Heather and isabelle play a two-person game which is won by the first person to accumulate 10 points. at each turn heather gains a point with probability of $\frac{2}{3}$ . if she doesn't get a point then isabelle gets a point. isabelle is now ahead 9 to 6. what is the probability that isabelle will win? express your answer as a common fraction.

Trent wants to buy 2 packs of trading cards for 3 dollars each. the trading card packs that trent normally buys tend to come in packs of 6, 10, 12, or 15 cards. after selecting 2 packs, trent found that the first pack of cards cost 25 cents per card, and the second pack cost 30 cents per card. trent uses this information to write the equations below in order to compare c, the number of cards in each pack.

Let f(x) = 3 − x . find the average rate of change of f(x) from x = a to x = a + h and simplify your answer so that no single factor of h is left in the denominator.

In each diagram, line p is parallel to line f, and line t intersects lines p and f. based on the diagram, what is the value of x? ( provide explanation)