Today we’re going to talk about Bayes Theorem and Bayesian hypothesis testing. Bayesian methods like these are different from how we've been approaching statistics so far, because they allow us to update our beliefs as we gather new information - which is how we tend to think naturally about the world. And this can be a really powerful tool, since it allows us to incorporate both scientifically rigorous data AND our previous biases into our evolving opinions.

CORRECTION: At 2:09 the righthand side of the equation should not have P()'s, it should just be the raw numbers.

Crash Course is on Patreon! You can support us directly by signing up at http://www.patreon.com/crashcourse

Thanks to the following Patrons for their generous monthly contributions that help keep Crash Course free for everyone forever:

Mark Brouwer, Erika & Alexa Saur Glenn Elliott, Justin Zingsheim, Jessica Wode, Eric Prestemon, Kathrin Benoit, Tom Trval, Nathan Taylor, Divonne Holmes à Court, Brian Thomas Gossett, Khaled El Shalakany, Indika Siriwardena, SR Foxley, Sam Ferguson, Yasenia Cruz, Eric Koslow, Caleb Weeks, Tim Curwick, D.A. Noe, Shawn Arnold, Ruth Perez, Malcolm Callis, Ken Penttinen, Advait Shinde, William McGraw, Andrei Krishkevich, Rachel Bright, Mayumi Maeda, Kathy & Tim Philip, Jirat, Eric Kitchen, Ian Dundore, Chris Peters
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*Click CC for English subtitles!* This is a story that was made spring semester 2022 on my Comprehensible Spanish channel.

I hope you enjoy it to practice with!

How did you do? Did you understand it? If not, watch it again and again to get more repetition of the words in the video! If this is a little too hard, try turning on the subtitles to follow along! Or watch my other Spanish in context videos or lessons for more Spanish help!

Or watch the past tense version!
https://youtu.be/VH2BpBlPlgo
~~~~~~~~~~~~~~~
👍Please share this video with others and like it to help me get the word out on my videos!

And let me know about other troublesome topics you’d like in bite-sized form.

🔔 Subscribe for more Spanish lessons: http://bit.ly/XGe7we

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~~~~~~~~~~~~~~~
Special thanks to Ely Saul Garcia for the intro music and Manuel García for the narration! And thanks to YOU for watching!

Original story:
https://youtube.com/playlist?l....ist=PLdVAUQOSGq76b_k

🚀 Become an AI Master – All-in-one AI Learning https://aimaster.me/pro

Go to my sponsor https://snhu.edu/arthurwiner and learn how you can get started
[Update] Free download: https://bit.ly/3V9ZgM7 batch upscale old/low quality photos to 4K/8K/10K in one click.

In this video, we'll take a look at how to process photos using AI. These unknown ai tools will destroy Photoshop, Lightroom, Afinity Photo and others. With the help of these neural networks, you can literally process photos in a few clicks and make them much more beautiful and high quality. Unleash the photographer in you and create perfect images in seconds. Let's take a look at Midjourney, Stable Defusion and other neural networks for working with graphics today.

🚀 Become an AI Master – All-in-one AI Learning https://aimaster.me/pro
Make short clips from long videos with Vidyo AI https://vidyo.ai/

In this video I will show you how to make 50 YouTube Shorts videos in just 5 minutes using an AI tool. You don't need to make up text in ChatGPT or remount the video in Davinci Resolve, Adobe Premier, etc. Just take a long video, upload it to the platform and in seconds artificial intelligence will create a bunch of cool short videos that can be uploaded to YouTube, Tik-tok, Instagram.

Prenumera gärna på kanalen för att få uppdatering när nya videos laddas upp.
