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a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . | how do i calculate the probablity of getting a royal flush in the game of poker ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | fair enough . how many 9 card hands are possible ? so let 's think about it . | how many triangles can be drawn by joining the vertices and centre of regular hexagon ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . | why is the part of the question : `` sorted however the layer chooses '' significant ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | we have 36 things . we chose 9 . so this numerator over here , this was 36 factorial . | there 's only one 9 of spades.. so how can we choose 9 of spade first in the first selection and then in the secend selection 9 of spade last ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | and this right here is called 36 choose 9 . and sometimes you 'll see this formula written like this , n choose k. and they 'll write the formula as equal to n factorial over n minus k factorial , and also in the denominator , k factorial . and this is a general formula that if you have n things , and you want to find ... | if we pick a spade , the probability of picking another spade increases , why do n't we have to worry about that affecting our result ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . | what is an undefined value ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | if we were thinking of these as two different hands , because we have the exact same cards , but they 're in different order , then what i just calculated would make a lot of sense , because we did it based on order . but they 're telling us that the cards can be sorted however the player chooses , so order does n't ma... | surely if the order does n't matter then one can include all numbers with and without order ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | we have 36 things . we chose 9 . so this numerator over here , this was 36 factorial . | it should be 9 cards numbered from 1-9 right ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | fair enough . how many 9 card hands are possible ? so let 's think about it . | then , after the 1st card is chosen , for the second card are n't we have 36-4=32 choices left ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | and then i have another . so then i have cards one , two , three , four , five , six , seven , eight . i have eight other cards . | i had a question on my statistics homework that neither myself or my teacher could figure out the correct answer to : how many combinations are possible when choosing a hand of five cards from a standard deck of cards consisting of four cards from one suit and one card from another suit ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | so at first we 'll say , well look , i have nine slots in my hand , right ? 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 . right ? | what is the probability of getting a multiple of 4 ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . | so what is the probability of a diamond flush ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | and then i have another . so then i have cards one , two , three , four , five , six , seven , eight . i have eight other cards . | what fraction of turns played on the machine will show five similar symbols in a row ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | we have 36 things . we chose 9 . so this numerator over here , this was 36 factorial . | why do i have to divide by 9 ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | so let 's think about it . there are 36 unique cards -- and i wo n't worry about , you know , there 's nine numbers in each suit , and there are four suits , 4 times 9 is 36 . but let 's just think of the cards as being 1 through 36 , and we 're going to pick nine of them . | by the way the question is asked would n't 4 be an acceptable answer meaning you can make 4 nine-card hands from 36 cards ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | we chose 9 . so this numerator over here , this was 36 factorial . but 36 factorial would go all the way down to 27 , 26 , 25 . it would just keep going . but we stopped only nine away from 36 . | what would be the factorial of a negative number ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | so you might want to say that there are 36 times 35 , times 34 , times 33 , times 32 , times 31 , times 30 , times 29 , times 28 possible hands . now , this would be true if order mattered . this would be true if i have card 15 here . | in terms of combinations vs permutations how do i decide whether a question takes into account order ( is it usually stated in the question ) ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | fair enough . how many 9 card hands are possible ? so let 's think about it . | what are the possible permutations of a , a , b , b in four slots ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | so we 're overcounting . we 're counting all of the different ways that the same number of cards can be arranged . so in order to not overcount , we have to divide this by the ways in which nine cards can be rearranged . | the number of ways of dividing 2p items into two equal groups of p each , groups having distinct identity ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | fair