Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/complex_num_precalc/e/the-imaginary-unit-and-complex-numbers?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

Watch the next lesson: https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/complex_num_precalc/v/plotting-complex-numbers-on-the-complex-plane?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

Missed the previous lesson?
https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/i_precalc/v/i-as-the-principal-root-of-1-a-little-technical?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus

Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!

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

Subscribe to Khan Academy’s Precalculus channel:
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The distinctive feature of the Italian Army in World War Two was its poor and insufficient armament.
Even though weapons produced at the famous Italian arms factory Beretta were of the highest quality, the rest were known for their very low quality or obsolete nature.

Copyright: DO NOT translate and re-upload our content on Youtube or other social media.

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Credit:
Created by Daniel Turner

Narrator:

Chris Kane
https://vocalforge.com/

Music Credit:
Failing Defense by Kevin MacLeod is licensed under a Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/)
Source: http://incompetech.com/music/r....oyalty-free/index.ht
Artist: http://incompetech.com/

Sources:
Bishop, Chris. The Encyclopedia of Weapons of World War II, 1998
Hogg, Ian. Encyclopedia of Infantry Weapons of World War II, 1986
Weeks, John. World War II Small Arms, 1989
Jowett, Phillip. The Italian Army 1940–45 (1): Europe 1940–43. 2000

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Copyright: DO NOT translate and re-upload our content on Youtube or other social media.

Today around 250,000 veterans are still disabled by a mysterious disease known as Gulf War Syndrome, a medical anomaly with a distinctive set of symptoms that strangely only affects soldiers who served in the 1991 Persian Gulf War.
For decades the causes of this peculiar chronic illness baffled and divided scientists, as they debated whether the malady had a psychological or biological explanation, and it is only recently, over 30 years after the end of the conflict, that some of them have claimed to have found a definitive answer.


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Created by Daniel Turner (B.A. (Hons) in History, University College London)

Narrator:

Chris Kane
https://vocalforge.com/

Learn history online by signing up for a free 7-day trial at http://www.americanhighschool.org

The 369th Infantry Regiment was constituted on 2nd June 1913 in the New York Army National Guard as the 15th New York Infantry Regiment. And would become known as the first ‘African-American regiment’ to serve with the American Expeditionary Forces during World War I.

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https://ckvox.com/

Artwork:
Daniel turner

Direction, Animation:
Daniel Turner

Music:

'The Descent',"Prelude and Action"

by Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0 License
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Credit:
Created by Daniel Turner

script:
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Narrator:

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www.vocalforge.com


Music Credit

Epic Battle Speech - Wayne Jones

This video provides a basic introduction into the top 10 most important formulas used in excel. These include the average function, autosum, Sum If, Count, Counta, Count If function, Concantenate, If logical function, Vlookup, and Drop Down Lists.

Excel Tutorial For Beginners:
https://www.youtube.com/watch?v=nK-uNYuvcag

Top 30 Excel Tips & Shortcuts:
https://www.youtube.com/watch?v=UMad9_-4rOU

_________________________________________
Excel - Statistics - Mean, Median, Mode:
https://www.youtube.com/watch?v=aRR86imVsxM

Excel Scatter Charts:
https://www.youtube.com/watch?v=hwqq0HYrers

Excel - Finding Slope & Y-Intercept:
https://www.youtube.com/watch?v=KwQsV77bYDY

Solving Polynomial Equations - Goal Seek:
https://www.youtube.com/watch?v=lomAl6XB_SM

__________________________________________
How To Calculate Loan Payments In Excel:
https://www.youtube.com/watch?v=ifbNN2SoKlk

How To Create an Amortization Table:
https://www.youtube.com/watch?v=QZfMW203v4U

How To Look Up Customer Data In Excel:
https://www.youtube.com/watch?v=HDda6ny40ZM

How To Create a Data Entry Form In Excel:
https://www.youtube.com/watch?v=_tZLGBgQCYo