Ladda ner geogebra här: https://www.geogebra.org/download?lang=en

🍌 Who likes bananas? Everybody likes bananas! 🥳 With this hilarious banana song for preschoolers, kindergarteners, babies, and kids of all ages, you and your kids can learn a few things about bananas, including how to peel them, all while singing and dancing to a funny song. 🎉

This sing-along educational video is the perfect way to get your kids excited about bananas! 🤩 The lyrics are catchy and easy for little ones to remember. Plus, it's a great way to teach them about the many benefits of this healthy fruit. ✨ Introduce your little ones to pop music and tasty treats the right way by making it a fun and exciting sing-along experience! 🎊

🎤 Banana Song Lyrics:

When I see bananas
I go bananas
When I see bananas
I go bananas
When I see bananas
I go bananas
bananas bananas bananas bananas

All I wanna eat is my bananas
All I wanna eat is my bananas
All I wanna eat is my bananas
bananas bananas bananas bananas

ba-ba-ba-ba-ba
ba-ba-ba-ba-ba
ba-ba-ba-ba-ba
bananana-nas!

Ooh… I need bananas!
Can you help me to peel bananas?
I wanna eat bananas!
bananas! bananas! bananas! bananas!

✔️ This video is available in ultra HD 4k for the highest possible video and audio quality. It stars everyone’s favorite animated buddies, 🦁 Lucas & friends, and it’s family-friendly, so everyone can enjoy it! 🕺

⭐ If our video entertains your child and makes them happy, please hit the LIKE button. SHARE it with your friends and family members so that more and more kids can sing and have fun. 👍 SUBSCRIBE to our channel to watch our other nursery rhymes, kids songs, and educational videos for children and parents. 🔔 And make sure you turn on the bell icon to get notified as soon as our new videos come up. 🔥

🛍️ Official Lucas & Friends Store Now Open - https://shop.rvappstudios.com

📢 Checkout Lucas & Friends Educational Children's Books: https://www.amazon.com/Lucas-F....riends-by-RV-AppStud

🎯 Try our FREE Educational Apps for Babies & Toddlers:
🟡 Google Play: https://play.google.com/store/....apps/dev?id=74300059
🟣 iOS: https://apps.apple.com/develop....er/rv-appstudios-llc
🟢 RV AppStudios: https://www.rvappstudios.com/kidsapp.html

🌟 Fun nursery rhymes and kids songs by RV AppStudios:
🥳 Hands In The Air Song - https://youtu.be/lKemaWQif4g
🌞 Ring Around The Rosie - https://youtu.be/z4PxLc8zHgQ
🐶 Bingo Song With Lyrics - https://youtu.be/wosclrdVHLE
😇 Peek A Boo Song for Kids - https://youtu.be/Nd4eAWJMuNk

Copyright © RV AppStudios

#KidsMusic #NurseryRhymes #KidsSongs

Grab the kids and turn up the volume, it's time to learn with Lucas & Friends! 🎉 The latest toddler learning video features so many wonderful educational activities for babies, you'll be amazed at how much your little ones will learn in such a short time! 🙌

👧 Baby's first words and baby talk are the focus of this video, and it's the perfect way to teach nursery rhymes, kids songs, first words, learn to talk, and important phrases like mommy, daddy, ball, car, and more, all in a fun and safe environment tailor-made for kids aged 9 to 18 months and 1 to 2 years old! 👶

If your baby is just beginning to learn baby talk and their first words, this is the perfect way to encourage their curiosity. 💡 Not only will Lucas, Ruby, Lilly, and pals teach basic vocabulary words, but they'll do it in a way that helps children recognize letters, learn to talk and spell, complete with fun baby learning activities that keep kids glued to the screen in all the right ways! 📚

◉ Check out all the lessons this Lucas & Friends educational baby learning video has to offer:

00:00 Baby Learning with Lucas and Friends 🦁

00:40 Baby Talk Mommy 👩 - Baby learn how to say 'mommy' through fun games, songs, and activities. Includes adorable images of Lucas hugging his mother and calling her 'mom', 'momma' and even dancing and having fun with her!

04:38 Baby Talk Daddy 👨- Songs and baby learning lessons about the word 'daddy' including Lucas playing and having fun with his very own dad!

09:03 Baby Learn To Talk ⚽ Ball - Learn about the word 'ball' including what a ball is, all the colors balls can be, and practice counting different balls.

