You randomly draw a marble from a bag of marbles that contains8 blue marbles, 5 green marbles, and 8 red marbles. What is \text{P(draw a blue or red marble})P(draw a blue or red marble)start text, P, left parenthesis, d, r, a, w, space, a, space, b, l, u, e, space, o, r, space, r, e, d, space, m, a, r, b, l, e, end text, right parenthesis? If necessary, round your answer to 222 decimal places.

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)

Prove that 16^4-2^13-4^5 is divisible by 11.

What is the surface area of the sphere?