Advanced Quizzes — Quiz 25

Questions in this quiz (13)

1. The graph shows a function $$f$$ that is a transformation of the parent square root function $$y=\sqrt{x}$$. The graph starts at the point $$(3,-2)$$ and passes through the point $$(12,4)$$. What is the value of $$f(28)$$?

   • $$6$$
   • $$7$$
   • $$8$$
   • $$10$$

2. The shaded region in the $$xy$$-plane represents the solution set for which system of inequalities?

   • $$y\le-\frac{3}{4}x+5$$$$y$$ > $$\frac{3}{2}x+2$$
   • $$y\le-\frac{16}{11}x+8$$$$y$$ > $$\frac{4}{5}x+2$$
   • $$y\ge-\frac{5}{4}x+5$$$$y$$ < $$\frac{3}{5}x+8$$
   • $$y\ge-\frac{11}{2}x+5$$$$y$$ < $$\frac{5}{4}x+8$$

3. A circle in the coordinate plane has its center on the line $$y=x-2$$. The circle is tangent to the $$x$$-axis at the point $$(5,0)$$. Which of the following is the equation of the circle?

   • $$(x-5)^2+(y-3)^2=9$$
   • $$(x-5)^2+(y-3)^2=25$$
   • $$(x-5)^2+(y+3)^2=9$$
   • $$(x-3)^2+(y-5)^2=25$$

4. A data set consists of $$21$$ distinct real numbers with mean $$\mu$$ and standard deviation $$\sigma$$. A new data set is formed by multiplying each number by $$-4$$ and then adding $$7$$. Which of the following must be true about the new data set?

   • The new mean is $$-4\mu+7$$ and the new standard deviation is $$4\sigma$$.
   • The new mean is $$-4\mu+7$$ and the new standard deviation is $$-4\sigma$$.
   • The new mean is $$4\mu+7$$ and the new standard deviation is $$4\sigma$$.
   • The new mean is $$-4\mu$$ and the new standard deviation is $$4\sigma-7$$.

5. A regular octagon is inscribed in a circle of radius $$10$$. A smaller circle is inscribed in the octagon. What is the area of the region that lies inside the octagon but outside the smaller circle? Round to the nearest hundredth.

   • $$82.84$$
   • $$117.16$$
   • $$165.69$$
   • $$14.70$$

6. The volume $$V$$ of a cone is given by $$V=\frac{1}{3}\pi r^2h$$ A company redesigns a cone-shaped container by increasing its radius by $$60\%$$ and decreasing its height by $$25\%$$. What is the ratio of the volume of the new container to the volume of the original container?

   • $$48:25$$
   • $$64:25$$
   • $$96:25$$
   • $$192:25$$

7. In the coordinate plane, the vertices of $$\triangle PQR$$ are $$P(1,4)$$, $$Q(7,1)$$, and $$R(x,13)$$. The area of $$\triangle PQR$$ is $$42$$. If $$x$$ > $$7$$, what is the value of $$x$$?

   • 11

8. In the coordinate plane, $$\triangle ABC$$ has vertices $$A(0,0)$$, $$B(8,0)$$, and $$C(14,6)$$. Line $$m$$ passes through $$A$$ and is parallel to $$BC$$. Line $$n$$ passes through $$B$$ and is parallel to $$AC$$. The lines intersect at point $$D$$. What is the $$y$$-coordinate of point $$D$$?

   • -6

9. A data set consists of $$17$$ distinct numbers arranged in ascending order. The mean is $$24$$ and the median is $$19$$. A new data set is created by increasing each of the $$8$$ numbers greater than the median by $$k$$ and decreasing each of the $$8$$ numbers less than the median by $$k$$, where $$k$$ > $$0$$. Which of the following statements must be true?

   • Only the mean remains unchanged.
   • Only the median remains unchanged.
   • Both the mean and the median remain unchanged.
   • The standard deviation remains unchanged.

10. If $$a$$ and $$b$$ are positive numbers such that $$\frac{a}{b}+\frac{b}{a}=10$$, what is the value of $$\frac{a^3}{b^3}+\frac{b^3}{a^3}$$?

    • $$820$$
    • $$970$$
    • $$980$$
    • $$990$$

11. In $$\triangle ABC$$, $$AD$$ is the angle bisector of $$\angle BAC$$, with point $$D$$ on $$BC$$. Through $$D$$, a line parallel to $$AB$$ intersects $$AC$$ at point $$E$$. If $$\angle ABC=75^\circ$$ and $$\angle ACB=45^\circ$$, what is the measure of $$\angle CED$$?

    • $$45^\circ$$
    • $$60^\circ$$
    • $$75^\circ$$
    • $$90^\circ$$

12. The polynomial $$P(x)=125x^3-nk^3$$ has a factor of $$5x-2k$$, where $$n$$ and $$k$$ are constants and $$k>0$$. What is the value of $$n$$?

    • $$8$$

13. Three machines, $$A$$, $$B$$, and $$C$$, produce electronic components. Machine $$A$$ produces components at a rate that is $$r$$ times the rate of Machine $$B$$. Machine $$C$$ produces components at a rate that is $$s$$ times the rate of Machine $$A$$. If Machine $$B$$ produces $$P$$ components in $$Q$$ hours, which expression represents the total number of components all three machines can produce working together for $$T$$ hours?

    • $$\frac{PT}{Q}(1+r+s)$$
    • $$\frac{PT}{Q}(1+r+rs)$$
    • $$\frac{PT}{Q}(r+s+rs)$$
    • $$\frac{PT}{Q}(1+rs)$$