Drag the tiles to the correct boxes to complete the pairs. The graph represents the average cost to produce pills, in dollars, as a function of the number of pills manufactured by a pharmaceutical company. Match each key feature of the function with its interpretation in the scenario. vertical asymptote at x = 0 decreasing on (0, ∞) horizontal asymptote at y = 0 positive on (0, ∞) As more pills are produced, the average cost per pill decreases. arrowRight The cost of producing pills can never reach 0. arrowRight The cost of producing pills cannot be negative. arrowRight As the number of pills produced gets smaller, the average cost of production greatly increases. arrowRight

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 graph below represents the number of dolphins in a dolphin sanctuary. select all the key features of this function.

What happens to the area as the sliders are adjusted? what do you think the formula for the area of a triangle is divided by 2?