13:02 Baby Learn To Speak 🐕 Dog - A fun learning lesson for baby with dogs where toddlers learn what a dog is and get to see Lucas playing with his own puppy companion. Includes a fun rendition of the famous B-I-N-G-O song (BINGO Dog Song)!

18:50 Learn To Talk Baby 🚗 Car - Discover how to say and spell 'car' with Ruby. Learn what a car is, what they do, learn about going fast and going slow, and more!

23:58 Learn To Talk Baby 🦆 Duck - Ducks are funny animals, and this part of the video celebrates that! Learn all about ducks as they swim, sleep, jump, and dance. The Five Little Ducks song helps teach this and so much more!

Join us as we explore the world with Lucas & Friends in this baby learning videos for 1 year old. 🎯 Help your child unlock exciting new words, all while they have fun singing and dancing along with animated friends! 🎶

✔️ Our ultra HD 4K baby learning with Lucas and Friends is packed with awesome graphics and catchy music that'll keep kids entertained while they learn. It's the perfect video for babies, toddlers, preschoolers, and kindergartners who are starting their educational journey. Gather your little ones and prepare for a wonderful family time together! 🔆

🥰 We hope our educational videos make learning fun for your whole family! Be sure to hit the LIKE button and SHARE it with friends and other family members! And don't forget to SUBSCRIBE for more free animated sing-along songs, nursery rhymes for kids and learning content by Lucas & Friends! 🦁

🛍️ Official Lucas & Friends Store Now Open - https://shop.rvappstudios.com

📢 Lucas & Friends GIFs & Stickers at Giphy - https://giphy.com/rvappstudios

📢 Check out the Lucas & Friends Educational Children's Books: https://www.amazon.com/Lucas-F....riends-by-RV-AppStud

🎯 Try our FREE Educational Apps for Babies & Toddlers:
🟡 Google Play: https://play.google.com/store/....apps/dev?id=74300059
🟣 iOS: https://apps.apple.com/develop....er/rv-appstudios-llc
🟢 RV AppStudios: https://www.rvappstudios.com/kidsapp.html

🌟 Fun educational videos for toddlers by RV AppStudios:
📖 Toddler Learning Videos https://youtu.be/vM-HavjlWoA
🔸 First Words For Babies & Toddlers https://youtu.be/c-aiPRcTpao
✏️ Learn ABC For Toddlers & Babies https://youtu.be/oIN4u__noGM
🎨 Babies and Toddlers Learn First Words https://youtu.be/50klx9Q5ls8

Copyright © RV AppStudios

#FirstWords #toddlers #babylearning #learning

✨ Be the best mom and dad and teach your child the name of each baby animal with the cute Animals and Their Young Ones YouTube video. 🤩 Baby, mother, and father will all be happy listening each baby animal sound in this adorable learning video for kids. Our video is in ultra-HD 4k, so you'll love watching your little one laugh and enjoy in high definition. Kids of all ages will love learning about wild animal sounds in this video. 🔉

😊 Kids will learn the name of a baby chicken, duck, hen, cat, and so much more. 🔸 They'll learn about both wild and farm animal sounds. Have a fun time watching and learning about baby animal sounds in educational video for toddlers. ✔️ Here's a list of each animal listed and their animal young ones.

