view the Section 6.5: Exponents and Scientific Notation lesson.

    Section 6.6: Sequences

    As children, we were taught to recognize patterns. We might have been given three shapes and been asked
    to provide the fourth shape based upon a recognizable pattern. As adults, we can recognize patterns or
    trends in things such as utility bills or gas prices. For example, we may expect an increase in our cable bill if
    that bill increased in previous years. In this section, we will learn how to recognize patterns in number
    sequences and predict the next number in a given sequence.

    Click the link to view the Section 6.6: Sequences lesson.

    Looking Forward

    After you review Sections 6.4, 6.5, and 6.6 of the unit lesson, begin your Unit III Homework assignment in
    MyLab Math. You will be instructed to watch several instructional videos before you complete your homework
    problems. It is recommended that you print the following reference sheet and note-taking guide to use while
    you watch the unit homework videos and complete the unit homework assignment.

    • Unit III Reference Sheet

    • Unit III Note-Taking Guide

    Suggested Unit Resources

    In order to access the following resources, click the links below.

    The following videos can be viewed here as well as in your homework assignment within MyLab Math. Please
    click the titles below to view the videos. Transcripts and closed captioning will be available once you access
    the videos.

    • Rational and Irrational Numbers video

    • Computations With Radicals video

    • Operations With Exponents video

    • Scientific Notation video

    • Multiplying and Dividing Numbers in Scientific Notation, Part I video

    • Multiplying and Dividing Numbers in Scientific Notation, Part II video

    • Arithmetic and Geometric Sequences, Part I video

    • Arithmetic and Geometric Sequences, Part II video

    • Arithmetic and Geometric Sequences, Part III video

    • Arithmetic and Geometric Sequences, Part IV video

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517514_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517514_1)

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517515_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517515_1)

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517512_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517512_1)

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517513_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517513_1)

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517511_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517511_1)

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

    [https://www.youtube.com/watch?v=PX5x138J5Ao](https://www.youtube.com/watch?v=PX5x138J5Ao)

    [https://www.youtube.com/watch?v=z6FPlGM4_p0](https://www.youtube.com/watch?v=z6FPlGM4_p0)

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

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

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

    [https://www.youtube.com/watch?v=4QVX0qELqDY](https://www.youtube.com/watch?v=4QVX0qELqDY)

    [https://www.youtube.com/watch?v=-oZNZEUO1Y0](https://www.youtube.com/watch?v=-oZNZEUO1Y0)

    [https://www.youtube.com/watch?v=dUHk4xZlZhY](https://www.youtube.com/watch?v=dUHk4xZlZhY)

    [https://www.youtube.com/watch?v=-7l2VLOTBGY](https://www.youtube.com/watch?v=-7l2VLOTBGY)

    **## TheUnitIIIJournal.docx**

    The Unit III Journal entry is a reflection of scientific notation, a concept covered in Unit III as well as personal time management strategies. Be sure to complete
    _both_ parts A and B.

    Part A: In this unit, we cover the concept of scientific notation. In your own words, explain what scientific notation is, where it could be used in the real world, and what benefit there is to using it in those particular fields.

    Part B: You may have noticed that learning mathematics can take a little more time than other subjects. In the same way that scientific notation can potentially help save time in calculations, there are different approaches to better managing your time when it comes to this course.

    · Share your routine or schedule for completing each unit. What are some time management strategies you are currently utilizing to help complete the assignments and tasks in this course?

    · Next, explain a new technique that you can adopt to help you improve your understanding and completion of each lesson. If you do not readily know of one, try doing a quick web search for ideas.

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

    **## UnitIIIStudyGuide.pdf**

    MAT 1301, Liberal Arts Math 1

    Course Learning Outcomes for Unit III

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

    3. Perform computations with real numbers.
    3.1 Identify rational and irrational numbers.
    3.2 Perform operations using exponents, radicals, and scientific notation.
    3.3 Compute future terms of arithmetic and geometric sequences.

    Required Unit Resources

    Chapter 6: Number Theory and the Real Number System: Understanding the Numbers All Around Us,

    Sections 6.4–6.6

    Unit Lesson

    Chapter 6: Number Theory and the Real Number System: Understanding the Numbers All Around Us

    Unit I introduced counting numbers, integers, and whole numbers. In this unit, we will learn about other types
    of numbers that make up the real number system. Specifically, we will learn about rational and irrational
    numbers.

    Rational numbers are numbers that can be expressed as fractions. Whole numbers, integers, and some
    decimals are rational numbers. You have probably used rational numbers when shopping or cooking.

    Irrational numbers are numbers that cannot be expressed as a fraction. The decimal expansion of an
    irrational number does not end and does not repeat.

    An example of an irrational number is pi where pi is approximately equal to 3.141592654. This number goes
    on forever without a repeating pattern. The number pi is utilized in anything that has a curvature. For
    example, the construction of a football involves a calculation with pi.

    As you learn more about rational and irrational numbers, you will learn how to compute radicals, perform
    operations with exponents, and use scientific notation, and you will be introduced to number patterns known
    as sequences.