enough . how many 9 card hands are possible ? so let 's think about it . | how many different hands can one draw in a game of 7-card rummy ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | fair enough . how many 9 card hands are possible ? so let 's think about it . | how many unique combinations are possible for a word with 2 different letters repeating twice in the same word ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . | same question..if 3 cards were identical remaining 33 were unique..how does that change the answer ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | if we were thinking of these as two different hands , because we have the exact same cards , but they 're in different order , then what i just calculated would make a lot of sense , because we did it based on order . but they 're telling us that the cards can be sorted however the player chooses , so order does n't ma... | so you use permutations when order matters and combinations when order does n't matter ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | fair enough . how many 9 card hands are possible ? so let 's think about it . | just curious , does anyone know what the card game in the problem is ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | so this is 36 factorial , so this part right here , that part right there , is not just 36 factorial . it 's 36 factorial divided by 36 , minus 9 factorial . what is 36 minus 9 ? it 's 27 . | without simplifying 36*35*34*33 ... ... ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | every , i guess we could say , natural number less than 9 . this is called 9 factorial , and you express it as an exclamation mark . so if we want to think about all of the different ways that we can have all of the different combinations for hands , this is the number of hands if we cared about the order , but then we... | what exactly is the factorial exclamation point thingy ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | so we have to divide this by the way nine cards can be rearranged . so how many ways can nine cards be rearranged ? if i have nine cards and i 'm going to pick one of nine to be in the first slot , well , that means i have 9 ways to put something in the first slot . | are there actually 94143280 different ways to split the 9 cards ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . | what 's the difference between permutation and combination ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | if we were thinking of these as two different hands , because we have the exact same cards , but they 're in different order , then what i just calculated would make a lot of sense , because we did it based on order . but they 're telling us that the cards can be sorted however the player chooses , so order does n't ma... | i mean does the order in which the cards are grouped matter ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | and then for the third slot , 34 , and then it just keeps going . then 33 to pick from , 32 , 31 , 30 , 29 , and 28 . so you might want to say that there are 36 times 35 , times 34 , times 33 , times 32 , times 31 , times 30 , times 29 , times 28 possible hands . | what is the probability that the sum is 30 ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | and this right here is called 36 choose 9 . and sometimes you 'll see this formula written like this , n choose k. and they 'll write the formula as equal to n factorial over n minus k factorial , and also in the denominator , k factorial . and this is a general formula that if you have n things , and you want to find ... | is it possible to have n choose k if k is larger than n ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | so in order to not overcount , we have to divide this by the ways in which nine cards can be rearranged . so we have to divide this by the way nine cards can be rearranged . so how many ways can nine cards be rearranged ? if i have nine cards and i 'm going to pick one of nine to be in the first slot , well , that mean... | does n't it matter which way the cards were dealt , and how many people were playing ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | fair enough . how many 9 card hands are possible ? so let 's think about it . | how many permutations can you make that are odd numbers ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . | what do you do when you have a subtraction sign and addition sign ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . | why does parentheses also work as a multiplication sign ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | 5 times 5 is just 25 , so we get the same answer either way . this is using the distributive law of multiplication over subtraction , usually just referred to as the distributive property . this is evaluating the inside of the parentheses first and then multiplying by 5 . | when using the distributive property on a problem like 2 ( 4+b ) , would your answer be 8+2b or would it be 6b ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | 5 times 5 is just 25 , so we get the same answer either way . this is using the distributive law of multiplication over subtraction , usually just referred to as the distributive property . this is evaluating the inside of the parentheses first and then multiplying by 5 . | is it possible to have the distributive law of division over addition/subtraction/multiplication ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | 5 times 5 is just 25 , so we get the same answer either way . this is using the distributive law of multiplication over subtraction , usually just referred to as the distributive property . this is evaluating the inside of the parentheses first and then multiplying by 5 . | why when using the distributive law we have to multiply vs any of the other concepts ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | so we have 45 minus -- what 's 5 times 4 ? well , that 's 20 . 