_________________________________________
YouTube Channel Growth Accelerator:
https://vimeo.com/ondemand/youtubeaccelerator

Algebra For Beginners:
https://www.video-tutor.net/al....gebra-for-beginners-

Final Exams and Video Playlists:
https://www.video-tutor.net/

Full-Length Math & Science Videos:
https://www.patreon.com/mathsc....iencetutor/collectio

This precalculus video tutorial provides a basic introduction into multiplying matrices. It explains how to tell if you can multiply two matrices together and how to determine the order of the new matrix. The order of the new matrix is based on the rows of the first matrix and the number of columns in the second matrix. To multiply two matrices together, multiply the rows of the first matrix by the columns of the second matrix and find the sum of the products. This video contains plenty of examples and practice problems on matrix multiplication.

Introduction to Matrices:
https://www.youtube.com/watch?v=yRwQ7A6jVLk

Adding and Subtracting Matrices:
https://www.youtube.com/watch?v=QXUbFzEd3Ww

Scalar Multiplication of Matrices:
https://www.youtube.com/watch?v=iJERwUVuwtY

Solving Matrix Equations:
https://www.youtube.com/watch?v=UHhvcj0doaA

Multiplying Matrices:
https://www.youtube.com/watch?v=vzt9c7iWPxs

__________________________________
Gaussian Elimination & Row Echelon Form:
https://www.youtube.com/watch?v=eDb6iugi6Uk

Gauss Jordan Elimination:
https://www.youtube.com/watch?v=eYSASx8_nyg

Gaussian Elimination With 4 Variables:
https://www.youtube.com/watch?v=4VAXv6yRULU

Inverse of a 2x2 Matrix:
https://www.youtube.com/watch?v=aiBgjz5xbyg

Inverse of a 3x3 Matrix:
https://www.youtube.com/watch?v=Fg7_mv3izR0

__________________________________
Determinant of 2x2 and 3x3 Matrix:
https://www.youtube.com/watch?v=3ROzG6n4yMc

Determinant of 4x4 Matrix:
https://www.youtube.com/watch?v=fWzUwrt1Z0s

Cramer's Rule - 2x2 Linear System:
https://www.youtube.com/watch?v=vXqlIOX2itM

Cramer's Rule - 3x3 Linear System:
https://www.youtube.com/watch?v=Ot87qLTODdQ

___________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/

Full-Length Videos and Worksheets:
https://www.patreon.com/MathSc....ienceTutor/collectio

This Calculus 2 video tutorial explains how to find the area of a polar curve in polar coordinates. It provides resources on how to graph a polar equation and how to find the area of the shaded region. It contains plenty of examples and practice problems on how to find the area of one loop or of one petal and how to find the area of the inner loop as well.

Area of Parametric Curves: https://www.youtube.com/watch?v=riEx7TcLfzk

Area of Polar Curves:
https://www.youtube.com/watch?v=GQ6cDvY8K9g

Area Between Polar Curves:
https://www.youtube.com/watch?v=TwKxDApaxVo

Arc Length of Polar Curves:
https://www.youtube.com/watch?v=bxswSV1utxg

Surface Area of Polar Curves:
https://www.youtube.com/watch?v=n-Zg7WgRzjA

_____________________________
Writing Equations of Ellipses:
https://www.youtube.com/watch?v=OPSCKXXvWiM

Eccentricity of an Ellipse:
https://www.youtube.com/watch?v=9hyQksn80ug

Area of an Ellipse:
https://www.youtube.com/watch?v=Mw3MeDLL8d4

Circumference of an Ellipse:
https://www.youtube.com/watch?v=r5pl_stL4c0

Hyperbolas - Conic Sections:
https://www.youtube.com/watch?v=Iu-4-fizlD4

______________________________
Parabolas - Conic Sections:
https://www.youtube.com/watch?v=KYgmOTLbuqE

Polar Equations of Conic Sections:
https://www.youtube.com/watch?v=rnvCG_BZcL4

Calculus 3 - Intro to Vectors:
https://www.youtube.com/watch?v=2_21erD-nBg

Final Exams and Video Playlists:
https://www.video-tutor.net/

Full-Length Videos and Worksheets:
https://www.patreon.com/MathSc....ienceTutor/collectio

This calculus video tutorial provides a basic introduction into the quotient rule for derivatives. It explains how to find the derivatives of fractions and rational functions.

