Theorem: A line parallel to one side of a triangle divides the other two proportionately. In the figure below, segment DE is parallel to segment BC and segment EF is parallel to AB:

The figure shows triangle ABC with segments DE and EF. Point D is on side AB, point E is on side AC, and point F is on side BC. Segment AD is 18, segment AE is 24, segment EC is 20, and segment FC is 30.

Which statement can be proved true using the given theorem?

Segment BF = 16
Segment BD = 20
Segment BD = 15
Segment BF = 32

Charlie tosses five coins.what is the probability that all five coins will land tails up.

After reading 80% of her e-mails in her inbox, danette still has m unread e-mails. which of the following expressions could represent the number of e-mails danette had in her inbox before she started reading? choose 2 answers: (choice a) 5m (choice b) 1.8m (choice c) 80m (choice d) m/0.8 (choice e) m/1−0.8

The resumâ´es of two male applicants for a college teaching position in chemistry are placed in the same file as the resumâ´es of two female applicants. two positions become available, and the first, at the rank of assistant professor, is filled by selecting one of the four applicants at random. the second position, at the rank of instructor, is then filled by selecting at random one of the remaining three applicants. using the notation m2f1, for example, to denote the simple event that the first position is filled by the second male applicant and the second position is then filled by the first female applicant, (a) list the elements of a sample space s; (b) list the elements of s corresponding to event a that the position of assistant professor is filled by a male applicant; (c) list the elements of s corresponding to event b that exactly one of the two positions is filled by a male applicant; (d) list the elements of s corresponding to event c that neither position is filled by a male applicant; (e) list the elements of s corresponding to the event a â© b; (f) list the elements of s corresponding to the event a âş c; (g) construct a venn diagram to illustrate the intersections and unions of the events a, b, and c.