91Ó°ÊÓ

Harry had grades of \(70,80,85,\) and 80 on his quizzes. If all quizzes have the same weight, what grade must he get on his next quiz so that his average will be 80\(?\) (A) 85 (B) 85 (B) 90 (D) 95 (D) 100 (E) more than 100

A sphere is inscribed in a cube. The ratio of the volume of the sphere to the volume of the cube is (A) \(0.79 : 1\) (B) \(1 : 2\) (C) \(0.52 : 1\) (D) \(1 : 3.1\) (E) \(0.24 : 1\)

The maximum value of 6 \(\sin x \cos x\) is (A) \(\frac{1}{3}\) (B) 1 (C) 2.6 (D) 3 (E) 6

Twenty-five percent of a group of unrelated students are only children. The students are asked one at a time whether they are only children. What is the probability that the 5 th student asked is the first only child? (A) 0.08098 (B) 0.08 (C) 0.24 (D) 0.25 (E) 0.50

The intersection of a plane with a right circular cylinder could be which of the following? I. A circle II. Parallel lines III. Intersecting lines (A) I only (B) II only (C) III only (D) I and II only (E) I, II, and III

The volume of the region between two concentric spheres of radii 2 and 5 is (A) 28 (B) 66 (C) 113 (D) 368 (E) 490

Of the following lists of numbers, which has the largest standard deviation? (A) \(2,7,15\) (B) \(3,7,14\) (B) \(5,7,12\) (D) \(10,11,12\) (E) \(11,11,11\)

The third term of an arithmetic sequence is \(15,\) and the seventh term is \(23 .\) What is the first term? (A) 1 (B) 6 (C) 9 (D) 11 (E) 13

The length of the radius of a circle is one-half the length of an arc of the circle. How large is the central angle that intercepts that arc? (A) \(60^{\circ}\) (B) \(120^{\circ}\) (C) \(1^{R}\) (D) \(2^{R}\) (E) \(\pi^{R}\)

Find all values of x that satisfy the determinant equation $$ \left|\begin{array}{rr}{2 x} & {1} \\ {x} & {x}\end{array}\right|=3 $$ (A) \(-1\) (B) \(-1\) or 1.5 (C) 1.5 (D) \(-1.5\) (E) \(-1.5\) or 1