Derivatives - Fast Review: https://www.youtube.com/watch?v=5yfh5cf4-0w&t=1s

Equation of the Tangent Line:
https://www.youtube.com/watch?v=5NyeGzbBJQM

Simplifying Derivatives:
https://www.youtube.com/watch?v=3lUOtjkqfQo

Derivatives - The Product Rule - f*g:
https://www.youtube.com/watch?v=17X5g9QArTc

Derivatives - Triple Product Rule - f*g*h:
https://www.youtube.com/watch?v=cUXW9cj_CpE

Derivatives - Quadruple Product Rule - f*g*h*k:
https://www.youtube.com/watch?v=U8u0VGvFgV0

___________________________________
Derivatives - The Quotient Rule:
https://www.youtube.com/watch?v=8jVDEcQ0wXk

Derivatives - The Chain Rule:
https://www.youtube.com/watch?v=HaHsqDjWMLU

Chain Rule With Trig Functions:
https://www.youtube.com/watch?v=ZyWHTWJ2XpM

Chain Rule - Harder Examples:
https://www.youtube.com/watch?v=_1LTThkXvSw

Chain Rule - Triple SQRT(x):
https://www.youtube.com/watch?v=BTuGkPj7ymE

_________________________________
Derivatives - Composite Functions:
https://www.youtube.com/watch?v=vNXjMTv4vHs

Implicit Differentiation:
https://www.youtube.com/watch?v=xbviQHhU1rA

Derivatives - Inverse Trig Functions:
https://www.youtube.com/watch?v=KbYW9FDm-Zk

Derivatives - Exponential Functions:
https://www.youtube.com/watch?v=yg_497u6JnA

Derivatives - Logarithmic Functions:
https://www.youtube.com/watch?v=Dp9sgIvaKPk

___________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/

Full-Length Videos and Worksheets:
https://www.patreon.com/MathSc....ienceTutor/collectio

This organic chemistry video tutorial provides a basic introduction into mass spectrometry. It explains how to match the correct molecular fragments with the corresponding m/z peaks in the mass spectrum. It discusses the difference between the base peak and the parent peak.

Access The Full 38 Minute Video on Patreon:
https://www.patreon.com/MathScienceTutor

Direct Link to The Full Video on Patreon:
https://bit.ly/38cqkAF



Full 38 Minute Video on YouTube:
https://www.youtube.com/watch?v=euk2Tg1WBA8

Join My YouTube Membership Program:
https://www.youtube.com/channe....l/UCEWpbFLzoYGPfuWUM

This physics video tutorial explains the concept of the first law of thermodynamics. It shows you how to solve problems associated with PV diagrams, internal energy, heat, and work. It addition, it provides plenty of examples and practice problems associated with isothermal, isochoric or isovolumetric, isobaric, and adiabatic processes.

