Given a sequence is defined by the explicit definition latex: t_n=\: n^2+nt n = n 2 + n, find the 4th term of the sequence. (ie latex: t_4t 4)

4

8

20

1806

You are constructing a histogram for scores that range from 70 to 100 in whole points. frequencies range from 3 to 10; that is, every whole-point score between 60 and 100 occurs at least 3 times, and at least one score occurs 10 times. which of these would probably be the best range and size for the score intervals along the x-axis?

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

Suppose y varies directly with x. write a direct variation equation that relates x and y. then find the value of y when x=12 y=7 when x=3