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.]

Which statements are true of the graph of h(x) = ^3 square root of x-4 ? check all that apply.the domain of h(x) is the set of all real numbers. the range of h(x) is the set of all real numbers. for all points (x, h( h(x) exists if and only if x – 4 0. the graph of h(x) is a translation of f(x) down 4 units. the graph of h(x) intercepts the x-axis at (4, 0).

The equation of a circle is (x - 3)2 + (y - 7)2 = 25. determine the length of the radius. 4 25 12.5 5 write the standard equation of the circle with center (2, 3) and a diameter of 12. (x - 2)2 + (y - 3)2 = 36 (x + 2)2 + (y + 3)2 = 12 (x - 2)2 + (y - 3)2 = 6 (x - 3)2 + (y - 2)2 = 36 the equation of a circle is (x + 3)2 + (y + 7)2 = 25. where is (3, 4) located in relation to the circle? on the circle in the interior of the circle in the exterior of the circle at the center of the circle

Write numerical coefficient of y² in the expression 2x² - 15xy – 7y²