Mini Exam 16 — Timed Mini Exams

Questions in this quiz (10)

1. $$\sin(P)=\cos(Q)$$The equation above is true for acute angles $$P$$ and $$Q$$. If angle $$P$$ is equal to $$((x+29)^\circ)$$ and angle $$Q$$ is equal to $$((17x-2)^\circ)$$, what is the value of $$x$$?

   • $$(\frac{11}{2})$$
   • $$(\frac{9}{2})$$
   • $$\frac{7}{2}$$
   • $$(\frac{5}{2})$$

2. The function $$g$$ is defined by $$g(x)=-x^2+bx-12$$, where $$b$$ is a constant. The graph of $$y=g(x)$$ in the $$xy$$ plane passes through the point $$(3,6)$$. What is the maximum value of $$g$$?

   • $$(\frac{35}{4})$$
   • $$(\frac{29}{4})$$
   • $$(\frac{25}{4})$$
   • $$\frac{33}{4}$$

3. The population density of Brookville is $$600$$ people per square mile. Brookville has a population of $$48,000$$ people. What is the area, in square miles, of Brookville?

   • $$90$$
   • $$80$$
   • $$70$$
   • $$60$$

4. An angle has a measure of $$\frac{11\pi}{45}$$ radians. What is the measure of the angle in degrees?

   • $$48^\circ$$
   • $$40^\circ$$
   • $$36^\circ$$
   • $$44^\circ$$

5. Which expression represents the product of $$(x^{-2}y^{5}z^{3})$$ and $$(x^{4}z^{-6}+y^{2}z^{-1})$$?

   • $$x^{2}y^{5}z^{-3}+x^{-2}y^{7}z^{2}$$
   • $$x^{2}y^{6}z^{-3}+x^{-2}y^{7}z^{2}$$
   • $$x^{2}y^{5}z^{-2}+x^{-2}y^{7}z^{2}$$
   • $$x^{2}y^{5}z^{-3}+x^{-2}y^{7}z^{3}$$

6. $$64x^2-(16c+32d)x+cd=0$$In the given equation, $$c$$ and $$d$$ are positive constants. The sum of the solutions to the given equation is $$k(2c+4d)$$, where $$k$$ is a constant. What is the value of $$k$$?

   • $$\frac{1}{8}$$
   • $$\frac{1}{10}$$
   • $$\frac{1}{6}$$
   • $$\frac{1}{4}$$

7. Which expression represents the product of $$(x^{-3}y^{4}z^{2})$$ and $$(x^{5}z^{-7}+y^{3}z^{-2})$$?

   • $$x^{2}y^{4}z^{-4}+x^{-3}y^{7}$$
   • $$x^{2}y^{5}z^{-5}+x^{-3}y^{7}$$
   • $$x^{2}y^{4}z^{-5}+x^{-3}y^{7}z$$
   • $$x^{2}y^{4}z^{-5}+x^{-3}y^{7}$$

8. The volume of right circular cylinder $$B$$ is $$40$$ cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with half the radius and three times the height of cylinder $$B$$?

   • $$20$$
   • $$30$$
   • $$50$$
   • $$60$$

9. A catering company is purchasing boxes of rice and beans for an event. The supplier will deliver no more than $$500$$ pounds in one shipment. Each box of rice weighs $$12$$ pounds, and each box of beans weighs $$8$$ pounds. The company wants to buy at least three times as many boxes of rice as boxes of beans. Let $$r$$ represent the number of boxes of rice and let $$b$$ represent the number of boxes of beans, where $$r$$ and $$b$$ are nonnegative integers. Which of the following systems of inequalities best represents this situation?

   • $$12r+8b\le500$$$$r\ge3b$$
   • $$12r+8b\le500$$ $$3r\ge b$$
   • $$24r+8b\le500$$$$r\ge3b$$
   • $$12r+16b\le500$$$$r\ge3b$$

10. The table shows the distance, in miles, and the average driving speed, in miles per hour, for each segment of the drive when there is no traffic delay.Mr. Lopez drives from his office to his home every weekday evening. If Mr. Lopez starts his drive at $$5:00$$ p.m., he can drive at his average driving speed with no traffic delay for each segment of the drive. If he starts his drive at $$5:30$$ p.m., the travel time from the highway entrance to the highway exit increases by $$25\%$$ due to heavier traffic, but the travel time for each of the other two segments does not change. Based on the table, how many more minutes does Mr. Lopez take to arrive home if he starts his drive at $$5:30$$ p.m. than if he starts at $$5:00$$ p.m.? Round your answer to the nearest minute.

    • $$5$$
    • $$4$$
    • $$10$$
    • $$8$$