Ralph owns a circular farm as shown. He is planning to fence a triangular pigpen ABC in the farm. Point M is the midpoint of the side CB. All dimensions are in yards. Given that the fence material cost $30 per yard, what is the total cost to fence the pigpen?

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?

Arley is building a model of a city map. in one part of the city, three roads form a right triangle, which harley draws as triangle abc, with the following measures: m∠b=90° and m∠a=30°. in his scale model, the hypotenuse of triangle abc, ac¯¯¯¯¯¯¯¯, has a length of 817−−√ cm. what is the value of a (the length of bc¯¯¯¯¯¯¯¯)?

Janie has $3. she earns $1.20 for each chore she does and can do fractions of chores. she wants to earn enough money to buy a cd for $13.50. write an inequality to determine the number of chores, c, janie could do to have enough money to buy the cd.