45 minus 20 , and that is equal to 25 , so this is using the distributive property right here . if we did n't want to use the distributive property , if we just wanted to evaluate what 's in the parentheses first , we would have gotten -- let 's go in this ... | would n't ( 45-20 ) be the real answer insted of 25 ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . you could just evaluate 9 minus 4 and then multiply that times 5 . | like is n't distrubitve property meaning only mutiple the numbers in the parenthiess only ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | so it 's 5 times 5 . 5 times 5 is just 25 , so we get the same answer either way . this is using the distributive law of multiplication over subtraction , usually just referred to as the distributive property . | what can be the way of finding the value of the variable is unknown ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . | what is the difference between pemdas and bodmas ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . you could just evaluate 9 minus 4 and then multiply that times 5 . | what happens if i do n't know a number ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | you multiply the 5 times the 9 and the 4 , so you end up with 5 times 9 minus 5 times 4 . notice , we distributed the 5 . we multiplied it times both the 9 and the 4 . | what would happen if the distributed number was a letter ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . | what was the simplified expression ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . | is ( a multiplication sign ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | 5 times 5 is just 25 , so we get the same answer either way . this is using the distributive law of multiplication over subtraction , usually just referred to as the distributive property . this is evaluating the inside of the parentheses first and then multiplying by 5 . | what is the point of using distributive property if you can just use pemdas ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | 45 minus 20 , and that is equal to 25 , so this is using the distributive property right here . if we did n't want to use the distributive property , if we just wanted to evaluate what 's in the parentheses first , we would have gotten -- let 's go in this direction -- 5 times -- what 's 9 minus 4 ? 9 minus 4 is 5 . | how would you use two digit numbers ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | you could just evaluate 9 minus 4 and then multiply that times 5 . but if you want to use the distributive property , you distribute the 5 . you multiply the 5 times the 9 and the 4 , so you end up with 5 times 9 minus 5 times 4 . | why did sal use the dot does that mean mulitpycation ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | you could just evaluate 9 minus 4 and then multiply that times 5 . but if you want to use the distributive property , you distribute the 5 . you multiply the 5 times the 9 and the 4 , so you end up with 5 times 9 minus 5 times 4 . | how do you use the distributive property when dealing with fractions ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . | why is the mutiplucation symble a dot not a `` x '' ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | if we did n't want to use the distributive property , if we just wanted to evaluate what 's in the parentheses first , we would have gotten -- let 's go in this direction -- 5 times -- what 's 9 minus 4 ? 9 minus 4 is 5 . let me do that in a different color . | when sal does 5 ( 9-4 ) why is n't a multiplication sighn next to the perenthasies ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | 5 times 5 is just 25 , so we get the same answer either way . this is using the distributive law of multiplication over subtraction , usually just referred to as the distributive property . this is evaluating the inside of the parentheses first and then multiplying by 5 . | what is the reason of the distributive law ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | you could just evaluate 9 minus 4 and then multiply that times 5 . but if you want to use the distributive property , you distribute the 5 . you multiply the 5 times the 9 and the 4 , so you end up with 5 times 9 minus 5 times 4 . | it what scenario would i ever want to use the distributive law of multication ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . | how many multiplication signs are there ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . | what does the question mean by simplify ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . | what if 3 variables are unknown ? |
