Answer with Step-by-step explanation:
Let us assume the 2 consecutive natural numbers are 'n' and 'n+1'
Thus the product of the 2 numbers is given by
We know that the sum of 'n' consecutive natural numbers starting from 1 is
Thus from equation 'i' we can write
As we know that any number multiplied by 2 is even thus we conclude that the product of 2 consecutive numbers is even.
Answer:
the pair that is not a solution is d
Step-by-step explanation:
5 > 2(2) + 1
5 > 4 + 1
5 > 5
it is equal to and not greater than
The movement of the minute hand is circular.
Tangence speed is V=2Rπ/T= 2*7*3.14/3600 inches/sec=0.012211 inches/sec
The path (distance) that minute hand past is D=V*t = 0.012211 * 5 min= 0.012211 * 300sec=>
D=3.663≈3.66 inches
Good luck!!!
Answer:
A. E(x) = 1/n×n(n+1)/2
B. E(x²) = 1/n
Step-by-step explanation:
The n candidates for a job have been ranked 1,2,3....n. Let x be the rank of a randomly selected candidate. Therefore, the PMF of X is given as
P(x) = {1/n, x = 1,2...n}
Therefore,
Expectation of X
E(x) = summation {xP(×)}
= summation {X×1/n}
= 1/n summation{x}
= 1/n×n(n+1)/2
= n+1/2
Thus, E(x) = 1/n×n(n+1)/2
Value of E(x²)
E(x²) = summation {x²P(×)}
= summation{x²×1/n}
= 1/n
