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Questions and Answers
Which point satisfies the inequality $y > 2x - 3$?
Which point satisfies the inequality $y > 2x - 3$?
What is the shaded solution region of the inequality $3x + y ≤ 6$?
What is the shaded solution region of the inequality $3x + y ≤ 6$?
By what factor is the earthquake in City A (6.3) more powerful than the one in City B (4.3)?
By what factor is the earthquake in City A (6.3) more powerful than the one in City B (4.3)?
If a star emits light intensity of $4 × 10^7$ watts and another of $2 × 10^5$ watts, what is the factor of brightness difference?
If a star emits light intensity of $4 × 10^7$ watts and another of $2 × 10^5$ watts, what is the factor of brightness difference?
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What distance is the base of the ladder from the wall if it is 13 meters long and reaches 12 meters high?
What distance is the base of the ladder from the wall if it is 13 meters long and reaches 12 meters high?
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If a tree casts a shadow of 15 meters long at an angle of elevation of 40°, what is the height of the tree?
If a tree casts a shadow of 15 meters long at an angle of elevation of 40°, what is the height of the tree?
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What would the height of the tree be if the shadow lengthens to 20 meters while maintaining the same angle of elevation?
What would the height of the tree be if the shadow lengthens to 20 meters while maintaining the same angle of elevation?
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If a rectangular field measures 24 meters wide and 70 meters long, what is the length of its diagonal?
If a rectangular field measures 24 meters wide and 70 meters long, what is the length of its diagonal?
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What is the probability that a student passes at least one of the tests given the probabilities provided?
What is the probability that a student passes at least one of the tests given the probabilities provided?
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Which probability indicates that two events, passing math and passing science, are independent?
Which probability indicates that two events, passing math and passing science, are independent?
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What is the probability of drawing two red marbles from a bag containing 3 red, 4 blue, and 5 green marbles, without replacement?
What is the probability of drawing two red marbles from a bag containing 3 red, 4 blue, and 5 green marbles, without replacement?
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In a tree diagram for rolling two dice, how many possible outcome combinations are there?
In a tree diagram for rolling two dice, how many possible outcome combinations are there?
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What is the probability of obtaining a sum of 7 when rolling two fair dice?
What is the probability of obtaining a sum of 7 when rolling two fair dice?
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Study Notes
Linear Equations and Inequalities
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Graphing Inequalities:
- Solution Set: The region on the graph that satisfies the inequality.
- Shading: Shade the region that represents the solution set.
- Testing Points: Check if points satisfy the inequality by substituting their coordinates into the inequality.
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Boundary Line: Plot the corresponding linear equation (with the equality sign) as a dashed line for strict inequalities (
>,<) and a solid line for non-strict inequalities (≥,≤).
Logarithmic Scales and Scientific Notation
- Richter Scale: Measures earthquake magnitude; each integer increase represents a tenfold increase in power.
- Scientific Notation: Expressing numbers as a product of a number between 1 and 10 and a power of 10.
- Comparing Large Values: Logarithmic scales are useful for representing and comparing very large or very small values.
Pythagorean Theorem and Trigonometry
- Pythagorean Theorem: In a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides: a² + b² = c².
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Trigonometric Ratios:
- Sine (sin): Opposite side / Hypotenuse
- Cosine (cos): Adjacent side / Hypotenuse
- Tangent (tan): Opposite side / Adjacent side
- Angle of Elevation: The angle formed between a horizontal line and the line of sight to an object above the horizon.
Conditional Probability and Tree Diagrams
- Conditional Probability: The probability of an event occurring given that another event has already occurred.
- Tree Diagrams: Visual representations that help visualize and calculate probabilities in multi-stage experiments.
- Independent Events: Two events are independent if the occurrence of one event does not affect the probability of the other event occurring.
- Dependent Events: Two events are dependent if the occurrence of one event affects the probability of the other event occurring.
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Description
Test your knowledge on linear equations and inequalities, including graphing techniques and solution sets. Explore logarithmic scales and scientific notation in measuring large values, like earthquake magnitudes. This quiz provides a comprehensive understanding of these mathematical concepts.