Open Vs Closed Vs Isolated System: https://www.youtube.com/watch?v=TFP6SvWPOQc

First Law of Thermodynamics:
https://www.youtube.com/watch?v=7Siv2NNCFag

Isobaric Process:
https://www.youtube.com/watch?v=BG-cUpnNmPM

Isochoric Process:
https://www.youtube.com/watch?v=SxfgHdfKjQA

Isothermal Process:
https://www.youtube.com/watch?v=m9h6qyWLscs

Internal Energy of an Ideal Gas:
https://www.youtube.com/watch?v=k3rJs_ioTHc

_________________________
Adiabatic Process:
https://www.youtube.com/watch?v=gaZmZjBtgAM

PV Diagrams:
https://www.youtube.com/watch?v=b-4U_s4e50o

2nd Law of Thermodynamics:
https://www.youtube.com/watch?v=DWiCaDPM7Hk

Heat Engines:
https://www.youtube.com/watch?v=O7TSo_up1Dw

Converting Heat Into Electricity:
https://www.youtube.com/watch?v=LX2cU27kUUc

________________________
Carnot Cycle:
https://www.youtube.com/watch?v=Qi3m9sD5w-A

Otto Cycle:
https://www.youtube.com/watch?v=vAeMmSRdQYY

Refrigerators and Heat Pumps:
https://www.youtube.com/watch?v=sKfgz6JLQRI

Entropy:
https://www.youtube.com/watch?v=Bdn3u2OHvKE

Heat Engines and Refrigerators Review:
https://www.youtube.com/watch?v=QBd2zraOe2k

Physics 1 Review:
https://www.video-tutor.net/ph....ysics-basic-introduc

Chemistry Review:
https://www.video-tutor.net/ch....emistry-basic-introd


Here is a list of topics:
1. First Law of Thermodynamics - Energy Transfer
2. Internal Energy, Heat, and Mechanical Work
3. System vs Surroundings
4. Sign Conventions for Q, Heat Absorbed vs Heat Energy Released
5. Work done on the system vs work done by the system
6. Positive Work - Gas Expansion vs Negative Work - Compression
7. Open System, Closed System and Isolated System
8. Isobaric Process - Constant Pressure
9. Work Done at Constant Pressure Formula / Equation
10. Units of Pressure - Converting atm to Pa
11. Units of Volume - m^3 and L conversion
12. Converting L and atm into Joules
13. PV Diagrams - Work Done = Area Under the Curve or Area of the Shaded Region
14. Cyclic Process, Q=W, Work is Positive for Clockwise Rotation and Negative for Counter Clockwise Direction
15. Ideal Gas Law, PV=nRT
16. Charles Law - Temperature and Volume Relationship
17. Converting Celsius to Kelvin Temperature
18. Heat Transferred During Isobaric Process Formula
19. Isochoric Process - Work Done is Zero
20. Isovolumetric Process - Constant Volume, Internal Energy, and Heat Transferred Equation
21. Thermodynamics Formula Sheet Summary
22. Molar Heat Capacity at Constant Pressure and Constant Volume
23. Monatomic Gases - He, Ne, and Ar - Helium, Neon, and Argon
24. Diatomic Gases - N2, O2, and H2
25. Cv and Cp values for ideal monatomic, diatomic and polyatomic gases
26. Gamma Ratio, Cp/Cv formula
27. Isochoric Process - Pressure and Temperature Formula
28. Combined Gas Law Equation
29. Isothermal Process - Constant Temperature
30. Work Done During an Isothermal Process - Natural Logarithms Derivation - Area under Curve
31. Boyle's Law - Pressure and Volume Relationship
32. Adiabatic Process - No Heat Transferred - Q=0
33. Adiabatic Expansion - Cooling Effect of an Ideal Gas
34. Adiabatic Compression - Increase in Temperature - No spark plugs needed in an internal combustion engine of this type
35. Work, Pressure, Volume and integration Formula, Calculus - Isothermal Process
36. Pressure and Volume Formula With Gamma Ratio
37. Temperature and Volume Equation With Gamma Ratio - Adiabatic Process
38. Internal Energy - State Function - Independent of Path
39. Work and Heat - Not a State Function, Path Dependent
40. PV diagram problems, work, heat, and internal energy calculations

This math video tutorial provides a basic introduction into the intersection of sets and union of sets as it relates to venn diagrams.

