Randy chooses to survey every fifth student in the cafeteria he surveys a total of 140 students and finds that 84th students support buying new PE equipment if this is a representative sample how many total students could he predict would support the purchase of the new equipment out of the entire student body?

i have not got your picture clearly so see it once again

answer: the proof is mentioned below.

step-by-step explanation:

since, given:   lines bc = ef

prove:   lines ac > ef

          statements                                           reason

1. bc=ef                                           1. given

2. ac= ab+bc                                 2. because b is the point between the  

                                                            line segment ac

3.   ac > bc                                       3. because if a line segment is equal to

                                                          the sum of two line segments then it is

                                                          always greater then each of these

                                                          individual line segments

4. ac > ef                                         4. by equality property.