45. Safety switch An industrial machine requires an emergency shutoff switch that must be designed so that it can be easily operated with either hand. Design an experiment to find out whether workers will be able to deactivate the machine as quickly
with their dominant hands as with their non-dominant hands. Be sure to explain the role of randomization in your design.

You will get 25 points an image of a rectangular prism is shown below: part a: a cross section of the prism is cut with a plane parallel to the base. what is the name of the shape created by the cross section? explain your answer. (5 points) part b: if a cross section of the prism is cut perpendicular to the base, what would be the shape of the resulting cross section? explain your answer. (5 points)

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?

In each diagram, line p is parallel to line f, and line t intersects lines p and f. based on the diagram, what is the value of x? ( provide explanation)