Factor the given expression. 64^3-343

63³-343 = 261801

Factor the following integer:

261'801

The sum of the digits of 261801 is 2 + 6 + 1 + 8 + 0 + 1 = 18, which is divisible by 9. This means 261801 is too.

261801 = 9×29089:

261801 = 9×29089

9 = 3^2:

261801 = 3^2×29089

Because 29089 is odd, only test odd numbers for divisibility.

29089 is not divisible by 3, 5, 7, 9, 11, 13, 15 or 17.

29089 = 19×1531 which means 29089 is divisible by 19:

261801 = 3^2×19×1531

3 is prime:

261801 = 3^2×19×1531

Because 19 is odd, only test odd numbers for divisibility.

19 is not divisible by 3.

Since 19 is not divisible by any integer up to 4, it is prime:

261801 = 3^2×19×1531

Because 1531 is odd, only test odd numbers for divisibility.

1531 is not divisible by 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37 or 39.

Since 1531 is not divisible by any integer up to 39, it is prime:

261801 = 3^2×19×1531

There are 2 copies of 3, 1 copy of 19 and 1 copy of 1531 in the product:

261801 = 3^2×19×1531

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560