Theorem: A line parallel to one side of a triangle divides the other two proportionately. In the figure below, segment DE is parallel to segment BC and segment EF is parallel to AB:

The figure shows triangle ABC with segments DE and DF. Point D is on side AB, point E is on side AC and point F is on side BC.

Which statement can be proved true using the given theorem? (6 points)

a
Segment BD = 32

b
Segment BD = 36

c
Segment BF = 15

d
Segment BF = 18

Atriangle has sides with lengths of 10 yards, 13 yards, and 18 yards. is it a right triangle?

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?

Study results indicate that the mean length of time people spend on a bus in a city is between 21.2 min and 24.5 min what is the study margin of the error?