⦿ Learn about various animals and their babies/ young ones:

🐱 Cat - Kitten
🐶 Dog - Puppy
🐔 Hen - Chick
🦆 Duck - Duckling
🐮 Cow - Calf
🐷 Pig - Piglet
🐏 Sheep - Lamb
🐐 Goat - Kid
🐎 Horse - Foal
🦢 Swan - Cygnet
🐘 Elephant - Calf
🐯 Tiger - Cub
🦁 Lion - Cub
◾ Donkey - Foal
🐒 Monkey - Infant
🦒 Giraffe - Calf
🦌 Deer - Fawn
🦓 Zebra - Foal
🐧 Penguin - Chick
🐻 Bear - Cub
🦘 Kangaroo - Joey
🐇 Rabbit - Bunny

⭐ RV AppStudios is thrilled to add our newest song for kids to our collection, and one we're sure your kids will love singing along-to! 👍 As always, be sure to LIKE and SHARE this kids song to show more families that it can be easy and fun to learn 🔔 And don't forget to SUBSCRIBE for more free animated sing-along songs and nursery rhymes for kids by RV Kids! 🔥

📢 Coloring pages for kids and much more - https://www.rvappstudios.com

🎯 Try our FREE Educational Apps for Babies & Toddlers:
🟡 Google Play: https://play.google.com/store/....apps/dev?id=74300059
🟣 iOS: https://apps.apple.com/develop....er/rv-appstudios-llc
🟢 RV AppStudios: https://www.rvappstudios.com/kidsapp.html

🌟 Fun educational videos for toddlers by RV AppStudios:
🚗 Learn Vehicle Names & Vehicle Sounds for Kids - https://youtu.be/pd-vSJW6VO8
✏️ Alphabet Learning Videos For Toddlers - https://youtu.be/X-ktkw8LY70
📖 Counting Numbers 1 to 20 for Kids - https://youtu.be/2KwCtfvvMsY
🐶 Animal Sounds for Kids - https://youtu.be/_wpG04sx84E

Copyright © RV AppStudios

#AnimalVideos #EducationalVideos #LearningVideos

Your nose uses quantum tunnelling to smell! This crazy conclusion comes from the latest interpretations of the evidence about how our smell receptors detect odour molecules. This video summarises the two models of smell: shape theory and vibration theory, and concludes that you need both to explain how we smell.

#quantum #biology #DomainOfScience

If you would like to buy a poster of this map, they are available here: https://www.redbubble.com/peop....le/dominicwalliman/w

I have also made a version available for educational use which you can find here: https://www.flickr.com/photos/....95869671@N08/3358166

Domain of Science forum: https://www.commonlounge.com/c....ommunity/7df58003ee8

The main reference I used for this video was "Life on the Edge" by JohnJoe McFadden and Jim Al-Khalili. Which I highly recommend, it is very well written and contains some brilliant science explanations. The field of quantum biology is utterly fascinating. https://www.amazon.com/Life-Ed....ge-Coming-Quantum-Bi
Here are some other links you can look at if you want to find out more:
https://en.wikipedia.org/wiki/....Vibration_theory_of_
https://phys.org/news/2011-03-....quantum-explanation.
http://www.physics.org/featuredetail.asp?id=83

To err is to human, and I human a lot. I always try my best to be as correct as possible, but unfortunately I make mistakes. This is the errata where I correct my silly mistakes. My goal is to one day do a video with no errors!

1. I misspelled Planck's Constant and wrote Plank's constant. Silly me!

Thanks so much to my supporters on Patreon. I hope to make money from my videos one day, but I’m not there yet! If you enjoy my videos and would like to help me make more this is the best way and I appreciate it very much. https://www.patreon.com/domainofscience

Also, if you enjoyed this video, you will probably like my science books, available in all good books shops around the work and is printed in 16 languages. Links are below or just search for Professor Astro Cat. They are fun children's books aimed at the age range 7-12. But they are also a hit with adults who want good explanations of science. The books have won awards and the app won a Webby.

Frontiers of Space: http://nobrow.net/shop/profess....or-astro-cats-fronti
Atomic Adventure: http://nobrow.net/shop/profess....or-astro-cats-atomic
Intergalactic Activity Book: http://nobrow.net/shop/profess....or-astro-cats-interg
Solar System App: http://www.minilabstudios.com/....apps/professor-astro

Find me on twitter, instagram, and my website:
http://dominicwalliman.com
https://twitter.com/DominicWalliman
https://www.instagram.com/dominicwalliman
https://www.facebook.com/dominicwalliman

In 1958, farmers digging for bat poop in a Chinese cave stumbled on something way stranger—a fossilized skull that would baffle scientists for decades. At first, experts thought it was a Neanderthal, but new micro-CT scans have revealed a twist: it doesn’t fit neatly into Neanderthals, Homo sapiens, or even Homo erectus. Instead, Maba 1 is a mash-up of features—part this, part that, and part “what on Earth is that?” The skull’s brain size is surprisingly modern, but its structure is just too weird to belong to any known species. Some researchers now think it might represent a completely unknown human lineage that lived in Asia 300,000 years ago. Join us as we uncover the mystery of Maba 1 and what it tells us about our strange, twisted evolutionary story.