    To complete the unit, read the unit lesson, and begin your unit assignments in MyLab Math. Do not forget to
    use the reference sheet and note-taking guide located in this lesson.

    Also, please be aware that you will need a scientific calculator to perform some of the calculations in this unit.
    Please email your professor if you need assistance with your calculator.

    Section 6.4: The Real Number System

    Mathematicians have categorized numbers into different sets. As shown previously, some sets of numbers
    have different rules when performing computations. For example, integer operations are dependent on the
    sign of the number, and fraction operations require that we manipulate the denominator when adding or
    subtracting. In this section, we will expand our knowledge of rational numbers and learn about another group
    of numbers called irrational numbers.

    UNIT III STUDY GUIDE

    The Real Number System Continued

    MAT 1301, Liberal Arts Math 2

    UNIT x STUDY GUIDE

    Title

    Click the link to view the Section 6.4: The Real Number System lesson.

    Section 6.5: Exponents and Scientific Notation

    Exponential and scientific notation is used to identify very small and very large numbers. For example, these
    notations will help us to express a number that is 100 digits long. Exponents and scientific notation will also
    aid in performing calculations with very small and very large numbers.

    Click the link to view the Section 6.5: Exponents and Scientific Notation lesson.

    Section 6.6: Sequences

    As children, we were taught to recognize patterns. We might have been given three shapes and been asked
    to provide the fourth shape based upon a recognizable pattern. As adults, we can recognize patterns or
    trends in things such as utility bills or gas prices. For example, we may expect an increase in our cable bill if
    that bill increased in previous years. In this section, we will learn how to recognize patterns in number
    sequences and predict the next number in a given sequence.

    Click the link to view the Section 6.6: Sequences lesson.

    Looking Forward

    After you review Sections 6.4, 6.5, and 6.6 of the unit lesson, begin your Unit III Homework assignment in
    MyLab Math. You will be instructed to watch several instructional videos before you complete your homework
    problems. It is recommended that you print the following reference sheet and note-taking guide to use while
    you watch the unit homework videos and complete the unit homework assignment.

    • Unit III Reference Sheet

    • Unit III Note-Taking Guide

    Suggested Unit Resources

    In order to access the following resources, click the links below.

    The following videos can be viewed here as well as in your homework assignment within MyLab Math. Please
    click the titles below to view the videos. Transcripts and closed captioning will be available once you access
    the videos.

    • Rational and Irrational Numbers video

    • Computations With Radicals video

    • Operations With Exponents video

    • Scientific Notation video

    • Multiplying and Dividing Numbers in Scientific Notation, Part I video

    • Multiplying and Dividing Numbers in Scientific Notation, Part II video

    • Arithmetic and Geometric Sequences, Part I video

    • Arithmetic and Geometric Sequences, Part II video

    • Arithmetic and Geometric Sequences, Part III video

    • Arithmetic and Geometric Sequences, Part IV video

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517514_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517514_1)

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517515_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517515_1)

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517512_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517512_1)

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517513_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517513_1)

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517511_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517511_1)

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

    [https://www.youtube.com/watch?v=PX5x138J5Ao](https://www.youtube.com/watch?v=PX5x138J5Ao)

    [https://www.youtube.com/watch?v=z6FPlGM4_p0](https://www.youtube.com/watch?v=z6FPlGM4_p0)

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

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

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

    [https://www.youtube.com/watch?v=4QVX0qELqDY](https://www.youtube.com/watch?v=4QVX0qELqDY)

    [https://www.youtube.com/watch?v=-oZNZEUO1Y0](https://www.youtube.com/watch?v=-oZNZEUO1Y0)

    [https://www.youtube.com/watch?v=dUHk4xZlZhY](https://www.youtube.com/watch?v=dUHk4xZlZhY)

    [https://www.youtube.com/watch?v=-7l2VLOTBGY](https://www.youtube.com/watch?v=-7l2VLOTBGY)

    **## TheUnitIIIJournal.docx**

    The Unit III Journal entry is a reflection of scientific notation, a concept covered in Unit III as well as personal time management strategies. Be sure to complete
    _both_ parts A and B.

    Part A: In this unit, we cover the concept of scientific notation. In your own words, explain what scientific notation is, where it could be used in the real world, and what benefit there is to using it in those particular fields.

    Part B: You may have noticed that learning mathematics can take a little more time than other subjects. In the same way that scientific notation can potentially help save time in calculations, there are different approaches to better managing your time when it comes to this course.

    · Share your routine or schedule for completing each unit. What are some time management strategies you are currently utilizing to help complete the assignments and tasks in this course?

    · Next, explain a new technique that you can adopt to help you improve your understanding and completion of each lesson. If you do not readily know of one, try doing a quick web search for ideas.

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

    **## UnitIIIStudyGuide.pdf**

    MAT 1301, Liberal Arts Math 1

    Course Learning Outcomes for Unit III

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

    3. Perform computations with real numbers.
    3.1 Identify rational and irrational numbers.
    3.2 Perform operations using exponents, radicals, and scientific notation.
    3.3 Compute future terms of arithmetic and geometric sequences.

