Advanced Quizzes — Quiz 30

Questions in this quiz (10)

1. In the figure, a cylindrical block of wood is sliced into two pieces as shown by the dashed curve. The cylinder has diameter $$6$$ centimeters and height $$8$$ centimeters. What is the volume of the top piece, in cubic centimeters?

   • $$18\pi$$
   • $$24\pi$$
   • $$36\pi$$
   • $$54\pi$$

2. In the figure, circle $$A$$ and circle $$B$$ each have a radius of $$4$$ and are tangent to each other. If $$\triangle ACB$$ is equilateral, what is the area of the shaded region?

   • $$16\pi$$
   • $$20\pi$$
   • $$24\pi$$
   • $$\frac{80\pi}{3}$$

3. A linear function $$f$$ is defined such that $$f(2)=10$$ and $$f(5)=22$$. Another linear function $$g$$ is parallel to $$f$$ and passes through the point $$(0,k)$$. If $$g(3)=15$$, what is the value of $$k$$?

   • $$1$$
   • $$3$$
   • $$5$$
   • $$7$$

4. In the figure described, line segments $$\overline{AE}$$ and $$\overline{BD}$$ are parallel. Segments $$\overline{AD}$$ and $$\overline{EB}$$ intersect at point $$C$$. The lengths of certain segments are given in terms of a variable $$x$$: $$AC=x$$, $$CD=x+4$$, $$EC=x-1$$, and $$CB=x+1$$. What is the length of segment $$\overline{AD}$$?

   • $$2$$
   • $$4$$
   • $$6$$
   • $$8$$

5. The decay of a certain radioactive isotope can be modeled by the function $$A(t)=A_0e^{-kt}$$, where $$A(t)$$ is the amount of the isotope remaining after $$t$$ hours, $$A_0$$ is the initial amount, and $$k$$ is a positive constant. If the isotope decays to $$12.5\%$$ of its initial amount in $$9$$ hours, what is the value of $$k$$?

   • $$\frac{\ln(2)}{9}$$
   • $$\frac{\ln(2)}{3}$$
   • $$3\ln(2)$$
   • $$9\ln(2)$$

6. A rectangular fish tank has a base measuring $$90$$ inches by $$40$$ inches and is filled with water to a depth of $$24$$ inches. A solid block with a volume of $$7,200$$ cubic inches is completely submerged in the tank. By how many inches does the water level rise?

   • $$1$$
   • $$2$$
   • $$3$$
   • $$4$$

7. A $$4\times5\times6$$ solid block is made up of $$1\times1\times1$$ unit cubes. The entire outside surface of the block is painted blue. How many unit cubes have exactly one face painted blue?

   • $$52$$
   • $$56$$
   • $$60$$
   • $$64$$

8. A sociologist collected data from $$150$$ cities to investigate the relationship between average commute time and population density. The data showed that cities with higher population density tend to have longer average commute times. Which of the following conclusions is best supported by these results?

   • In cities, there is a positive association between population density and average commute time.
   • Increasing population density causes average commute times to increase.
   • Reducing population density will reduce average commute times.
   • Population density is the only factor affecting average commute time.

9. The graph shows the gas mileage for Car $$Y$$ at different speeds. Based on the graph, how many gallons of gas are needed to drive Car $$Y$$ for $$6$$ hours at a constant speed of $$40$$ miles per hour?

   • $$4$$
   • $$5$$
   • $$6$$
   • $$8$$

10. Marcus works at a call center. The graph shows the average number of calls he answered per hour during his $$7$$-hour work shift. What is the total number of calls he answered during his shift?

    • $$46$$
    • $$62$$
    • $$54$$
    • $$45$$