rewrite the expression five times 9 minus 4 -- that 's in parentheses -- using the distributive law of multiplication over subtraction . then simplify . so let me just rewrite it . this is going to be 5 times 9 minus 4 , just like that . now , if we want to use the distributive property , well , you do n't have to . yo... | you could just evaluate 9 minus 4 and then multiply that times 5 . but if you want to use the distributive property , you distribute the 5 . you multiply the 5 times the 9 and the 4 , so you end up with 5 times 9 minus 5 times 4 . | also , what does `` distribute '' literally mean ? |
phobia is this extreme and unreasonable or irrational fear of something . that something can be anything from an animal to an inanimate object , to situations or activities . having a phobia is n't just your everyday worries , stress , or fears though . it 's not just being scared of a dark alley or being worried abou... | well , the answer to that is not really known . one thing that is known is you 're more likely to have a phobia if you have a family member with a phobia . another way someone might develop a phobia , though , is from specific bad experiences . | can a word be a phobia ? |
phobia is this extreme and unreasonable or irrational fear of something . that something can be anything from an animal to an inanimate object , to situations or activities . having a phobia is n't just your everyday worries , stress , or fears though . it 's not just being scared of a dark alley or being worried abou... | oftentimes they 're fearful of not being able to escape . someone might also have a fear of heights or falling which is acrophobia , or a fear of flying , aerophobia . and finally , you could be afraid of some natural phenomenon , too , like lightning , which is called astraphobia . | what 's the fear of parasites called ? |
phobia is this extreme and unreasonable or irrational fear of something . that something can be anything from an animal to an inanimate object , to situations or activities . having a phobia is n't just your everyday worries , stress , or fears though . it 's not just being scared of a dark alley or being worried abou... | oftentimes they 're fearful of not being able to escape . someone might also have a fear of heights or falling which is acrophobia , or a fear of flying , aerophobia . and finally , you could be afraid of some natural phenomenon , too , like lightning , which is called astraphobia . | is acrophobia ( fear of heights ) common ? |
phobia is this extreme and unreasonable or irrational fear of something . that something can be anything from an animal to an inanimate object , to situations or activities . having a phobia is n't just your everyday worries , stress , or fears though . it 's not just being scared of a dark alley or being worried abou... | for example , someone that suffered a severe bite by a rabid dog might develop cynophobia or fear of dogs . or even seeing someone else being very afraid of something could trigger a specific phobia . those that have a phobia will likely be diagnosed by a healthcare professional that asks specific questions about your ... | what is the phobia of being afraid of singing ? |
phobia is this extreme and unreasonable or irrational fear of something . that something can be anything from an animal to an inanimate object , to situations or activities . having a phobia is n't just your everyday worries , stress , or fears though . it 's not just being scared of a dark alley or being worried abou... | this might lead to physical symptoms like sweating , muscle control issues , or fast heart rates . even though certain things like spiders can cause anxiety with a lot of people , it 's super important to emphasize the difference between an everyday anxiety about something and a specific phobia . as an example , an eve... | anxiety disorder is same as phobia ? |
phobia is this extreme and unreasonable or irrational fear of something . that something can be anything from an animal to an inanimate object , to situations or activities . having a phobia is n't just your everyday worries , stress , or fears though . it 's not just being scared of a dark alley or being worried abou... | this avoidance might interfere with your social life and your relationship with your friends . obviously , a fear of moths is n't the only phobia , though . it 's not even in the top 10 . | how do people get a fear of moths ? |
phobia is this extreme and unreasonable or irrational fear of something . that something can be anything from an animal to an inanimate object , to situations or activities . having a phobia is n't just your everyday worries , stress , or fears though . it 's not just being scared of a dark alley or being worried abou... | it 's not even in the top 10 . anyway , some of the more common phobias are things like fear of blood , or hemophobia , as well as fears of medical procedures , especially things like injections and needles . there can also be fears of animals , though , especially snakes or ophidiophobia , dogs or cynophobia , and spi... | what is the name for the fear of sharp things ? |
phobia is this extreme and unreasonable or irrational fear of something . that something can be anything from an animal to an inanimate object , to situations or activities . having a phobia is n't just your everyday worries , stress , or fears though . it 's not just being scared of a dark alley or being worried abou... | oftentimes they 're fearful of not being able to escape . someone might also have a fear of heights or falling which is acrophobia , or a fear of flying , aerophobia . and finally , you could be afraid of some natural phenomenon , too , like lightning , which is called astraphobia . | if someone had a family member with a fear , would another family member develop a fear of the same thing , or is it possible to develop a fear of something else because a family member had a fear ? |