    Required Unit Resources

    Chapter 6: Number Theory and the Real Number System: Understanding the Numbers All Around Us,

    Sections 6.4–6.6

    Unit Lesson

    Chapter 6: Number Theory and the Real Number System: Understanding the Numbers All Around Us

    Unit I introduced counting numbers, integers, and whole numbers. In this unit, we will learn about other types
    of numbers that make up the real number system. Specifically, we will learn about rational and irrational
    numbers.

    Rational numbers are numbers that can be expressed as fractions. Whole numbers, integers, and some
    decimals are rational numbers. You have probably used rational numbers when shopping or cooking.

    Irrational numbers are numbers that cannot be expressed as a fraction. The decimal expansion of an
    irrational number does not end and does not repeat.

    An example of an irrational number is pi where pi is approximately equal to 3.141592654. This number goes
    on forever without a repeating pattern. The number pi is utilized in anything that has a curvature. For
    example, the construction of a football involves a calculation with pi.

    As you learn more about rational and irrational numbers, you will learn how to compute radicals, perform
    operations with exponents, and use scientific notation, and you will be introduced to number patterns known
    as sequences.

    To complete the unit, read the unit lesson, and begin your unit assignments in MyLab Math. Do not forget to
    use the reference sheet and note-taking guide located in this lesson.

    Also, please be aware that you will need a scientific calculator to perform some of the calculations in this unit.
    Please email your professor if you need assistance with your calculator.

    Section 6.4: The Real Number System

    Mathematicians have categorized numbers into different sets. As shown previously, some sets of numbers
    have different rules when performing computations. For example, integer operations are dependent on the
    sign of the number, and fraction operations require that we manipulate the denominator when adding or
    subtracting. In this section, we will expand our knowledge of rational numbers and learn about another group
    of numbers called irrational numbers.

    UNIT III STUDY GUIDE

    The Real Number System Continued

    MAT 1301, Liberal Arts Math 2

    UNIT x STUDY GUIDE

    Title

    Click the link to view the Section 6.4: The Real Number System lesson.

    Section 6.5: Exponents and Scientific Notation

    Exponential and scientific notation is used to identify very small and very large numbers. For example, these
    notations will help us to express a number that is 100 digits long. Exponents and scientific notation will also
    aid in performing calculations with very small and very large numbers.

    Click the link to view the Section 6.5: Exponents and Scientific Notation lesson.

    Section 6.6: Sequences

    As children, we were taught to recognize patterns. We might have been given three shapes and been asked
    to provide the fourth shape based upon a recognizable pattern. As adults, we can recognize patterns or
    trends in things such as utility bills or gas prices. For example, we may expect an increase in our cable bill if
    that bill increased in previous years. In this section, we will learn how to recognize patterns in number
    sequences and predict the next number in a given sequence.

    Click the link to view the Section 6.6: Sequences lesson.

    Looking Forward

    After you review Sections 6.4, 6.5, and 6.6 of the unit lesson, begin your Unit III Homework assignment in
    MyLab Math. You will be instructed to watch several instructional videos before you complete your homework
    problems. It is recommended that you print the following reference sheet and note-taking guide to use while
    you watch the unit homework videos and complete the unit homework assignment.

    • Unit III Reference Sheet

    • Unit III Note-Taking Guide

    Suggested Unit Resources

    In order to access the following resources, click the links below.

    The following videos can be viewed here as well as in your homework assignment within MyLab Math. Please
    click the titles below to view the videos. Transcripts and closed captioning will be available once you access
    the videos.

    • Rational and Irrational Numbers video

    • Computations With Radicals video

    • Operations With Exponents video

    • Scientific Notation video

    • Multiplying and Dividing Numbers in Scientific Notation, Part I video

    • Multiplying and Dividing Numbers in Scientific Notation, Part II video

    • Arithmetic and Geometric Sequences, Part I video

    • Arithmetic and Geometric Sequences, Part II video

    • Arithmetic and Geometric Sequences, Part III video

    • Arithmetic and Geometric Sequences, Part IV video

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517514_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517514_1)

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517515_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517515_1)

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517512_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517512_1)

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517513_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517513_1)

    [https://online.columbiasouthern.edu/bbcswebdav/xid-150517511_1](https://online.columbiasouthern.edu/bbcswebdav/xid-150517511_1)

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

    [https://www.youtube.com/watch?v=PX5x138J5Ao](https://www.youtube.com/watch?v=PX5x138J5Ao)

    [https://www.youtube.com/watch?v=z6FPlGM4_p0](https://www.youtube.com/watch?v=z6FPlGM4_p0)

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

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

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

    [https://www.youtube.com/watch?v=4QVX0qELqDY](https://www.youtube.com/watch?v=4QVX0qELqDY)

    [https://www.youtube.com/watch?v=-oZNZEUO1Y0](https://www.youtube.com/watch?v=-oZNZEUO1Y0)

    [https://www.youtube.com/watch?v=dUHk4xZlZhY](https://www.youtube.com/watch?v=dUHk4xZlZhY)

    [https://www.youtube.com/watch?v=-7l2VLOTBGY](https://www.youtube.com/watch?v=-7l2VLOTBGY)

    – 1
    – 2

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