A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1),
2 answers:
Answer: 1 (certain)
Step-by-step explanation:
Given : A single die is rolled twice.
The set of 36 equally likely outcomes is
{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}.
We can see that the maximum sum of two numbers on dice is 12 .
So the number of pairs that make sum less than 13 = 36
Now, the probability of getting two numbers whose sum is less than 13 will be :-
Hence, the probability of getting two numbers whose sum is less than 13 is 1 ( certain event)
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From your equation, you can see that you have a difference of two cubes (aka two cubes being subtracted): 64, which is 
, and 
.
There is rule for the difference of two cubes:
The difference of two cubes is equal to the difference of the cube roots times a binomial, which is the sum of the squares of the roots plus the product of the roots.
That sounds pretty confusing, but it's much easier to understand when put mathematically. Let's say our two cubes are
and 
. The difference of those two cubes is:
In our problem, a = 4 (since = 64) and b = y (since 
. Plug these values into the rule to find the factor of 
:
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Answer:
There is rule for the difference of two cubes:
The difference of two cubes is equal to the difference of the cube roots times a binomial, which is the sum of the squares of the roots plus the product of the roots.
That sounds pretty confusing, but it's much easier to understand when put mathematically. Let's say our two cubes are
In our problem, a = 4 (since
-----
Answer: