Select the instances in which the variable described is binomial. Based on the parents' genetics, each of 6 children from a particular pair of parents has a 0.16 probability of having red hair. The random variable represents the total number of children from this pair of parents with red hair. A quality check on a particular product must meet five guidelines. All products are made in the same factory under the same conditions. The random variable represents the total number of products out of 35 tested that pass inspection. There are two candidates for the position of student council president, Martina and Ronnie. The random variable represents the total number out of 106 students who voted for Ronnie. The probability of drawing a queen in a standard deck of cards is 0.08. Seven cards are drawn without replacement. The random variable represents the total number of queen cards observed. A coin flip has two outcomes: heads or tails. The probability of each outcome is 0.50. The random variable represents the total number of flips required to get tails.

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)