( piano playing ) dr. zucker : in the brancacci chapel in santa maria del carmine just to the left of masaccio 's great painting the tribute of money is another painting by masaccio , the expulsion from eden . dr. harris : the fresco 's in this chapel all tell the story of the life of st. peter except for the expulsion... | dr. harris : it makes christ 's coming necessary to redeem us , but it also makes necessary the church that st. peter found . sometimes mary and christ are seen as the second adam and eve . adam and eve who caused the fall into sin and mary and christ who make possible salvation . dr. zucker : that idea is something th... | why does eve make an effort to 'cover ' herself , but adam only covers his face ? |
( piano playing ) dr. zucker : in the brancacci chapel in santa maria del carmine just to the left of masaccio 's great painting the tribute of money is another painting by masaccio , the expulsion from eden . dr. harris : the fresco 's in this chapel all tell the story of the life of st. peter except for the expulsion... | there is a physicality here , there 's a sense of weight and there 's a sense of musculature that i ca n't remember seeing in earlier painting . dr. harris : masaccio 's employing modeling very clearly from light to dark . he 's so interested in modeling because that 's what makes the forms appear three dimensional and... | what is `` modeling '' ? |
( piano playing ) dr. zucker : in the brancacci chapel in santa maria del carmine just to the left of masaccio 's great painting the tribute of money is another painting by masaccio , the expulsion from eden . dr. harris : the fresco 's in this chapel all tell the story of the life of st. peter except for the expulsion... | adam and eve who caused the fall into sin and mary and christ who make possible salvation . dr. zucker : that idea is something that everybody in this church would be familiar with . i love the architecture on the extreme left , the gate of heaven itself , that they 've just left , reminds me of the indebtedness that m... | since many people were illiterate during this period , would these paintings have been considered a tool to help people grasp what they have leaned orally ? |
( piano playing ) dr. zucker : in the brancacci chapel in santa maria del carmine just to the left of masaccio 's great painting the tribute of money is another painting by masaccio , the expulsion from eden . dr. harris : the fresco 's in this chapel all tell the story of the life of st. peter except for the expulsion... | one is that you can really see the giornata . you can see that adam was painted separately from eve and you can see the darker blue and back of adam that really highlight those different patches of plaster . dr. harris : those were not differentiatable in the 15th century . | why is there a different shade around adam and eve ? |
( piano playing ) dr. zucker : in the brancacci chapel in santa maria del carmine just to the left of masaccio 's great painting the tribute of money is another painting by masaccio , the expulsion from eden . dr. harris : the fresco 's in this chapel all tell the story of the life of st. peter except for the expulsion... | dr. zucker : they are , they 're moving forward . dr. harris : masaccio is first artist in a very long time to attempt to paint the human body naturalistically . dr. zucker : yup . | did the artist intend that ? |
( piano playing ) dr. zucker : in the brancacci chapel in santa maria del carmine just to the left of masaccio 's great painting the tribute of money is another painting by masaccio , the expulsion from eden . dr. harris : the fresco 's in this chapel all tell the story of the life of st. peter except for the expulsion... | dr. zucker : right , no that 's changed over time . dr. harris : by giornata you mean that the different days , the different parts of the fresco were painted in ? dr. zucker : right , giornata means a days work . | does oxidized silver remain silver or does oxidation convert it to a different element ? |
( piano playing ) dr. zucker : in the brancacci chapel in santa maria del carmine just to the left of masaccio 's great painting the tribute of money is another painting by masaccio , the expulsion from eden . dr. harris : the fresco 's in this chapel all tell the story of the life of st. peter except for the expulsion... | dr. harris : by giornata you mean that the different days , the different parts of the fresco were painted in ? dr. zucker : right , giornata means a days work . dr. harris : this is buon fresco , which means that it was painted onto wet plaster and so an artist could only do a small section at a time because the plast... | why would n't masaccio do a better job of hiding the seams of the giornata around the contours of the figures instead of so obvious a halo surrounding them ? |
