Ratios and Rates of Change: Unit Rates and Proportional Relationships
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Questions and Answers

What is the unit rate of a car traveling 240 miles in 4 hours?

  • 40 miles per hour
  • 120 miles per hour
  • 60 miles per hour (correct)
  • 10 miles per hour

    • Which of the following is a characteristic of a proportional relationship?

  • The graph is a curve
  • The ratio of x to y is constant
  • The ratio of y to x is constant (correct)
  • The graph passes through the point (0, 1)

    • If a shirt originally costs $20 and is now on sale for $18, what is the percentage decrease?

  • 5%
  • 15%
  • 10% (correct)
  • 20%

    • A bakery sells 480 muffins at $2 each. If they increase the price by 15%, how much will each muffin cost?

    <p>$2.30</p> Signup and view all the answers

    Which of the following represents a unit rate?

    <p>30 miles per hour</p> Signup and view all the answers

    If x and y have a proportional relationship, which of the following is true?

    <p>The ratio of x to y is constant</p> Signup and view all the answers

    What is the main function of the right ventricle?

    <p>Pump blood to the lungs</p> Signup and view all the answers

    Which layer of the heart is made up of cardiac muscle?

    <p>Myocardium</p> Signup and view all the answers

    What is the path of blood circulation from the lungs to the rest of the body?

    <p>Lungs → left atrium → left ventricle → rest of the body</p> Signup and view all the answers

    What is the purpose of the left atrium?

    <p>Receive oxygenated blood from the lungs</p> Signup and view all the answers

    What is the purpose of the cardiovascular system?

    <p>To circulate blood throughout the body and return it to the heart</p> Signup and view all the answers

    What is the primary function of the left ventricle in the human body?

    <p>Pumping blood to the rest of the body</p> Signup and view all the answers

    What is the normal range for systolic blood pressure in millimeters of mercury?

    <p>90-120 mmHg</p> Signup and view all the answers

    What factor affects blood pressure by increasing the amount of blood in the circulatory system?

    <p>Blood volume</p> Signup and view all the answers

    What is the role of the SA node in the cardiac conduction system?

    <p>Generating electrical impulses</p> Signup and view all the answers

    What type of blood vessel is responsible for carrying oxygenated blood away from the heart?

    <p>Arteries</p> Signup and view all the answers

    What is the function of the endothelium in blood vessels?

    <p>Regulating blood flow and pressure</p> Signup and view all the answers

    What is the term for high blood pressure, which can lead to cardiovascular disease and other health problems?

    <p>Hypertension</p> Signup and view all the answers

    What is the function of the bundle of His in the cardiac conduction system?

    <p>Transmitting impulses to the ventricular muscle</p> Signup and view all the answers

    Study Notes

    Ratios and Rates of Change

    Unit Rates

    • A unit rate is a ratio that compares the number of units of one quantity to one unit of another quantity.
    • Unit rates are used to describe a quantity per unit, such as miles per hour or dollars per pound.
    • Unit rates are often used to make comparisons between different quantities or to describe a rate of change.
    • Examples:
      • 30 miles per hour (distance per time)
      • $5 per pound (price per weight)

    Proportional Relationships

    • A proportional relationship exists between two quantities when the ratio of one quantity to the other is constant.
    • If one quantity increases, the other quantity increases by the same factor.
    • Proportional relationships can be represented by an equation of the form y = kx, where k is the constant of proportionality.
    • Characteristics of proportional relationships:
      • The graph is a straight line through the origin.
      • The ratio of y to x is constant.
      • If x increases, y increases by the same factor.

    Percentage Increases

    • A percentage increase is a way to describe a change in a quantity as a fraction of the original amount.
    • Percentage increase = (new value - original value) / original value * 100
    • Examples:
      • A 25% increase from 100 to 125: (125 - 100) / 100 * 100 = 25%
      • A 10% decrease from 100 to 90: (90 - 100) / 100 * 100 = -10%
    • To find the new value after a percentage increase, multiply the original value by (1 + percentage increase as a decimal):
      • 100 x (1 + 0.25) = 125

    Ratios and Rates of Change

    Unit Rates

    • A unit rate is a ratio that compares the number of units of one quantity to one unit of another quantity.
    • Unit rates are used to describe a quantity per unit, such as miles per hour or dollars per pound.
    • Examples of unit rates include 30 miles per hour (distance per time) and $5 per pound (price per weight).

    Proportional Relationships

    • A proportional relationship exists between two quantities when the ratio of one quantity to the other is constant.
    • The constant of proportionality (k) is the ratio of one quantity to the other in a proportional relationship.
    • Characteristics of proportional relationships include:
      • Graph is a straight line through the origin
      • The ratio of y to x is constant
      • If x increases, y increases by the same factor
    • Proportional relationships can be represented by an equation of the form y = kx.

    Percentage Increases

    • A percentage increase is a way to describe a change in a quantity as a fraction of the original amount.
    • Formula to calculate percentage increase: (new value - original value) / original value * 100
    • Examples:
      • 25% increase from 100 to 125: (125 - 100) / 100 * 100 = 25%
      • 10% decrease from 100 to 90: (90 - 100) / 100 * 100 = -10%
    • To find the new value after a percentage increase, multiply the original value by (1 + percentage increase as a decimal).
      • 100 x (1 + 0.25) = 125

    Heart Structure

    • The heart is a muscular organ that pumps blood throughout the body, divided into four chambers: right atrium, right ventricle, left atrium, and left ventricle.
    • The right atrium receives deoxygenated blood from the body, while the right ventricle pumps blood to the lungs.
    • The left atrium receives oxygenated blood from the lungs, and the left ventricle pumps blood to the rest of the body.
    • The heart is made up of three layers: epicardium (outer layer), myocardium (middle layer, made up of cardiac muscle), and endocardium (inner layer, lines the heart chambers).

    Blood Circulation

    • The cardiovascular system is a closed system, meaning blood is circulated throughout the body and returns to the heart.
    • Deoxygenated blood from the body enters the right atrium, then flows to the right ventricle, and is pumped to the lungs.
    • Oxygenated blood from the lungs enters the left atrium, then flows to the left ventricle, and is pumped to the rest of the body.
    • Blood circulation is a vital function that supplies oxygen and nutrients to tissues and organs.

    Arterial Blood Pressure

    • Blood pressure is the force exerted by blood on the walls of arteries, measured in millimeters of mercury (mmHg).
    • Normal blood pressure range is 90-120 mmHg (systolic) and 60-80 mmHg (diastolic).
    • Factors that affect blood pressure include cardiac output, peripheral resistance, and blood volume.
    • High blood pressure (hypertension) can lead to cardiovascular disease and other health problems.

    Cardiac Conduction

    • The cardiac conduction system generates and propagates electrical impulses that regulate the heartbeat.
    • The SA node generates electrical impulses, which are relayed by the AV node to the ventricles through the Bundle of His and Purkinje fibers.
    • The cardiac conduction system ensures a coordinated and efficient heartbeat.

    Vascular Function

    • Blood vessels are responsible for transporting blood throughout the body, and include arteries, veins, and capillaries.
    • Arteries carry oxygenated blood away from the heart, while veins carry deoxygenated blood back to the heart.
    • Capillaries allow for exchange of oxygen and nutrients with tissues, and are lined with endothelium, which helps to regulate blood flow and pressure.
    • Vascular function is essential for maintaining healthy blood pressure and overall cardiovascular health.

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    Description

    Test your understanding of unit rates and proportional relationships, including their definitions, examples, and applications in making comparisons and describing rates of change.

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