Using the principle of mathematical induction, show that 41^n-14^n is a multiple of 27​

Arestaurant gives out a scratch-off card to every customer. the probability that a customer will win a prize from a scratch-off card is 25%. design and conduct a simulation using random numbers to find the experimental probability that a customer will need more than 3 cards in order to win a prize. justify the model for your simulation, and conduct at least 10 trials.

Answer asap! show all work! find the number of complex roots, the possible number of real roots and the possible rational roots of the polynomial function. then, solve for all roots. x^3 + 2x^2 + 3x + 6 = 0

Multiply and simplify. 2x^2 y^3 z^2 · 4xy^4 x^2 i will mark you brainliest if right. show how you got the answer, !