Animation is created by Bright Side.
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Check our Bright Side podcast on Spotify and leave a positive review! https://open.spotify.com/show/....0hUkPxD34jRLrMrJux4V
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This video is made for entertainment purposes. We do not make any warranties about the completeness, safety and reliability. Any action you take upon the information in this video is strictly at your own risk, and we will not be liable for any damages or losses. It is the viewer's responsibility to use judgement, care and precaution if you plan to replicate.

Class 5 - Mathematics - Chapter 3 - Lecture 1 - Addition & Subtraction of Fractions - Allied Schools

PBS Member Stations rely on viewers like you. To support your local station, go to: http://to.pbs.org/DonateOKAY
↓ More info and sources below ↓

In a world of distractions, how do we pay attention?

It seems like every week someone tells us how the internet and the digital age are overloading our brains. Sure, sometimes it feels like we're being fed more information than we can handle, that we're paying attention to the wrong things. Are we giving our brain a fair shot?

I explore some science that show how paying attention can be a bad thing, and then some science about how paying attention can be a very helpful thing
Special cameos by Hank Green and Mike Rugnetta!

Further reading:

The original Simons and Chabris experiment: http://www.youtube.com/watch?v=vJG698U2Mvo

The cocktail party effect: http://www.npr.org/blogs/healt....h/2013/03/07/1736136

The illusion of attention: http://www.guardian.co.uk/scie....nce/neurophilosophy/

How is the internet changing our brains? (Harold Rheingold and more) http://www.edge.org/q2010/q10_index.html#responses

Sherry Turkle - Alone Together http://www.ted.com/talks/sherr....y_turkle_alone_toget

Written and hosted by Joe Hanson
Produced by Painted On Productions (http://www.paintedon.com/)

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An Infographic trip through the wonders of the solar system.

The solar system - well known from countless documentaries. 3D animation on black background. This infographic videos tries something different. Animated infographics and a focus on minimalistic design puts the information up front. We take the viewer on a trip through the solar system, visiting planets, asteroids and the sun.

Short videos, explaining things. For example Evolution, the Universe, the Stock Market or controversial topics like Fracking. Because we love science.


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Get Merch designed with ❤ from https://kgs.link/shop
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Steve Taylor: https://kgs.link/youtube-voice


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Spotify: https://kgs.link/music-spotify
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The Solar System -- our home in space

Help us caption & translate this video!

http://www.youtube.com/timedtext_cs_panel?c=UCsXVk37bltHxD1rDPwtNM8Q&tab=2

The Perseverance Rover and helicopter Ingenuity have landed safely on Mars. A few years back I got to visit NASA JPL to interview the scientists to find out their goals for the mission. I made this clip as a correspondent for Bill Nye Saves the World on Netflix.

Touring the Jet Propulsion Lab (JPL) in Pasadena was an awesome experience. I didn't think we were going to get into the control room but we got lucky. Some of the greatest moments in the history of space exploration have taken place there. They have a giant vacuum chamber where they can take the rover down to the atmospheric pressure on Mars (roughly .01x Earth's atmosphere) and test all of the devices to make sure there are no electrical discharges due to the reduced pressure. I also enjoyed seeing how the rocks will be cored and stored in tubes and deposited on the Martian surface awaiting pickup by the following mission.

Images courtesy of NASA.

Filmed by Raquel Nuno from 3:30 onwards.

