R.2. Using the AM-GM inequality (last proposition in section 4.3), prove that if a and b are positive real numbers, then 응+ 음 > 2.

The probabil ariable x is a om this dens Is between

The first thing “e” wanted to do is to “Calculuize” his favourite game, apples to apples. So, one day, hisfriend, pi worked with “e” to do the following experiment. They decided to construct a box for the apples to apples game such that its width isexactly three times its length and its volume is 36 cubic centimeters. Assuming that the box is closed on all sides and using calculus methods only,determine the smallest amount of material needed for its construction. Show allyour work.

This is a discrete problem and I need to prove the statement.

Given that P(A)=0.3 and P(B)=0.7, answer the following:(please round all numerical answers to four decimal placesa) Assuming that A and B are independent, what is P(A and B)? b) Assuming that A and B are independent, what is P(A or B)? c) Assuming that A and B are independent, what is P(A|B)? d) If we are given that P(A and B) = 0.1, what is P(A|B)?

could you pls show all the work handwritten for this question