For all integer values of x and constant k, if (x+6)(x+k)=x^2+14x+48, what is the value of k?

  8

Step-by-step explanation:

The product of terms on the left of the equal sign is ...

  (x+6)(x+k) = x^2 +(6+k)x +6k

So, you have two clues to the value of k. The coefficient of x must match, and the constant must match.

  6+k = 14   ⇒   k = 8

  6k = 48   ⇒   k = 8

The value of k is 8.

0.999987

Step-by-step explanation:

Given that

The user is a legitimate one = E₁

The user is a fraudulent one = E₂

The same user originates calls from two metropolitan areas  = A

Use Bay's Theorem to solve the problem

P(E₁) = 0.0131% = 0.000131

P(E₂) = 1 - P(E₁)  = 0.999869

P(A/E₁) = 3%  = 0.03

P(A/E₂) = 30% = 0.3

Given a randomly chosen user originates calls from two or more metropolitan, The probability that the user is fraudulent user is :

= 0.999986898 ≈ 0.999987