In a class of 40 students, everyone has either a pierced nose or a pierced ear. the professor asks everyone with a pierced nose to raise his or her hand. nine hands go up. then the professor asked everyone with a pierced ear to do likewise. this time there are 33 hands raised. how many students have piercings both on their ears and their noses?

33+9=42. 42-40=2. These simple calculations show that two people must have raised there hands for both because the sum of the two groups who raised hands is two more than the amount of people in the actual class

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.