Questions and Answers
What is the unit rate of a car traveling 240 miles in 4 hours?
Which of the following is a characteristic of a proportional relationship?
If a shirt originally costs $20 and is now on sale for $18, what is the percentage decrease?
A bakery sells 480 muffins at $2 each. If they increase the price by 15%, how much will each muffin cost?
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Which of the following represents a unit rate?
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If x and y have a proportional relationship, which of the following is true?
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What is the main function of the right ventricle?
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Which layer of the heart is made up of cardiac muscle?
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What is the path of blood circulation from the lungs to the rest of the body?
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What is the purpose of the left atrium?
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What is the purpose of the cardiovascular system?
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What is the primary function of the left ventricle in the human body?
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What is the normal range for systolic blood pressure in millimeters of mercury?
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What factor affects blood pressure by increasing the amount of blood in the circulatory system?
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What is the role of the SA node in the cardiac conduction system?
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What type of blood vessel is responsible for carrying oxygenated blood away from the heart?
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What is the function of the endothelium in blood vessels?
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What is the term for high blood pressure, which can lead to cardiovascular disease and other health problems?
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What is the function of the bundle of His in the cardiac conduction system?
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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.