Music: http://epidemicsound.com "Serene Story 2"

🐰 Get ready to laugh with these Easter jokes for kids from Homeschool Pop! You will laugh about eggs and the Easter bunny as we share some amusing jokes, in the amusing Homeschool Pop format.

❤️ Homeschool Pop? Join our team and get tattoos here: http://homeschoolpop.com

Thanks for learning with us today! We hope to see you next video!

Homeschool Pop Team

Lesson 15. Comparing Numbers from 0 to 9 | Grade Kindergarten | Math For Kids
Watch more lessons at: https://bitly.com.vn/dqlw27
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In this lesson, kids will learn to compare numbers using the number line introduced in lesson 13. Kids will be introduced to the idea that:
• On the number line, a number to the right is greater than a number to the left
• And, a number to the left is less than a number to the right.
As a result, kids will be able to make number comparisons given a pair of numbers and the number line. Learning to compare numbers using the number line helps kids develop number sense, which allows kids to confidently work with numbers.

Orientação de como acessar a conta da sua instituição pela plataforma do Google for Education

A,B,C,D... which answer is most common on multiple choice questions? Is the old advice to "go with C when in doubt" actually true?

In this video, I'll reveal the answer. Additionally, we'll go over five useful strategies you can use to improve your performance on these types of questions - whether they're on your ACT/SAT/GCSE exams or just on a pop quiz.

Need more test tactics? Check out The Ultimate Guide to Acing your Final Exams:

https://collegeinfogeek.com/fi....nal-exams-ultimate-g

My book "10 Steps to Earning Awesome Grades" is completely free, so check it out if you're interested in improving your grades!

http://collegeinfogeek.com/get-better-grades/

----------

Videos you might want to watch next:

Confidence Tracking: A Brain Hack for Your Exams - https://www.youtube.com/watch?v=USkDbcGPKP0&list=PLx65qkgCWNJIgq1Mj0rtsthmpqDGFL8Yn

How to Stop Making Dumb Mistakes on Exams - https://www.youtube.com/watch?v=OY6Z8gNKp-w&list=PLx65qkgCWNJIgq1Mj0rtsthmpqDGFL8Yn

----------

If you want to get even more strategies and tips on becoming a more productive, successful student, subscribe to my channel right here:

http://buff.ly/1vQP5ar

This week's podcast episode - How to Build Your Vocabulary:

https://collegeinfogeek.com/build-your-vocabulary/

Twitter ➔ https://twitter.com/tomfrankly
Instagram ➔ https://instagram.com/tomfrankly

~ created by Thomas Frank

Music:

"The Catch" by MAESON: https://soundcloud.com/maeson-1/2-the-catch

"Nola by Broke" for Free: http://brokeforfree.com/

Graphics: https://paper.dropbox.com/doc/....078-Multiple-Choice-

#basicsentencesforgrade1
#readingenglishgrade1
#readingenglishkinder
#readingenglishsentences
#practicereadingenglish
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#TeacherAyasreadinglesson

This reading lesson will help kids develop their reading skills. Kids are expected to become fast readers and comprehend different English words throughout this reading lesson.
#ReadingLessonForBeginners
#ReadingTutorialforBeginners
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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/algebra/x2f8bb115

We've learned about order of operations and combining like terms. Let's layer the distributive property on top of this.

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra/introduction-to-algebra/manipulating-expressions/e/combining_like_terms_2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Watch the next lesson: https://www.khanacademy.org/math/algebra/introduction-to-algebra/manipulating-expressions/v/distributive-property-with-rational-terms?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI

Missed the previous lesson?
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Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

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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Equivalence point when titrating a weak acid
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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.

For free. For everyone. Forever. #YouCanLearnAnything

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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/ma....th/old-ap-calculus-a

Stepping it up a notch, our solid is now defined in terms of two separate functions. Created by Sal Khan.

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-definite-integrals/ab-shell-method/e/volumes-of-solids-of-revolution-by-shells?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

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AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

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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