The hardware store sells sparklers for the 4th of july. they charge 19 cents apiece. the firework stand charges 85 cents for four. which is the better deal? how can you tell

The ksp expression for the system pbcl2(s) pb+2(aq) + 2 cl-(aq) is: [pbc12][pb+2][2cl-] [pb+2][cl-]2 [pb+2][2cl-]2 [pbcl2][pb+2][cl-]2 [pb+2][2cl-]2[pbcl2]

1- 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.2- 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 the first question?

Math it's appreciated. (picture provided)