As a simplified model for weather forecasting, suppose that the weather (either wet or dry) tomorrow will be the same as the weather today with probability p. show that the weather is dry on january 1, then
pn
, the probability that it will be dry n days layer, satisfies
pn=(2p−1)pn−1+(1−p)n≥1
p0=1
prove that
pn=1/2+1/2(2p−1)nn≥0

Marcus needs to rewrite f(x) = x2 + 6x + 4 in vertex form.

Need to finish my juan wants to build a greenhouse in his back yard. he needs to maximize the ratio of floor area to structure volume in order to provide the most room for plants while minimizing the area to be heated. find the description of the structure that best meets juan’s criteria. a.) a hemisphere with a diameter of 12 feet b.) a cube with a side length of 12 feet c.) a cone with a diameter of 12 feet and a height of 10 feet d.) a square pyramid with a base side length of 12 feet and a height of 9 feet

If you were constructing a triangular frame, and you had wood in the length of 4inches, 4 inches, and 7 inches, would it make a triangle? would you be able to create a frame from these pieces of wood?