2-adic representation of 100 is 100 = 1.22 +1.25 +1.26, and the 3-adic representation of 100 is 100 = 1+2.3² +1.34. The 10-adic representation of 217 is 217= 7+1 10¹ + 2.10². 1

In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach both physics and mathematics. How many teach physics ?

Widget Sales Jesaki Inc. is trying to enter the widget market. The research department established the following price-demand, cost, and revenue functions: p(x) = 60 1.20x Price- demand function Cost function C(x) = 210 + 12x R(x) = xp(x) = x(60 - 1.20x) where x is in thousands of widgets and C(x) and R(x) are in thousands of dollars. The price p(x) is the price in dollars of one widget when the demand is a thousand widgets. All three functions have domain 1 ≤ x ≤ 50. Revenue function

Please finish the entire question; it has multiple parts.

Mr. Imperfecto teaches another math class.  This time he has 23 students take a test, the average score on which is an 87.  Mr. Imperfecto realizes he put the wrong grade in for a student.  He entered a 35, and the score should have been an 85.  To the nearest integer, what is the new class average?