There are 30 (not necessarily distinct) real numbers written on a board. We know that no matter how we divide these numbers into 10 groups of size 3, there would be at least 2 groups with equal sums. Find the maximum number of distinct numbers on the board.

The triangles are similar. what is the value of x? show your work.

Which choice represents the sample space ,s for this event

Kayla wants to find the width, ab, of a river. she walks along the edge of the river 65 ft and marks point c. then she walks 25 ft further and marks point d. she turns 90° and walks until her location, point a, and point c are collinear. she marks point e at this location, as shown. (a) can kayla conclude that δ and δ are similar? why or why not? (b) suppose de = 15 ft. what can kayla conclude about the width of the river?