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Logarithmic And Exponential Functions

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Logarithmic & Exponential Functions All-in-One Theory Sheet 2.1 Logarithms to Base 10 Definition: If 10 x = y , then log 10 y = x (written log y for short). ┌-----┐ │ 10 │ │ ^ │ ← Exponent │ y │ └-----┘ log 1000 = 3 because 10³ = 1000 log 0.01 = –2 because 10 –2 = 0.01 2.2 Logarithms to Any Base a Definition: If a x = y with a > 0 and a ≠ 1 , then log a y = x . log₂ 32 = 5 because 2⁵ = 32 log₅ 1 = 0 because 5⁰ = 1 2.3 The Three Laws of Logarithms ┌-------┐ │ Laws │ └-------┘ Product: log a (xy) = log a x + log a y Quotient: log a (x / y) = log a x – log a y Power: log a (x n ) = n log a x 2.4 Solving Logarithmic Equations Golden Rule: Logs only exist for positive numbers. Use the laws to get a single log on each side. Drop the log...
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Lines, Angles and Shapes

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Quiz 1: Fullscreen Mode Other Quiz Lines, Angles and Shapes - Theory and Formulas 3.1 Lines and Angles Types of Angles Angles can be classified based on their size: Type Size Example Acute angle Less than 90° 30°, 45°, 70° Right angle Exactly 90° Corner of a book Obtuse angle More than 90° but less than 180° 100°, 120°, 150° Reflex angle More than 180° but less than 360° 200°, 270°, 300° Special Pairs of Angles Complementary Angles: Two angles that add up to 90° . Supplementary Angles: Two angles that add up to 180° . Fundamental Angle Rules Angles on a Straight Line: The sum of angles on a straight line is 180° . ∑ ∠ on line = 180° Angles Around a Point: The sum of all angles around a single point is 360° . ∑ ...
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Continuous random variables

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Other Source Ringkasan Teori & Rumus Variabel Acak Kontinu 1. Definisi Variabel Acak Kontinu Variabel acak kontinu X dapat memiliki nilai apa pun dalam interval kontinu . Contoh: tinggi badan, waktu tunggu, suhu, laju peluruhan radioaktif. 2. Fungsi Kepadatan Peluang (PDF) Syarat PDF f(x) : 1. f(x) ≥ 0 untuk semua x 2. ∫ -∞ ∞ f(x) dx = 1 (total luas = 1) Grafik PDF f(x) x 3. Menghitung Peluang Karena P(X = a) = 0 , peluang hanya bisa dihitung untuk interval: P(a ≤ X ≤ b) = ∫ a b f(x) dx Untuk grafik sederhana bisa juga dengan geometri (luas segiempat, trapesium, segitiga). 4. Nilai Tengah (Median) Median m adalah nilai yang memenuhi: ∫ -∞ m f(x) dx = 0.5 Intuisi: letak vertikal yang membelah luas kurva menjadi dua bagian sama besar. 5. Persentil Umum Persentil- p (0 < p < 1) adalah q sedemikian hingga: ∫ -∞ q f(x) dx = p 6. Nilai Harapan (Mean) E(X) = μ = ∫ -∞ ∞ x f(x) dx 7. Varia...
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