Consider this polynomial, where a is an unknown real number p() = 4 + 513 + ax2 – 3x + 11
The remainder of the quotient of p(), and (x + 1) is 17.
Braulio uses synthetic division to find the value of a, and Zahra uses the remainder theorem to find the value of a. Their work is shown.

Abby is preparing fruit punch for her party. she starts with a bowl filled with liquid that has 1/2 fruit juice and 1/2 sprite, but she decides it's too fruity. so she pours out 1/4 of the liquid, and then fills the bowl up again with sprite. what fraction of the punch is now sprite?

The number of branches on a tree demonstrates the fibonacci sequence. how many branches would there be on the next two levels of this tree? 13 | | | m branches

The number if marbles of different colors stored in a hat is listed below: 4 red marbles 10 green marbles 7 blue marbles. without looking in the hat, dan takes out a marble at random. he replaces the marble and then takes out another marble from the hat. what is the probability that dan takes out a blue marble in both draws?