Bobby is holding onto the end of a spring that is attached to a ball. As he moves his hand slightly up and down, the ball
moves up and down. With a little concentration, he can repeatedly get the ball to reach a maximum height of 30 cm and a
minimum height of 8 cm from the top of the surface. If he begins out with the ball at the lowest position and then starts a
timer, the first maximum height will occur after 0.3 seconds. Determine the equation of the sinusoidal function that
represents the height of the ball in terms of time.

Do more republicans (group a) than democrats (group b) favor a bill to make it easier for someone to own a firearm? two hundred republicans and two hundred democrats were asked if they favored a bill that made it easier for someone to own a firearm. how would we write the alternative hypothesis?

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?

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