Translating Words to Algebraic Expressions: https://www.youtube.com/watch?v=QEnFIgN8UBw

Words to Equations - More Problems:
https://www.youtube.com/watch?v=VjPX-XlN7Ok

Consecutive Integers Word Problems:
https://www.youtube.com/watch?v=hPnoxAf60c0

Age Word Problems - Past, Present, Future:
https://www.youtube.com/watch?v=7x7Hl9ztYbk

Upstream and Downstream - Problems:
https://www.youtube.com/watch?v=nW9WDlcicxE

_______________________________________
Distance, Rate, & Time - Word Problems:
https://www.youtube.com/watch?v=r4ff6KjPKHE

Time and Work - Word Problems:
https://www.youtube.com/watch?v=zUE59CNlFsI

Acid Mixture Word Problems:
https://www.youtube.com/watch?v=e2FAAMlAJ3c

Percent Increase & Decrease Problems:
https://www.youtube.com/watch?v=T6-0MwmCpE8

Percentage Word Problems:
https://www.youtube.com/watch?v=kjpwBu6DmkM

________________________________________
Ratios and Proportions - Word Problems:
https://www.youtube.com/watch?v=JOZSFwuyqok

Ratios and Proportions - SAT Math:
https://www.youtube.com/watch?v=Y4fgwWEGQlg

Arithmetic Sequences - Word Problems:
https://www.youtube.com/watch?v=XZJdyPkCxuE

Venn Diagram - Word Problems:
https://www.youtube.com/watch?v=32iNIZJ2dI4

Probability With Marbles - Word Problems:
https://www.youtube.com/watch?v=UORztmWGY6Q

_______________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/

Full-Length Videos and Worksheets:
https://www.patreon.com/MathSc....ienceTutor/collectio

⁣Boost Your Child’s Learning with Kids Academy! 🌟
Are you a parent or educator seeking an engaging and effective learning app for kids? Look no further! Thousands of parents and educators are turning to Kids Academy, the app that makes real learning truly fun. Try it now with a 3-day FREE TRIAL1
How to Count Coins - Counting Coins Worksheets
In this captivating video from Kids Academy, a real teacher will guide your child through the world of coin values. Your little learner will recall different coins and their worth. Afterward, watch as the teacher counts the coins on the worksheet, matching them to the prices listed.
By watching this video, your child will enhance:
Mental Math and Addition Skills
Recollection and Ability to Add Using Money
Counting coins isn’t just about addition—it’s a practical skill that connects math to real-life scenarios! Use this video to give your child the practice needed for success in both math and life.
Counting Coins Worksheets for 1st, 2nd, and 3rd Grades
🌟 TalentedAndGifted 🌟 🌟 LearnWithKidsAcademy 🌟

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It's Kids Academy, and welcome back to our channel! In this video for kids you will see Rapunzel animated bedtime story. Rapunzel is one of the famous fairy tales by the Grimm Brothers. Rapunzel fairy tale was written and published in 1812 and is just two pages long, but it is one of the most loved and favored bed times stories ever. Kids can’t stop listening to the story about a beautiful girl.
Rapunzel who is locked in a high tower in the woods. A Witch comes to the tower and asks Rapunzel to let her beautiful long fair hair down, so the Witch can climb up and get to her.
Rapunzel is a very nice girl but she is very lonely in the tower, so she sings songs not to feel bored. Once a Prince hears Rapunzel singing songs with her sweet voice and sees how the Witch asks the girl to let her golden braids down. He decides to try his luck and asks Rapunzel to let her hair down for him. As soon as the Prince sees the girl he falls in love with her and makes plans to save her. His plan doesn’t work out however, as the Witch finds about it and she sends Rapunzel far into the woods and plans to kill the Prince. The Prince manages to escape but his eyes get wounded and he becomes blind.
Luckily, wandering through the woods the Prince hears the sweet voice and recognizes it. The Prince and Rapunzel meet each other and Rapunzel starts crying. Her tears touch Prince’s eyes and he can see again.
Your kids are sure to enjoy Rapunzel fairy tale and will be prone to listen to it again and again. The video by Kids Academy is a nice combination of real books reading and cartoon watching. It is a perfect way to listen and follow the pages of the animated book.
At some point kids will stars recognizing the words and it helps to develop not only narrative but also reading skills. This fairy tale is also professionally illustrated and kids will definitely enjoy the bright and colorful pictures.