( piano playing ) dr. zucker : in the brancacci chapel in santa maria del carmine just to the left of masaccio 's great painting the tribute of money is another painting by masaccio , the expulsion from eden . dr. harris : the fresco 's in this chapel all tell the story of the life of st. peter except for the expulsion... | his body is exposed to us and actually that 's interesting . this whole chapel was fairly recently cleaned and for a very long time there was a vine that covered up his genitals . dr. harris : that someone had painted over it . | why was the nudity covered up ? |
( jazzy music ) male : impressionism is so often painting of modern life , of activities that we engage in now . female : things that we do every day . we go to cafes . we go to performances . we sit in bars , we have a drink . we stroll down the boulevards . this is the stuff of modern life and the stuff of impression... | male : in fact , art historians think that perhaps the woman who 's seated is mary cassatt 's sister , lydia . female : degas and mary cassatt were friends for 40 years and degas actually was the one who suggested that mary cassatt exhibit with the impressionist group , which she did . she was the only american to do s... | why is it that monet , picasso , degas , and van gogh are artists that everybody knows something about but artists like mary cassat , winslow homer , casper david friedrich , and rosa bonheur are just as good but less well known ( i for one had n't heard of any of them til i watched these ) ? |
( jazzy music ) male : impressionism is so often painting of modern life , of activities that we engage in now . female : things that we do every day . we go to cafes . we go to performances . we sit in bars , we have a drink . we stroll down the boulevards . this is the stuff of modern life and the stuff of impression... | ( jazzy music ) male : impressionism is so often painting of modern life , of activities that we engage in now . female : things that we do every day . | what causes an artist to become famous ? |
( jazzy music ) male : impressionism is so often painting of modern life , of activities that we engage in now . female : things that we do every day . we go to cafes . we go to performances . we sit in bars , we have a drink . we stroll down the boulevards . this is the stuff of modern life and the stuff of impression... | male : this is a painting that 's in some ways about the way we read the visual . it 's a painting about seeing . the subject is somebody looking at art as we , the viewers in the museum , are looking at art , so there 's this perfect replication . | what is the name of that painting ? |
( jazzy music ) male : impressionism is so often painting of modern life , of activities that we engage in now . female : things that we do every day . we go to cafes . we go to performances . we sit in bars , we have a drink . we stroll down the boulevards . this is the stuff of modern life and the stuff of impression... | ( jazzy music ) male : impressionism is so often painting of modern life , of activities that we engage in now . female : things that we do every day . | i may be jumping the gun here , but has the term `` impressionism '' come about by the time this painting was painted ? |
alright , so we left off with the battle of gettysburg , from july 1st to 3rd , 1863 . and as i mentioned in the last video , gettysburg was a really significant battle in the civil war . it was a real turning point for the civil war , at which lee brought the forces of the south up into the north for a second attempt... | and remember that , after the battle , lee is kinda fleeing for the life of his army . and not too long after that , meade pursues him . so the armies make kind of an incredible mess , and then they take off , leaving this tiny town of gettysburg , which has i think about 2,500 people , to deal with 50,000 casualties . | why did meade remain so passive at such a crucial moment ? |
alright , so we left off with the battle of gettysburg , from july 1st to 3rd , 1863 . and as i mentioned in the last video , gettysburg was a really significant battle in the civil war . it was a real turning point for the civil war , at which lee brought the forces of the south up into the north for a second attempt... | alright , so we left off with the battle of gettysburg , from july 1st to 3rd , 1863 . and as i mentioned in the last video , gettysburg was a really significant battle in the civil war . it was a real turning point for the civil war , at which lee brought the forces of the south up into the north for a second attempt... | do we have a `` fog of war '' moment with inadequate intelligence ? |
alright , so we left off with the battle of gettysburg , from july 1st to 3rd , 1863 . and as i mentioned in the last video , gettysburg was a really significant battle in the civil war . it was a real turning point for the civil war , at which lee brought the forces of the south up into the north for a second attempt... | and it 's extremely short , it 's only 272 words . now lincoln delivered the gettysburg address , on november 19th , 1863 . so it 's about three and a half months after the battle of gettysburg . | kim describes the individuals in the photograph taken at gettysburg on november 19 , 1863. who is the tall , bearded man in the top hat to the left of lincoln ( to the right of the viewer of the photograph ) ? |
