Milo bought 12 nails for $6. use the unit rate of cost per nail to complete the table of values for the proportional relationship. enter your answers in the boxes

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?

Gravel is being dumped from a conveyor belt at a rate of 25 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. how fast is the height of the pile increasing when the pile is 14 ft high? (round your answer to two decimal places.) ft/min

‼️‼️‼️‼️‼️the pressure exerted on the walls of a container by a gas enclosed within it is directly proportional to the temperature of the gas. if the pressure is 6 pounds per square inch when the temperature is 440 f, find the pressure exerted when the temperature of the gas is 380°f. (show work)