I’ll ! after surveying students in her homeroom, katie decided to use a number cube to predict the probability that a randomly
chosen student in her school planned to stay after school today for extracurricular activities. in katie's simulation, a roll of 1
represents staying after school, while rolls of 2, 3, 4, 5, or 6 represent leaving school at the end of classes.
according to katie's model, what is the probability that three randomly chosen students will all stay after school for
extracurricular activities today?

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?

Drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. identify the domain for each of the given functions.

50 plz, given the system of equations, match the following items. x + 3 y = 5 x - 3 y = -1 a) x-determinant b) y-determinant c) system determinant match the following to the pictures below.