1. kayla wants to find the width, ab, of a river. she walks along the edge of the river 100 ft and marks point c. then she walks 22 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 triangle abc and triangle edc are similar? why or why not? (be sure to state a triangle similarity postulate) (b) suppose de = 32 ft. what can kayla conclude about the width of the river? explain.

Ablock of wood is a cube whose side is x in. long. you cut off a 1-inch thick piece from the entire right side. then you cut off a 3-inch thick piece from the entire top of the remaining shape. the volume of the remaining block is 2,002 in3. what are the dimensions of the original block of wood?

Miranda is braiding her hair.then she will attach beads to the braid.she wants 1_3 of the beads to be red.if the greatest number of beads that will fit on the braid is 12,what other fractions could represent the part of the beads that are red?

Max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.