Proof Part 2 Minimizing Squared Error to Line Watch the next lesson: https://www.khanacademy.org/math/probability/regression/regression-correlation/v/proof-part-3-minimizing-squared-error-to-regression-line?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics Missed the previous lesson? https://www.khanacademy.org/math/probability/regression/regression-correlation/v/proof-part-1-minimizing-squared-error-to-regression-line?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it! 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. ... https://www.youtube.com/watch?v=f6OnoxctvUk Note: All Khan Academy content is available for free at (www.khanacademy.org)

From the 3rd to the 5th centuries, the Roman Empire gets divided and less stable. The Western Roman Empire considered to end in 476 with control of Italy by Odoacer. Watch the next lesson: https://www.khanacademy.org/humanities/world-history/ancient-medieval/roman-empire-survey/v/ara-pacis-augustae-altar-of-augustan-peace-13-9-b-c-e-rome Missed the previous lesson? Watch here: https://www.khanacademy.org/humanities/world-history/ancient-medieval/roman-empire-survey/v/emperors-of-pax-romana World History on Khan Academy: From the earliest civilizations to the modern world, geography, religion, trade, and politics have bound peoples and nations together — and torn them apart. Take a journey through time and space and discover the fascinating history behind the complex world we inhabit today. 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. ... https://www.youtube.com/watch?v=UZ3oEn5Q7U4 Note: All Khan Academy content is available for free at (www.khanacademy.org)

Analog information can be digitized and stored reliably in computer memory. This way it can be sent over long distances as a series of wave pulses. Learn about the differences between digital and analog information and how digital information is created. Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help! Donate or volunteer today! Donate here: https://www.khanacademy.org/donate Volunteer here: https://www.khanacademy.org/contribute ... https://www.youtube.com/watch?v=oSZNQ1LZjHg Note: All Khan Academy content is available for free at (www.khanacademy.org)

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geometry/similarity/similarity-and-transformations/e/defining-similarity-through-angle-preserving-transformations?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Watch the next lesson: https://www.khanacademy.org/math/geometry/similarity/triangle_similarlity/v/similar-triangle-basics?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Missed the previous lesson? https://www.khanacademy.org/math/geometry/similarity/similarity-and-transformations/v/testing-similarity-through-transformations?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry. ... https://www.youtube.com/watch?v=W-itq-SYw0I Note: All Khan Academy content is available for free at (www.khanacademy.org)