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Ethics: The study of morality and the difference between right and wrong. Epistemology: The study and theory of knowledge. Metaphysics: The purpose of why things exist. What must be fulfilled? Why do we exist? Pre-Socrates: The very first thinkers in Western philosophy, active in ancient Greece during the 6th and 5th centuries BCE. They are called "Pre-Socratic" because they lived and wrote before Socrates. Thales: Water was the fundamental substance for all life. Anaximander: First to make a map Pythagoras: The father of mathematics Heraclitus: Fundamental substance was fire. He believed everything changes. Permenides: Believed everything did not change. Socrates Plato (Forms) Aristotle (The Observer) Came up with the cave theory. The Physical Realm: The world we see and touch. Everything here is temporary, constantly changing, and flawed. The Realm of Forms: An invisible, unchanging world where the perfect, ideal versions of everything exist. Women possess the same mental capacities as men and should be allowed to rule, he also consistently referred to women as the "weaker" sex. (The soul has no gender) Head/Reasoning: This is the seat of reason, logic, and intellect. It seeks the ultimate truth, makes calculated decisions, and distinguishes between what is real and what is an illusion. The Chest/Spirit: this is the seat of emotion, courage, pride, and willpower. It is the part of you that gets angry at injustice, drives you to overcome challenges, and seeks honor or social recognition. The Abdomen/Appetite: This is the seat of basic physical desires and instincts. It drives cravings for food, drink, sex, wealth, and material comforts. It is purely driven by pleasure and lacks any logical restraint. Hylomorphism (the theory that everything is a mix of matter and form). 1. Material cause, or the elements out of which an object is created; 2. Efficient cause, or the means by which it is created; 3. Formal cause, or the expression of what it is; 4. Final cause, or the end for which it is. He argued that knowledge must come from sensory experience and careful observation, not just pure meditation. Rationalism vs Empiricism (How do we know things) Rationalism (Plato) Empiricism The intellect, logic, and deductive reasoning. Rationalists believe humans are born with "innate ideas"—built-in concepts, truths, or structures inside the mind that we don't need to learn from the outside world (e.g., mathematical truths, the concept of God, or basic laws of logic). Empiricists argue that the ultimate source of all knowledge is sensory experience—what we can see, hear, touch, taste, and smell. They believe that if you cannot observe or measure something, you cannot truly know it. Logic for reasoning Deductive Reasoning Inductive reasoning Deductive reasoning starts with a general statement, theory, or universal rule and narrows it down to a specific conclusion. If your initial rules are true, your conclusion must be true.🔺 Inductive reasoning starts with specific observations or data points and broadens them out to form a general rule or theory. 🔻 Fallicies Ad Hominem: Attacking the opponent’s character, looks, or personality instead of their argument. Straw Man: Misrepresenting, exaggerating, or oversimplifying an opponent’s argument to make it easier to attack. Bandwagon Appeal (Ad Populum): Arguing that something must be true, right, or good simply because a large number of people believe it. Non Sequitur: (A statement that does not logically follow from what preceded it; a conclusion that does not follow from the premises.): “Person ‘A’ is incredibly athletic. Her siblings must be very athletic as well.” Appeal to tradition: If it's a tradition, then it must be true. Appeal to popularity: When someone argues that a claim must be true, right, or good simply because a large number of people believe it or do it. Groupthink is when a group of people makes really bad decisions because everyone cares more about fitting in and keeping the peace than finding the actual truth. Instead of thinking for themselves, people just go along with what the group leader or the majority says. Consequentialism says that an action is good if it brings about a good result. The action itself isn't good or bad; you have to wait and see how it turns out. "The ends justify the means." Non-Consequentialism (also called Deontology) says that some actions are just inherently right or wrong, no matter what the outcome is. You have a duty to follow moral rules. Carl Rogers defined a fully functioning person as someone who is completely in touch with their true desires and feelings, and is actively working to reach their full potential
