1 N P 1 N P stands for "One Nitrogen, One Phosphorus," which is a notation often used in the context of fertilizers or nutrient ratios in agriculture. It typically indicates a balanced ratio of nitrogen (N) and phosphorus (P) essential for plant growth. This kind of formulation is used to ensure that crops receive adequate nutrients for optimal development.
N - p% = N - p% of N = N*(1 - p%) = N*(1 - p/100) or N*(100 - p)/100
We have to use the expression P(X=x) = nCx px (1--p)(n--x) Here n = n and p=p and x = 1 or x>1 P(X>/=1) = 1 -- P(X</=1) So, P(X<=1) = P(X=0) + P(X=1) This gives nC0 p0 (1--p)(n-0)+ nC1 p1 (1--p)(n--1) ie (1--p)n + n p (1--p)(n--1)
The letters P N in this case stand for "prime numbers".
Induction is not a formula, it is a method of proof. Anyway, state the property you wish to prove about each natural number n. This is usually the given P(n). Prove this for the zeroth case, i.e. P(0). Assume the nth case is true, i.e. P(n). Show P(n) => P(n+1). Example: Prove 2 + 4 + ... + 2n = n(n+1) for n >= 0 Proof: P(0) = 0 trivially. Assume: P(n) Show P(n) => P(n+1). 1. 2 + 4 + ... + 2n = n(n+1) 2. 2 + 4 + ... + 2n + 2(n+1) = n(n+1) + 2(n+1) = (n+1)(n+2). QED
Proof: P{T>n+m/T>n}=P{T>n+m,T>n}/P{T>n} (Bayes theorem) =P{T>n+m}/P{T>n} =((1-p)^(n+m))/(1-p)^n = (1-p)^(n+m-n) = (1-p)^m (1-p)^m = {T>m} So T>m has the same probability as T>m+n given that T>n, which means it doesn't care (or don't remember) that n phases had passed.
Formally, a number n, has an inverse mod p only if p is prime. The inverse of n, mod p, is one of the numbers {0, 1, 2, ... , k-1} such that n*(p-1) = 1 mod p If p is not a prime then: if n is a factor of p then there is no such "inverse"; and if n is not a factor of p then there may be several possible "inverses".
P = 1 For K = 1 to M . P = P * N Next K PRINT "N raised to the power of M is "; P
Five pennies in a nickel. (US coinage)
United Nations Development Programme
Seven players in a netball team.
R.D.=P*n+P(n+1)/2400
P(2x3) - 1/4 where P(n) is the n-th prime.