June 2010 Algebra 2 / Trigonometry Regents – Parts 3 and 4

36. The members of a men’s club have a choice of wearing black or red vests to their club meetings. A study done over a period of many years determined that the percentage of black vests worn is 60%. If there are 10 men at a club meeting on a given night, what is the probability, to the nearest thousandth, that at least 8 of the vests worn will be black?

37. Find all values of θ in the interval 0º ≤ θ ≤ 360º that satisfy the equation sin2θ = sinθ.

38. The letters of any word can be rearranged. Carol believes that the number of different 9-letter rearrangements of the word “TENNESSEE” is greater than the number of different 7-letter rearrangements of the word “VERMONT.” Is she correct? Justify your answer.

• (The three questions above are Part 3. They are worth 4 points each.)
• ( The question below is part 4. It is worth 6 points)

39. In a triangle, two sides that measure 6 cm and 10 cm form an angle that measures 80º. Find, to the nearest degree, the measure of the smallest angle in the triangle.