Відео

I suggest to speak less slow and less ok,

do not just read it, explain it !

Lovely vibes ❤

Very clear explanation!

what is the meaning of "W"" on the Table ?

what is the meaning of "W"" on the Table ?

so sir i can use this video to our may lesson.. if ok to you ??

Hi Chard, I was wondering if you could take a look at this transitivity proof and let me know whether or not it is valid: Prove the transitive property: If a|b and b|c, then a|c for all positive integers a,b,c. Let’s analyze our first given. We know that a|b. What does it mean for a to divide b? Let l be any positive integer. lℤ+. This means that a times some integer l equals b. Algebraically, we can say: al=b Manipulating this expression to solve for a, we find that: a=b/l Let’s analyze our second given: We know that b|c. What does it mean for b to divide c? Let m be any positive integer. mℤ+. This means that b times some integer m equals c. Algebraically, we can say: bm=c What are we trying to prove? We are trying to prove that a|c. What does it mean for a to divide c? Let n be any positive integer. nℤ+. This means that a times some integer n equals c. Algebraically, we can say: an=c We are trying to prove that a|c. We are trying to prove that an=c where n is some integer. This means we are trying to demonstrate that n=c/a is an integer. We have n=c/a. Recall that c=bm and a=b/l. Let’s replace c with bm. Let’s replace a with (b/l). n=(bm)/(b/l) We multiply bm by the reciprocal of (b/l). n=bm*(l/b) The bs here cancel, leaving us with: n=ml Recall that m is a positive integer. Recall that l is a positive integer. Positive integers are closed under multiplication. This means that the product of two positive integers yields a positive integer. Thus, n must be a positive integer. Since we have confirmed that n is a positive integer, we have confirm that a indeed divides c. Thank you so much :)

thanks you so much, You are a life saver.

ari amon sir

Sir u didnt explain it you are merely reading! I didnt understand your thoughts about it poh..

binabasa amp

Tagalugin mo nalang sir mukhang mas madali pa intindihin lol

Hi, I would like to ask about the W symbol in the Dwass-Steel-Critchlow-Fligner Test column. What does it stands for and what does it shows? Thank you.

❤

Just use paper and pencil.

Sir why r is taken positive always?

If you were so inclined, when subtracting a bigger number from a smaller number, could you make the difference all bar numbers and factor it out at the end? 25-40 is bar2 5 or bar1 bar5 or -15. 255-400 is bar2 5 5 or bar1 bar4 bar5 or -145.

Because the only divisor common to both n and (n+1) is 1, the sequence of prime numbers is unlimited. For example, pick any number greater than 1, say 15: 15+1= 16 (15×16)+1 = 241 (15×16×241)+1 = 57841... etc... 15, 16, 241, 57841 are the first four terms in an endless sequence. Each term has at least one prime number as a divisor but no two terms share the same prime divisor. This means the sequence of prime numbers is unlimited. We have a clever ancient Greek called Euclid to thank for this line of reasoning.

i really like your video s thumbnail

Hoping your channel blows up!

Thank you for the vid. I'm gonna use it for the PMO.

Lovely explanation, Thank you

very beautifully explained ❤ your teaching is easy to understand😊

thank you poew sir omg omgg , paano nman po pag interpret nang data? or result ?

ayon omgg

omggg i hope this can help me poew huhuuuhuh

2Q

Thank you sir. Many people get the following question wrong, so please explain. [Question] Find the probabilities that the following events will occur when two dice are rolled. ①Both show odd numbers ②One shows odd number and another shows evenn number ③Both show even number P(E):the probability that event E occurs. 【Distinguishable dice A and B】 (the number that dice A shows,the number dice B shows):event If we only judge whether the numbers indicated by the dice are odd or even, the following four events will occur. 　　(odd,odd) (odd,even) 　　(even,odd) (even,even) If each event occurs with equal probability, the probability is 1/4. Therefore, P(①)=1/4, P(②)=1/2, P(③)=1/4 (1) If we judge the number(1,2,···,6) indicated by the dice ,the following 36 events will occur. (1,1), (1,3),(1,5) (1,2),(1,4),(1,6) (3,1), (3,3),(3,5) (3,2),(3,4),(3,6) (5,1), (5,3),(5,5) (5,2),(5,4),(5,6) (2,1), (2,3),(2,5) (2,2),(2,4),(2,6) (4,1), (4,3),(4,5) (4,2),(4,4),(4,6) (6,1), (6,3),(6,5) (6,2),(6,4),(6,6) If each event occurs with equal probability, the probability is 1/36. Therfore P(①)=9×(1/36)=1/4, P(②)=18×(1/36)=1/2, P(③)=9×(1/36)=1/4 (2) (2) matches (1). 【Indistinguishable two dice】 (odd,even)is the same event as(even,odd). Thererore, if we only judge whether the numbers indicated by the dice are odd or even, the following three events will occur. 　　(odd,odd) 　　(even,odd) (even,even) If each event occurs with equal probability, the probability is 1/3. Therefore P(①)=1/3, P(②)=1/3, P(③)=1/3 (3) (1,3) is the same event as (3,1). If we judge the number(1,2,···,6) indicated by the dice ,the following 21 events will occur. (1,1) (3,1), (3,3) (5,1), (5,3),(5,5) (2,1), (2,3),(2,5) (2,2) (4,1), (4,3),(4,5) (4,2),(4,4) (6,1), (6,3),(6,5) (6,2),(6,4),(6,6) If each event occurs with equal probability, the probability is 1/21. Therefore P(①)=6×(1/21)=2/7, P(②)=9×(1/21)=3/7, P(③)=6×(1/21)=2/7 (4) (4) contradicts (3).

Thank you so much for this lecture sir! Now I understand on how to name the tesselations

Hi, I am wondering what your thoughts are on the origins of math in pre-history? We know about the math in the third millennium BC Egypt, but it was developed enough at that time that it surely had earlier origins. What earlier evidence of math is there? I know that there have been discovered animal bones with series of human made notches that likely represent counting that are from 12,000 to 40,000 years old.

I really like your video

Thank you so much po Sir! Very helpful 🤍🤍

Good evening po sir pwedi po ba maka hingi ng ppt mo sa nano world ☺

yay finally. thank you po. super helpful and i can easily understand it

Thank you so much sir 👍

Hello po, Sir Aye! May I request your permission po to let me use your video about Egyptian Arithmetic? I'll incorporate it po sana into my MMW presentation.

This will be my report tomorrow,thank you🥺❤️

nice

NICE

Very nice!

Informative and nice!

Naysu❤

What a nice video

Naysu❤

Naysu❤️

Nice

Wow

Thank u sir❤

VERY HELPFUL THANKS SIR]