Timed Mini Exam 19 — Timed Mini Exams

Questions in this quiz (10)

1. If $$y = 2^4$$, then what is the value of $$y^{y}$$?

   • $$2^{64}$$
   • $$2^{8}$$
   • $$2^{16}$$
   • $$16^{16}$$

2. In equilateral triangle $$UVW$$, each side has length $$a$$. Point $$Y$$ is the midpoint of segment $$UW$$, and point $$X$$ is the midpoint of segment $$YW$$. What is the perimeter of triangle $$VXY$$ in terms of $$a$$?

   • $$\frac{a(\sqrt{13} + 1 + 2\sqrt{3})}{4}$$
   • $$\sqrt{13}$$
   • $$22$$
   • $$2\sqrt{13}$$

3. If $$|x - y| = |x - z| - |y - z|$$ is always true, what can be determined about the relationship between $$|x|$$ and $$|y|$$?

   • $$|x| > |y|$$
   • $$|x|$$ < $$|y|$$
   • $$|x| \leq |y|$$
   • $$|x| \geq |y|$$

4. Mr. Sjogren invested a total of 2000 in two certificates of deposit. He deposited $$x$$ dollars in one CD earning 1 percent annual simple interest, and the rest in another CD earning 2 percent annual simple interest. At the end of one year, the total interest earned from both CDs was 25. What amount did Mr. Sjogren invest in each CD?

   • 600 dollars at 1 percent and 1400 dollars at 2 percent.
   • 1000 dollars at 1 percent and 100 dollars at 2 percent.
   • 1500 dollars at 1 percent and 500 dollars at 2 percent.
   • 400 dollars at 1 percent and 1600 dollars at 2 percent.

5. Billie clocked in at 8:57 AM and clocked out at 5:16 PM on July 2. She spent 80 percent of her total work time stacking shelves. Approximately how many hours did Billie spend stacking shelves on that day?

   • $$5 \frac{2}{3}$$
   • $$6 \frac{3}{4}$$
   • $$7 \frac{3}{4}$$
   • $$7 \frac{1}{3}$$

6. What is the least possible distance between a point on the circle $$x^2 + y^2 = 1$$ and a point on the line $$y = \frac{3}{4}x - 3$$?

   • $$\sqrt{2}$$
   • $$\frac{11}{7}$$
   • $$\frac{7}{5}$$
   • $$\sqrt{7}$$

7. The dimensions of a rectangular floor are 16 feet by 20 feet. When a rectangular rug is placed on the floor, a strip of floor 3 feet wide is exposed on all sides. What are the dimensions of the rug, in feet?

   • $$13 \text{ feet by } 14 \text{ feet}$$
   • $$16 \text{ feet by } 16 \text{ feet}$$
   • $$10 \text{ feet by } 10 \text{ feet}$$
   • $$14 \text{ feet by } 10 \text{ feet}$$

8. Every student of a certain school must take one and only one elective course. In last year, $$\frac{1}{2}$$ of the students took biology as an elective, $$\frac{1}{3}$$ of the students took chemistry as an elective, and all of the other students took physics. In this year, $$\frac{1}{3}$$ of the students who took biology and $$\frac{1}{4}$$ of the students who took chemistry left school, other students did not leave, and no fresh students came in. What fraction of all students took biology and took chemistry?

   • $$\frac{7}{9}$$
   • $$\frac{3}{4}$$
   • $$\frac{1}{4}$$
   • $$\frac{1}{3}$$

9. Which statement is true for the shaded region between$$y = -x^2 + 4x + 3$$ and $$y = x - 4$$?

   • $$-x^2 + 4x + 3 \le 0$$
   • $$-x^2 + 4x + 3 \ge 0$$
   • $$y \le x-4$$
   • $$-x^2 + 3x + 7 \ge 0$$

10. Let the vectors $$u = \langle 1, 3 \rangle$$ and $$v = \langle 5, 8 \rangle$$. If $$u - 2v + w = \langle -13, 25 \rangle$$, which of the following must be $$w$$?

    • $$\langle -9, -13 \rangle$$
    • $$\langle 13, 28 \rangle$$
    • $$\langle -4, 38 \rangle$$
    • $$\langle 11, 19 \rangle$$