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MATH 0925 MODULE 6 EXAM STUDY PACK TOPICS COVERED: * Decimals * Place Value * Expanded Form * Word Form * Standard Form * Rounding * Decimals to Fractions * Fractions to Decimals * Comparing and Ordering Decimals * Perfect Squares * Square Roots * Rational and Irrational Numbers * Adding Decimals * Subtracting Decimals * Multiplying Decimals * Dividing Decimals * Mean * Median * Mode * Range FLASHCARDS Q: What is the tenths place? A: The first digit to the right of the decimal. Q: What is the hundredths place? A: The second digit to the right of the decimal. Q: What is the thousandths place? A: The third digit to the right of the decimal. Q: Write 0.352 in expanded form. A: 3(0.1) + 5(0.01) + 2(0.001) Q: Write 4.2706 in expanded form. A: 4 + 2(0.1) + 7(0.01) + 6(0.0001) Q: How do you write a decimal in word form? A: Read the whole number, say “and,” then read the decimal part and its place value. Q: Write 24.9 in word form. A: Twenty-four and nine tenths. Q: How do you round decimals? A: Look at the digit to the right of the rounding place. Q: What happens when the next digit is 5 or more? A: Round up. Q: What happens when the next digit is less than 5? A: Keep the digit the same. Q: Convert 0.46 to a fraction. A: 46/100 = 23/50. Q: Convert 0.12 to a fraction. A: 12/100 = 3/25. Q: Convert 0.105 to a fraction. A: 105/1000 = 21/200. Q: How do you convert a fraction to a decimal? A: Divide numerator by denominator. Q: How do you compare decimals? A: Compare digits from left to right. Q: Which is greater, 0.20 or 0.12? A: 0.20. Q: Which is greater, -8 or -9? A: -8. Q: What is 1²? A: 1. Q: What is 2²? A: 4. Q: What is 3²? A: 9. Q: What is 4²? A: 16. Q: What is 5²? A: 25. Q: What is 6²? A: 36. Q: What is 7²? A: 49. Q: What is 8²? A: 64. Q: What is 9²? A: 81. Q: What is 10²? A: 100. Q: What is 11²? A: 121. Q: What is 12²? A: 144. Q: What is √36? A: 6. Q: What is √49? A: 7. Q: What is √81? A: 9. Q: What is √121? A: 11. Q: What is √(16/49)? A: 4/7. Q: Is √(-100) a real number? A: No. It is not a real number. Q: What is a rational number? A: A decimal that stops or repeats. Q: What is an irrational number? A: A decimal that never stops and never repeats. Q: Is π rational or irrational? A: Irrational. Q: Is √2 rational or irrational? A: Irrational. Q: What is the rule for adding decimals? A: Line up decimal points. Q: What is the rule for subtracting decimals? A: Line up decimal points. Q: What is the rule for multiplying decimals? A: Multiply normally and count decimal places. Q: What is the rule for dividing decimals? A: Make the divisor a whole number. Q: What is the mean? A: Average. Q: How do you find the mean? A: Add all values and divide by the number of values. Q: What is the median? A: The middle value after ordering the data. Q: What is the mode? A: The value that appears most often. Q: What is the range? A: Largest value minus smallest value. IMPORTANT EXAM RULES 1. Line up decimals when adding and subtracting. 2. Count decimal places when multiplying. 3. Make the divisor a whole number before dividing. 4. Memorize perfect squares from 1² through 12². 5. Rational numbers stop or repeat. 6. Irrational numbers never stop and never repeat. 7. Mean = Average. 8. Median = Middle. 9. Mode = Most Common. 10. Range = Largest − Smallest. COMMON MISTAKES * Forgetting to line up decimals. * Forgetting to simplify fractions. * Mixing up mean and median. * Forgetting to count decimal places in multiplication. * Forgetting to move BOTH decimals in division. * Thinking all square roots are rational. * Forgetting that negative numbers closer to zero are larger. PRACTICE QUESTIONS 1. Round 45.0193 to the nearest hundredth. Answer: 45.02 2. Convert 0.36 to a fraction. Answer: 9/25 3. Convert 3/8 to a decimal. Answer: 0.375 4. Which is larger: 0.205 or 0.25? Answer: 0.25 5. Find √64. Answer: 8 6. Is √5 rational or irrational? Answer: Irrational 7. Add: 14.563 + 6.29 Answer: 20.853 8. Subtract: 24 − 8.0731 Answer: 15.9269 9. Multiply: 4.8 × 0.13 Answer: 0.624 10. Find the mean of 10, 20, 30. Answer: 20
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Factoring & Simplifying, AII
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simplify fraction
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SIMPLISIA
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