Around robin tounament of n contestants is a set of matches where each of the n 2 pairs of contestants play each other exactly once, with the outcome of play being that one contestant wins and one loses. for an integer k < n, let’s consider whether it is possible that the tournament outcome is such that for every set of k player, there is a player that beat each member of that set. show that if n k · 1 − 1 2 kn−k < 1 then such an outcome is possible. you may assume that the probability that any contestant beats another is 50/50

Your family has $745 for vacation. they spend 40℅ of the money on a hotel. they spend the remaining 1/3 on food. enter the amount of money your family will have left for activities

I’m stuck on this equation, anyone got the answer?

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)