Mini Exam 4 — Timed Mini Exams

Questions in this quiz (10)

1. $$\sqrt[3]{18m(\sqrt[4]{18m})^{6}}$$For what value of $$w$$ is the given expression equivalent to $$(18m)^{12w},$$ where $$m\gt1$$?

   • $$\frac{5}{6}$$
   • $$\frac{5}{18}$$
   • $$\frac{5}{72}$$
   • $$\frac{18}{5}$$

2. $$5w^2-6=2w+7$$Which of the following is a solution to the equation above?

   • $$\frac{1-\sqrt{66}}{5}$$
   • $$\frac{1+\sqrt{7}}{5}$$
   • $$\frac{1+\sqrt{13}}{5}$$
   • $$\frac{1+\sqrt{33}}{5}$$

3. $$2|7-p|+5|7-p|=63$$What is the positive solution to the given equation?

   • $$2$$
   • $$7$$
   • $$9$$
   • $$16$$

4. The function $$f$$ is defined by $$f(x)=\frac{x+4}{x-3}.$$ Which of the following defines the function $$g$$ such that $$g(x)=f(x-2)$$?

   • $$g(x)=\frac{x+6}{x-1}$$
   • $$g(x)=\frac{x+2}{x-5}$$
   • $$g(x)=\frac{x+4}{x-5}$$
   • $$g(x)=\frac{x-2}{x-5}$$

5. Triangle $$ABC$$ is similar to triangle $$DEF$$, where $$A$$ corresponds to $$D$$ and $$C$$ corresponds to $$F$$. Angles $$C$$ and $$F$$ are right angles. If $$\sin(A)=\frac{\sqrt{3}}{2}$$ and $$EF=30$$, what is the length of $$DF$$?

   • $$10$$
   • $$15$
   • $$10\sqrt{3}$$
   • $$15\sqrt{3}$$

6. $$\frac{9x^2-n}{3x-p}$$In the expression above, $$p$$ and $$n$$ are positive integers. If the expression is equivalent to $$3x+p$$ and $$x\ne\frac{p}{3}$$, which of the following could be the value of $$n$$?

   • $$n=p^2$$
   • $$n=2p^2$$
   • $$n=\frac{p^2}{2}$$
   • $$n=\frac{3p^2}{2}$$

7. A researcher surveyed $$800$$ randomly selected US residents about their views on the use of remote work. The table below summarizes the responses:Preferences for Remote WorkIf the population of the United States was $$340$$ million when the survey was conducted, based on the sample data of $$800$$ US residents, what is the best estimate, in millions, of the difference between the number of US residents who somewhat or strongly support remote work and the number of those who somewhat or strongly oppose it?

   • $$52$$
   • $$80$$
   • $$102$$
   • $$240$$

8. In the $$(x,y)$$-plane, the graph of line $$m$$ has a slope of $$2$$. Line $$n$$ is perpendicular to line $$m$$ and passes through the point $$(4,8)$$. What is the sum of the $$x$$- and $$y$$-intercepts of line $$n$$?

   • $$30$$
   • $$-10$$
   • $$20$$
   • $$10$$

9. The point with coordinates $$(k,6)$$ lies on the line shown. What is the value of $$k$$?

   • $$\frac{5}{4}$$
   • $$\frac{16}{5}$$
   • $$\frac{4}{5}$$
   • $$6$$

10. A market research firm surveyed $$300$$ laptop users about their laptop brand and its primary use. The results are summarized in the table below.Laptop Usage by Brand and PurposeBased on the survey data, what is the probability that a user who primarily uses their laptop for entertainment owns a Brand B laptop?

    • $$\frac{10}{17}$$
    • $$\frac{17}{85}$$
    • $$\frac{7}{17}$$
    • $$\frac{12}{17}$$