In a carnival game, a person wages $2 on the roll of two dice. if the total of the dice is 2,3,4,5,6 then the person gets $4. if the total of the dice is 8,9,10,11,12 then the person loses $2. if the total of the two dice is 7, the person loses $0.25. what is the expected value of playing the game once?

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?

How many days was the temperature above 90 degrees?

The volume of a cone is 37x3 cubic units and its height is x units. which expression represents the radius of the cone's base, in units? 1 s o 3x o 6x obx 93x2