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

Hye ryung is the president of the local chapter of the american medical students association (amsa). she is organizing local outreach and informational meetings. at her first meeting there are five people present (including herself). every month after that her group grows by 5 people. a. how many members are in the group after 6 months? b. the logistics of hosting and feeding her group at meetings was more complicated than expected. the cost of feeding 5 people at her first meeting was $30, for 10 people it was $35, for 15 it was $45, and after 6 months all of the costs had added up to $100. write a function to model the cost with the number of people attending meetings. c. what connections can you make between the linear growth of the group’s membership and the increasing costs of running meetings?

True or false? a circle could be circumscribed about the quadrilateral below.

The sum of the first eight terms of an arithmetic progression is 9m + 14. the fifth term of the06 progression is 2m - 6, where m is a constant.given that the first term of the progression is 26,find the value of the common difference, d and thevalue of m.