Answer:
240
Step-by-step explanation:
The x^k term will be ...
(6Ck)(x^k)(4^(6-k))
For k=4, this is ...
(6C4)(x^4)(4^2) = 15·16·x^4 = 240x^4
The coefficient of x^4 is 240.
_____
nCk = n!/(k!(n-k)!)
Answer:
-1.428571429y
Step-by-step explanation:
add -10y to each side
We're told that
where the last fact is due to the law of total probability:
so that 
and 
are complementary.
By definition of conditional probability, we have
We make use of the addition rule and complementary probabilities to rewrite this as
![\implies P(B)-[1-P(A\cup B)^C]=[1-P(B)]-P(A\cup B^C)](https://tex.z-dn.net/?f=%5Cimplies%20P%28B%29-%5B1-P%28A%5Ccup%20B%29%5EC%5D%3D%5B1-P%28B%29%5D-P%28A%5Ccup%20B%5EC%29)
![\implies2P(B)=2-[P(A\cup B)^C+P(A\cup B^C)]](https://tex.z-dn.net/?f=%5Cimplies2P%28B%29%3D2-%5BP%28A%5Ccup%20B%29%5EC%2BP%28A%5Ccup%20B%5EC%29%5D)
![\implies2P(B)=[1-P(A\cup B)^C]+[1-P(A\cup B^C)]](https://tex.z-dn.net/?f=%5Cimplies2P%28B%29%3D%5B1-P%28A%5Ccup%20B%29%5EC%5D%2B%5B1-P%28A%5Ccup%20B%5EC%29%5D)
By the law of total probability,
and substituting this into 
gives
![2P(B)=P(A\cup B)+[P(B)-P(A\cap B)]](https://tex.z-dn.net/?f=2P%28B%29%3DP%28A%5Ccup%20B%29%2B%5BP%28B%29-P%28A%5Ccap%20B%29%5D)
Answer:
T(n) = [n(n + 1)] ÷ 2
Step-by-step explanation:
Sequence = 1, 3, 6
First term = 1
Second term = first term + 2 = 3
Third term = second term + 3 = 6
From the sequence :
Each successive term is doubled together with an increment of '1', that is;
Term 'n' : n(n + 1)
Then, the total is divided by the term 'n'.
Therefore, the nth term is expressed as
T(n) = [n(n + 1)] ÷ 2
For instance,
n = 1
T(1) = [1(1 + 1)] ÷ 2
T(1) = 1
n = 3
T(3) = [3(3 + 1)] ÷ 2
T(3) = 12 ÷ 2 = 6
.......
