You throw a ball straight up from a rooftop 40 feet high with an initial speed of 48 feet per second. The function s(t) = -16t^2 + 48t + 40 models the​ ball's height above the​ ground, s(t) in​ feet, t seconds after it was thrown. During which time period will the​ ball's height exceed that of the​ rooftop? When will the ball exceed the height of the​ rooftop?

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

The length of the largest fish is 967.74 times greater than the length of the smallest fish. select a variable expression that shows the length of the largest fish, if 8 is the length of the smallest fish. a. s + 967.74 b. \[ \frac{967.74}{s} \] c. 967.74 - s d. 967. 74s

Піf x = y and y= z, which statement must be true? оа. -x = -2 b. x= z ос. —x = 2 od. 2= x