Finding the range and mid-range | Descriptive statistics | Probability and Statistics | Khan Academy
The range is the difference between the largest and smallest numbers. The midrange is the average of the largest and smallest number. Practice with this problem.
First example of solving an exact differential equation.
Watch the next lesson: https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/exact-equations/v/exact-equations-example-2?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations
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https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/exact-equations/v/exact-equations-intuition-2-proofy?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialEquations
Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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https://www.youtube.com/watch?v=Pb04ntcDJcQ
More practice carrying with multiple digit numbers
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/arithmetic/addition-subtraction/addition_carrying/e/addition_4?utm_source=YT&utm_medium=Desc&utm_campaign=Arithmetic
Watch the next lesson: https://www.khanacademy.org/math/arithmetic/addition-subtraction/sub_borrowing/v/subtracting-2-digit-numbers-without-regrouping?utm_source=YT&utm_medium=Desc&utm_campaign=Arithmetic
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https://www.khanacademy.org/math/arithmetic/addition-subtraction/addition_carrying/v/example-adding-with-carrying?utm_source=YT&utm_medium=Desc&utm_campaign=Arithmetic
Arithmetic on Khan Academy: So you're ready to have some arithmetic fun? You've come to the right spot! It's the first "official" math topic and chalked full of fun exercises and great videos which help you start your journey towards math mastery. We'll cover the big ones: addition, subtraction, multiplication, and division, of course. But we don't stop there. We'll get into negative numbers, absolute value, decimals, and fractions, too. Learning math should be fun, and we plan on having some with you. Ready to get started?
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https://www.youtube.com/watch?v=fOXo4p4WDKM
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Learn how to apply the distributive property of multiplication over subtraction and why it works. This is sometimes just called the distributive property or distributive law.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/order-of-operations/ditributive_property/e/distributive_property?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra
Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/order-of-operations/ditributive_property/v/distributive-property-example-1?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra
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Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!
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https://www.youtube.com/watch?v=Badvask-UDU
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Systems of Linear Inequalities
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https://www.youtube.com/watch?v=5xQqwgS3O4U
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Basics of how a mortgage back security works. Created by Sal Khan.
Watch the next lesson:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/mort-backed-secs-tut/v/mortgage-backed-securities-i?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets
Missed the previous lesson? Watch here:
https://www.khanacademy.org/economics-finance-domain/core-finance/derivative-securities/forward-futures-contracts/v/interpretting-futures-fair-value-in-the-premarket?utm_source=YT&utm_medium=Desc&utm_campaign=financeandcapitalmarkets
Finance and capital markets on Khan Academy: In many commodities markets, it is very helpful for buyers or sellers to lock-in future prices. This is what both forwards and futures allow for. This tutorial explains how they work and what the difference is between the two.
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https://www.youtube.com/watch?v=dwleadLC2Dw
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Approximating e_ with a Maclaurin series (which is like a Taylor polynomial centered at x=0 with infinitely many terms). It turns out that this series is exactly the same as the function itself! Created by Sal Khan.
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-bc/bc-series/bc-maclaurin-series/v/euler-s-formula-and-euler-s-identity?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-bc/bc-series/bc-maclaurin-series/v/sine-taylor-series-at-0-maclaurin?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusBC
AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
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https://www.youtube.com/watch?v=JYQqml4-4q4
Note: All Khan Academy content is available for free at (www.khanacademy.org)
If waves are disruptions traveling through a medium and light is a wave, what medium does it travel through? A luminiferous ether?
Watch the next lesson: https://www.khanacademy.org/science/physics/special-relativity/michelson-and-morleys-luminiferous-ether-experiment/v/potential-ways-to-detect-an-ether-wind?utm_source=YT&utm_medium=Desc&utm_campaign=physics
Missed the previous lesson? https://www.khanacademy.org/science/physics/geometric-optics/mirrors-and-lenses/v/diopters-aberration-and-the-human-eye?utm_source=YT&utm_medium=Desc&utm_campaign=physics
Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. To get the most out of physics, you'll need a solid understanding of algebra and a basic understanding of trigonometry.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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https://www.youtube.com/watch?v=iAPYsOaq-VY
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Worked example using trig ratios to solve for missing information and evaluate other trig ratios
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/trigonometry/basic-trigonometry/reciprocal-trig-functions/e/reciprocal_trig_funcs?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry
Watch the next lesson: https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/radians_tutorial/v/introduction-to-radians?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry
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https://www.khanacademy.org/math/trigonometry/basic-trigonometry/reciprocal-trig-functions/v/example-the-six-trig-ratios?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry
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https://www.youtube.com/watch?v=rufFQZDDXCE
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Problems 17-18 on page 476
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https://www.youtube.com/watch?v=EDEg7SY2-VU
Note: All Khan Academy content is available for free at (www.khanacademy.org)