Mini Exam 10 — Timed Mini Exams

Questions in this quiz (10)

1. Sphere $$A$$ has a radius of $$4k$$ and sphere $$B$$ has a radius of $$20k$$, where $$k$$ is a positive constant. The volume of sphere $$B$$ is how many times the volume of sphere $$A$$?

   • $$125$$
   • $$1000$$
   • $$25$$
   • $$5$$

2. Line $$k$$ is defined by $$4y-8x=16$$. Line $$m$$ is perpendicular to line $$k$$ in the $$xy$$-plane. What is the slope of line $$m$$?

   • $$-2$$
   • $$-\frac{1}{4}$$
   • $$\frac{1}{2}$$
   • $$-\frac{1}{2}$$

3. A data set of $$20$$ integers has a mean of $$50$$. A new data set is formed by including one additional integer, $$w$$. Let $$S_1$$ be the standard deviation of the new data set if $$w=30$$, and let $$S_2$$ be the standard deviation of the new data set if $$w=80$$. Which of the following best describes the relationship between $$S_1$$ and $$S_2$$?

   • The relationship cannot be determined from the information given
   • $$S_1$$ < $$S_2$$
   • $$S_1=S_2$$
   • $$S_1$$ > $$S_2$$

4. Triangle $$ABC$$ is similar to triangle $$DEF$$, where angle $$B$$ corresponds to angle $$E$$ and angle $$C$$ corresponds to angle $$F$$. Angles $$C$$ and $$F$$ are right angles. If $$\tan(A)=\frac{5}{12}$$, what is the value of $$\tan(D)$$?

   • $$\frac{5}{13}$$
   • $$\frac{12}{5}$$
   • $$\frac{5}{12}$$
   • $$\frac{13}{12}$$

5. A container is made from a cylindrical base and a hemispherical top that share the same circular base. The total height of the container is $$5$$ times the radius of the base. If the total volume of the container is $$252\pi$$ cubic feet, what is the radius, $$r$$, of the base in feet?

   • $$\sqrt[3]{81}$$
   • $$\sqrt[3]{64}$$
   • $$\sqrt[3]{54}$$
   • $$\sqrt[3]{27}$$

6. A table shows the results of two different surveys, $$A$$ and $$B$$, that were conducted to estimate the proportion of students at a large university who prefer online classes. Random samples were selected from the same population, and the margins of error were calculated using the same method.Based on the table, which survey most likely used the larger sample size?

   • $$A$$
   • Both surveys used the same sample size
   • $$B$$
   • It cannot be determined from the information given

7. The table below gives selected values of a polynomial function $$g$$.Based on the values in the table, which of the following must be a factor of $$g$$?

   • $$(x+4)(x-3)$$
   • $$(x+4)(x+3)$$
   • $$(x+1)(x-5)$$
   • $$(x-4)(x+3)$$

8. Line $$m$$ in the $$xy$$-plane is perpendicular to the line with equation $$x=4$$. What is the slope of line $$m$$?

   • Undefined
   • $$0$$
   • $$-1$$
   • $$1$$

9. Solve the equation:$$8(x-3)=24(x+5)(x-3).$$What is the sum of the solutions to the given equation?

   • $$-\frac{8}{3}$$
   • $$\frac{5}{3}$$
   • $$-\frac{5}{3}$$
   • $$-\frac{1}{3}$$

10. The function $$h(t)=-4(t-3)^2+36$$ models the height of a frog, $$h(t)$$, in feet above the ground, $$t$$ seconds after it jumps, where $$0\le t\le6$$. Which of the following is the best interpretation of the vertex of the graph of $$y=h(t)$$ in the $$ty$$-plane?

    • At $$t=6$$ seconds, the frog is at its maximum height of $$36$$ feet.
    • At $$t=3$$ seconds, the frog is at its minimum height of $$36$$ feet.
    • At $$t=3$$ seconds, the frog is at its maximum height of $$36$$ feet.
    • At $$t=0$$ seconds, the frog is at its maximum height of $$36$$ feet.