Advanced Quizzes — Quiz 8

Questions in this quiz (10)

1. In triangle $$ABC$$, the sum of the measures of angle $$A$$ and angle $$B$$ is $$90$$ degrees. The value of $$\sin(A)$$ is $$\frac{2\sqrt{7}}{8}$$. What is the value of $$\cos(B)$$?

   • $$\frac{2\sqrt{7}}{8}$$
   • $$\frac{2\sqrt{7}}{6}$$
   • $$\frac{6\sqrt{2}}{14}$$
   • $$\frac{8}{23\sqrt{2}}$$

2. A container in the shape of a right circular cylinder is just large enough to fit exactly $$3$$ tennis balls, each with a radius of $$2$$ inches. If the container were emptied out and filled to the top with water, what would be the volume of water, in cubic inches, held by the container?

   • $$16\pi$$
   • $$24\pi$$
   • $$32\pi$$
   • $$48\pi$$

3. A rectangular storage container has an outer length of $$14$$ inches, an outer width of $$12$$ inches, and an outer height of $$5$$ inches. The floor and all four walls are each $$1$$ inch thick. How many one-inch cubic blocks can fit completely inside the container?

   • $$240$$
   • $$288$$
   • $$360$$
   • $$480$$

4. In the $$xy$$-plane, the graph of the equation $$(x-4)^2+(y+3)^2=36$$ is a circle. Which of the following points lies on the circle?

   • $$(4,-3)$$
   • $$(10,-3)$$
   • $$(4,3)$$
   • $$(0,0)$$

5. The area of a triangle is $$3x^2$$ square units. The base is $$x+6$$ units, and the height is $$x$$ units. What is the value of $$x$$?

   • $$\frac{3}{2}$$
   • $$6$$
   • $$8$$
   • $$\frac{6}{5}$$

6. A circle in the $$xy$$-plane has center $$(5,-2)$$ and radius $$13$$. An equation of this circle is $$x^2+y^2+ax+by+c=0$$ where $$a$$, $$b$$, and $$c$$ are constants. What is the value of $$c$$?

   • $$-140$$
   • $$-120$$
   • $$-100$$
   • $$-80$$

7. Sphere $$A$$ has radius $$4x$$ and sphere $$B$$ has radius $$20x$$. The volume of sphere $$B$$ is how many times the volume of sphere $$A$$?

   • $$25$$
   • $$64$$
   • $$125$$
   • $$250$$

8. In the figure, lines $$l$$, $$m$$, and $$n$$ are parallel. What is the value of $$x+y$$?

   • 240

9. In the figure below, $$AB\parallel GH$$ and $$DF\parallel BC$$. Also, $$DE=2$$, $$EH=6$$, $$EG=4$$, and $$HC=15$$. What is the length of $$AD$$?

   • $$3$$
   • $$4$$
   • $$\frac{16}{3}$$
   • $$6$$

10. A bakery requires that each loaf of bread weigh between $$15\frac{3}{4}$$ ounces and $$16\frac{1}{4}$$ ounces, inclusive. If $$w$$ is the weight of a loaf of bread, which of the following inequalities correctly represents the acceptable values of $$w$$?

    • $$|w-16|\le\frac{1}{4}$$
    • $$|w-16|\le\frac{1}{2}$$
    • $$|w-15\frac{3}{4}|\le\frac{1}{4}$$
    • $$|w-16\frac{1}{4}|\le\frac{1}{2}$$