Of the 35 students in my class, 11 practice taekwondo, 11 play piano, and 20 take lessons at AoPS. 4 students play piano and go to AoPS, 3 students do taekwondo and play piano, 5 students
go to AoPS and practice taekwondo, and 3 students do none of these. How many students do all 3?

Colby and jaquan are growing bacteria in an experiment in a laboratory. colby starts with 50 bacteria in his culture and the number of bacteria doubles every 2 hours. jaquan starts with 80 of a different type of bacteria that doubles every 3 hours. let x equal number of days. colbys experiment follows the model: a.) y=50*2^x b.) y=50*2^8x c.) y=50*2^12x jaquans experiment follows the model: a.)80*2^x b.)80*2^8x c.)80*2^12x

Complex numbers multiply √-4 * √-25 and show all intermediate steps. alternative notation is sqrt(-4) * sqrt(-25).

What is the frequency of the sinusoidal graph?