Given the simultaneous equations:

3x + 4y = 27

5x - 2y = 19

(I) Write the equations in the form AX =B, where A, X, and B are matrices

(ii) Calculate the determinant of A.

(iii) Determine the A adjoint.

(iv) Determine the inverse of A.

(v) Solve for x and y

An office supply company conducted a survey before marketing a new paper shredder designed for home use. in the survey, 80 % of the people who tried the shredder were satisfied with it. because of this high satisfaction rate, the company decided to market the new shredder. assume that 80 % of all people are satisfied with this shredder. during a certain month, 100 customers bought this shredder. find the probability that of these 100 customers, the number who are satisfied is 69 or fewer.