Let n have a bin(100, 1/4) distribution. given that n = n flip a fair coin n times and let x be the number of heads observed. (a) what is the distribution of x given n = n. be sure to provide a range and a proper conditional probability mass function. (b) find the random variable e(x|n). (c) using part (b), compute e(x). (if you do not use part (b), and instead just give an educated guess, you will receive zero points.)

State one method by which you can recognize a perfect square trinomial.

(50 ) mrs. julien’s and mrs. castillejo’s classes are selling cookie dough for a school fundraiser. customers can buy packages of macadamia nut chip cookie dough and packages of triple chocolate cookie dough. mrs. julien’s class sold 25 packages of macadamia nut chip cookie dough and 30 packages of triple chocolate cookie dough for a total of $221.25. mrs. castillejo’s class sold 5 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $191.25. (a) write the system of equations that model the problem. be sure to explain which equation represents which situation. (b) find the cost of each type of cookie. show your work. (c) explain which method you used to solve the system and why you chose that method.

Four equations are shown below.equation 1: y=2*equation 2: y=2x-5equation 3: y=x2 + 6equation 4: tdentify one linear equation and one nonlinear equation from the list.why each equation you identified is linear or nonlinear.nd one nonlinear equation from the list. state a reasonlinear equation