A parallelogram has coordinates (0, 0), (144, 0), (377, 89) and (233, 89).
Determine the number of lattice points strictly within the interior of the parallelogram.
In the rally point scoring method
now widely adopted in volleyball,
either team can score a point by
winning the rally after a serve,
regardless of who serves the ball.
The first team to earn 25 points
wins the set, except that a team
must win by at least two points —
that is, if the score is 24-24, then
the final score must be 26-24,
27-25, 28-26, etc.
Assume two
evenly matched teams are playing each other.
To at least four significant figures, what is the expected
number of rallies (total points
scored) per set?
Suppose a type of glass is such
that, for any incoming light: 70
percent of light shining from one
side is transmitted through to the
other side; 20 percent of the light is
reflected (off of the outer surface)
back in the direction from which it
came; the remaining 10 percent is
absorbed in the glass.
How much
of an original light source will be
transmitted through three panes of
glass? It is assumed that the panes
are parallel and at a small distance
from each other.
Ignore any loss
of light above or below the panes
(which is the same as assuming the
panes extend infinitely in all four
directions). Express your answer as
a ratio of integers.
Find all nonnegative integer solutions to the following equation
64 + 3x5y = 17z
