AWARDING BrainiestQuadrilateral CDEF is inscribed in circle A. Which statements complete the proof to show that ∠CFE and ∠CDE are supplementary? Quadrilateral CDEF is inscribed in circle A. Quadrilateral CDEF is inscribed in circle A, so m arc CDE + m arc CFE= 360°. ∠CFE and ∠CDE are inscribed angles, which means that their measures are . So, . Using the substitution property of equality, 2 ⋅ m∠CFE + 2 ⋅ m∠CDE = 360°. Using the division property of equality, divide both sides of the equation by 2, resulting in m∠CFE + m∠CDE = 180°. Therefore, ∠CFE and ∠CDE are supplementary. A twice the measure of their intercepted arcs; 2 ⋅ m arc CDE= m∠CFE and 2 ⋅ arc CDE = m∠CDE B twice the measure of their intercepted arcs; marc CDE= 2 ⋅ m∠CFE and arc CFE = 2 ⋅ m∠CDE C one half the measure of their intercepted arcs; m arc CDE= 2 ⋅ m∠CFE and arc CFE= 2 ⋅ m∠CDE D one half the measure of their intercepted arcs; 2 ⋅ m arc CDE= m∠CFE and 2 ⋅ arc CFE= m∠CDE

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.