alright , so we left off with the battle of gettysburg , from july 1st to 3rd , 1863 . and as i mentioned in the last video , gettysburg was a really significant battle in the civil war . it was a real turning point for the civil war , at which lee brought the forces of the south up into the north for a second attempt... | so the armies make kind of an incredible mess , and then they take off , leaving this tiny town of gettysburg , which has i think about 2,500 people , to deal with 50,000 casualties . so men who are dead , or wounded , maybe missing in action somewhere . and they really just do n't have the capacity for it , so the gov... | is there something that says somewhere that `` when you join the union , there is no way out , and if you try to we will fight you to the death until you give up and remain part of the union ... '' , perhaps in the constitution or otherwise ? |
alright , so we left off with the battle of gettysburg , from july 1st to 3rd , 1863 . and as i mentioned in the last video , gettysburg was a really significant battle in the civil war . it was a real turning point for the civil war , at which lee brought the forces of the south up into the north for a second attempt... | so gettysburg was this tremendously destructive battle with 50,000 casualties . and remember that , after the battle , lee is kinda fleeing for the life of his army . and not too long after that , meade pursues him . | but how did these leaders ( and the other important union and confederate army leaders ) relate in position and time to each other ? |
alright , so we left off with the battle of gettysburg , from july 1st to 3rd , 1863 . and as i mentioned in the last video , gettysburg was a really significant battle in the civil war . it was a real turning point for the civil war , at which lee brought the forces of the south up into the north for a second attempt... | that 's cuz he worked really hard at it . so we 're fairly certain , that lincoln spent some time drafting the gettysburg address in the white house , long before he left . so , the day arrives , november 19th , 1863 , and everett gets set up in a tent , cuz he 's the real headliner of the day . | were there any slave-owners in the crowd at the time ? |
: hi sal . : hey britt . : how are you ? : good , looks like we have a game going on here . : not a game . yeah , kind of a challenge question for you . what i did is , i put 1 grain of rice in the first square . : that 's right . : there 's 64 squares on the board . : yup . : and in each consecutive square i ... | : what if we just went , you know , 4 steps ahead . how much rice would be here ? :4 steps ahead , so we 're going to multiple by 2 , then multiple by 2 again , then multiply by 2 again , the multiply by 2 again . | can anybody tell me how many actual grains of rice would be on the last ? |
: hi sal . : hey britt . : how are you ? : good , looks like we have a game going on here . : not a game . yeah , kind of a challenge question for you . what i did is , i put 1 grain of rice in the first square . : that 's right . : there 's 64 squares on the board . : yup . : and in each consecutive square i ... | : this is , this is interesting . this is also why when i look at a tree there 's thousands of leaves but just 1 trunk . and when you actually go up and you look inside the tree it only branches 3 or 4 times . : and that shows the power of exponential growth . | if a tree that splits twice is a binary tree , what is a tree that splits four times ? |
: hi sal . : hey britt . : how are you ? : good , looks like we have a game going on here . : not a game . yeah , kind of a challenge question for you . what i did is , i put 1 grain of rice in the first square . : that 's right . : there 's 64 squares on the board . : yup . : and in each consecutive square i ... | : well i guess why not ? it 's different . it 's not going to be 2 anymore . | are exponents the same as indices or is it completely different ? |
: hi sal . : hey britt . : how are you ? : good , looks like we have a game going on here . : not a game . yeah , kind of a challenge question for you . what i did is , i put 1 grain of rice in the first square . : that 's right . : there 's 64 squares on the board . : yup . : and in each consecutive square i ... | and actually , it would be neat if there was a notation for that . : i did n't count this one out but it is the size of mount everest , the pile of rice . and it would feed 485 trillion people . | why when i think of a mount everest sized mound of rice , it feels impossible ? |
: hi sal . : hey britt . : how are you ? : good , looks like we have a game going on here . : not a game . yeah , kind of a challenge question for you . what i did is , i put 1 grain of rice in the first square . : that 's right . : there 's 64 squares on the board . : yup . : and in each consecutive square i ... | : yeah , well , i mean , this one , the one you were making , right , every time you were kind of adding these popsicle sticks , you 're kind of branching out . 1 popsicle stick now becomes 2 popsicles sticks . then you keep doing that . | so the grains of rice and the game broad and the popsicle sticks all are divided by two ... 246810 ? |
: hi sal . : hey britt . : how are you ? : good , looks like we have a game going on here . : not a game . yeah , kind of a challenge question for you . what i did is , i put 1 grain of rice in the first square . : that 's right . : there 's 64 squares on the board . : yup . : and in each consecutive square i ... | : yeah , well , i mean , this one , the one you were making , right , every time you were kind of adding these popsicle sticks , you 're kind of branching out . 1 popsicle stick now becomes 2 popsicles sticks . then you keep doing that . | what is the point of the rice and popsicle sticks ? |