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Learn how to skip count by 10 for kids. Toby can't fall asleep help him to count sheep.

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In this video, we will learn how to make fun and easy Easter craft for kids. Using simple materials like paper, glue, and paint, we will create an adorable Easter card. The step-by-step instructions are easy to follow and perfect for children of all ages.
So, let's get crafting and make some bunnies-citing Easter decorations!
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Do you already know how to count from 1 to 10? If yes, then this video for kids is definitely for you. Now together with us you know how to count from 1 to 10. And next you can learn numbers from 1 to 100, and then you will be able to count in the same way on your own. Join us, let's learn numbers and counting from 1 to 100 together.

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Learn to Read | Read Words In Order | Reading for Kids | Kids Academy

Reading forms a very important part of the child’s initial academics. It is also a very difficult lesson for kids and mostly it is seen that kids struggle with it. However, if it is made easy and everything is explained to the kid in an easy way this can also become a very easy and a very interesting lesson.

It is important for teachers and parents to know that each kid is different, and each kid takes a different amount of time to grasp a concept. Therefore, putting pressure on the kid will not help him/her to get any better.
Now how can you help the kid to read fluently? There are some simple tips and tricks that you can follow to make reading for preschool and kindergarten kids easy.

1. Practice makes a man perfect
Read with your kid as much as you can. Be patient and don’t expect the child to start reading just after a few readings. With more and more practice the kid will slowly start understanding the sounds and alphabets and how they are working together. Start with small words.

2. Don’t burden the child
It is important the kid does not feel too much pressurized. If you burden the kid with a new difficult word every day it would become very difficult for him/her to cope up with it. So, take things slowly let the kid get familiarized with some words and then move forward.

3. Read what the kid likes
It’s better than you read a storybook that the kid likes, it would create more interest in the child and he would be more curious to read and understand what his/her favorite characters are saying. It would enhance the learning process.

4. Encourage participation
Encourage the kid to participate in the process and read with you. Ask questions while reading for example if you are reading a story with a dog in it, every once in a while, ask ‘so where is the dog?’. This will keep the child attentive and also, they will be better able to identify individual words.

So, these are some of the best ways in which you can learn to read for kids


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Hickory Dickory Dock song is a freshly modified video version of the traditional rhyme for kids aged 4 and under. It mimics the sounds of a grandfather's clock ticking and chiming on the wall.
Originally the words ‘hickory’, ‘dickory’ and ‘dock’ meant ‘eight’, ‘nine’ and ‘ten’ in the Celtic language. These days this is number one rhyme for introducing the basics for time telling. Kids listen, repeat and sing the rhyme to learn to tell the times. Below you can find lyrics to Hickory Dickory Dock song.

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Lyrics:

Hickory dickory dock,
The mouse went up the clock.
The clock struck one,
The mouse went down,
Hickory dickory dock.
Hickory dickory dock,
The bear went up the clock.
The clock struck two,
The bear ran down,
Hickory dickory dock.
Hickory dickory dock,
The parrot went up the clock.
The clock struck three,
The parrot went down,
Hickory dickory dock.
Hickory dickory dock,
The monkey went up the clock.
The clock struck four,
The monkey went down,
Hickory dickory dock.
Hickory Dickory dock,
The pig went up the clock.
The clock struck five,
The pig went down,
Hickory dickory dock.
Hickory Dickory dock,
The elephant went up the clock.
The clock struck six,
The elephant went down,
Hickory Dickory dock.

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The video is an ideal resource to introduce and learn the names of animals for toddlers. They will learn animals in no time! Not only the rhyming song is a hundred percent fun and crowd-pleaser, but also a perfect time saver.

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