Give a combinatorial proof that . [hint: count in two ways the number of ways to select a committee, with n members from a group of n mathematics professors and n computer science professors, such that the chairperson of the committee is a mathematics professor.]

The triangles are similar. what is the value of x? enter your answer in the box. x = two right triangles. the larger right triangle is labeled x on the longer leg, 12 on the shorter leg and 20 on the hypotenuse. the smaller triangle is labeled 4 on the longer leg, 3 on the shorter leg, and 5 on the hypotenuse.

Simplify 5 square root of 7 end root plus 12 square root of 6 end root minus 10 square root of 7 end root minus 5 square root of 6 . (1 point) 5 square root of 14 end root minus 7 square root of 12 5 square root of 7 end root minus 7 square root of 6 7 square root of 12 end root minus 5 square root of 14 7 square root of 6 end root minus 5 square root of 7

Which of the following is the result of expanding the series