: hi sal . : hey britt . : how are you ? : good , looks like we have a game going on here . : not a game . yeah , kind of a challenge question for you . what i did is , i put 1 grain of rice in the first square . : that 's right . : there 's 64 squares on the board . : yup . : and in each consecutive square i ... | and actually , it would be neat if there was a notation for that . : i did n't count this one out but it is the size of mount everest , the pile of rice . and it would feed 485 trillion people . | is n't mount everest too much for the pile of rice which is 2^63 ? |
: hi sal . : hey britt . : how are you ? : good , looks like we have a game going on here . : not a game . yeah , kind of a challenge question for you . what i did is , i put 1 grain of rice in the first square . : that 's right . : there 's 64 squares on the board . : yup . : and in each consecutive square i ... | 1 popsicle stick becomes 2 but now you have 2 of them . so here you have 1 , now you have 1 times 2 . now each of these 2 branch into 2 , so now you have 2 times 2 , or you have 4 popsicle sticks . | does any number to the 0 power equal 1 ? |
: hi sal . : hey britt . : how are you ? : good , looks like we have a game going on here . : not a game . yeah , kind of a challenge question for you . what i did is , i put 1 grain of rice in the first square . : that 's right . : there 's 64 squares on the board . : yup . : and in each consecutive square i ... | 1 popsicle stick becomes 2 but now you have 2 of them . so here you have 1 , now you have 1 times 2 . now each of these 2 branch into 2 , so now you have 2 times 2 , or you have 4 popsicle sticks . | i have to ask is it possible to divide a number by 1 ? |
: hi sal . : hey britt . : how are you ? : good , looks like we have a game going on here . : not a game . yeah , kind of a challenge question for you . what i did is , i put 1 grain of rice in the first square . : that 's right . : there 's 64 squares on the board . : yup . : and in each consecutive square i ... | 1 times 2 times 2 times 2 , which is 8 . this is 2 to the third power . : when i see 2 to the power of something , let 's just say n. n could also be number of steps up this tree . | what is four squared to the 3rd power ? |
: hi sal . : hey britt . : how are you ? : good , looks like we have a game going on here . : not a game . yeah , kind of a challenge question for you . what i did is , i put 1 grain of rice in the first square . : that 's right . : there 's 64 squares on the board . : yup . : and in each consecutive square i ... | so that is , take 63 , 2 's and multiply them all together . : this is the first square on our board . we have 1 grain of rice . | what would be the amount on the first square on the back of the board ? |
: hi sal . : hey britt . : how are you ? : good , looks like we have a game going on here . : not a game . yeah , kind of a challenge question for you . what i did is , i put 1 grain of rice in the first square . : that 's right . : there 's 64 squares on the board . : yup . : and in each consecutive square i ... | 9 , 2 's . 10 , 11 , 12 , 13 . so all of this stuff multiplied together . | why does a tree appear ? |
: hi sal . : hey britt . : how are you ? : good , looks like we have a game going on here . : not a game . yeah , kind of a challenge question for you . what i did is , i put 1 grain of rice in the first square . : that 's right . : there 's 64 squares on the board . : yup . : and in each consecutive square i ... | : hi sal . : hey britt . | what kind of drawing program does sal use ? |
: hi sal . : hey britt . : how are you ? : good , looks like we have a game going on here . : not a game . yeah , kind of a challenge question for you . what i did is , i put 1 grain of rice in the first square . : that 's right . : there 's 64 squares on the board . : yup . : and in each consecutive square i ... | : yeah , they have things to do . they have to go home and count grains of rice . : right . | how many grains of rice be on the chessboard if they finish putting all the rice ? |
: hi sal . : hey britt . : how are you ? : good , looks like we have a game going on here . : not a game . yeah , kind of a challenge question for you . what i did is , i put 1 grain of rice in the first square . : that 's right . : there 's 64 squares on the board . : yup . : and in each consecutive square i ... | : yeah , they have things to do . they have to go home and count grains of rice . : right . | how many grains of rice be on the chessboard if they finish putting all the rice ? |
: hi sal . : hey britt . : how are you ? : good , looks like we have a game going on here . : not a game . yeah , kind of a challenge question for you . what i did is , i put 1 grain of rice in the first square . : that 's right . : there 's 64 squares on the board . : yup . : and in each consecutive square i ... | : and that 's what we have here . 1 times 2 times 2 times 2 , which is 8 . this is 2 to the third power . : when i see 2 to the power of something , let 's just say n. n could also be number of steps up this tree . i could think about it that way . | why could n't of they just stop after sal wrote 2 to the power of 63 ? |
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