Polya’s urn model supposes that an urn initially contains r red and b blue balls. At each stage a ball is randomly selected from the urn and is then returned along
with m other balls of the same color. Let Xk be the number of red balls drawn in
the first k selections.
(a) Find E[X1].
(b) Find E[X2].
(c) Find E[X3].
(d) Conjecture the value of E[Xk], and then verify your conjecture by a conditioning
argument.

Find the average rate of change for f(x) = x2 − 3x − 10 from x = −5 to x = 10.

Melanie is buying a bathing suit that costs 39.99. she is given a discount at the cash register of $6.00 when she scratched 15% off on a game piece for a store promotion. what will the sale price of melanie’s bathing suit be?

Statements reasons 1. ab ? cd; ad ? bc 1. given 2. ac ? ac 2. reflexive property 3. ? adc ? ? cba 3. ? 4. ? dac ? ? bca; ? acd ? ? cab 4. cpctc 5. ? dac and ? bca are alt. int. ? s; ? acd and ? cab are alt. int. ? s 5. definition of alternate interior angles 6. ab ? cd; ad ? bc 6. converse of the alternate interior angles theorem 7. abcd is a parallelogram 7. definition of parallelogram what is the missing reason in step 3?