Advanced Quizzes — Quiz 23

Questions in this quiz (10)

1. A set of $$13$$ distinct positive integers has a mean of $$48$$ and a median of $$41$$. If the largest number in the set is increased by $$26$$, which of the following statements about the new set must be true?

   • The median of the new set is greater than $$41$$.
   • The range of the new set increases by $$13$$.
   • The mean of the new set is smaller than $$49$$.
   • The standard deviation of the new set is greater than the standard deviation of the original set.

2. The temperature $$T$$, in degrees Fahrenheit, of a chemical solution $$t$$ minutes after cooling begins is modeled by the function $$T(t)=68+240e^{-0.08t}$$ According to the model, what is the initial temperature of the solution, and what temperature does the solution approach as $$t$$ increases indefinitely?

   • Initial: $$68^\circ F$$ Approaching: $$240^\circ F$$
   • Initial: $$240^\circ F$$Approaching: $$68^\circ F$$
   • Initial: $$308^\circ F$$ Approaching: $$68^\circ F$$
   • Initial: $$308^\circ F$$ Approaching: $$240^\circ F$$

3. In triangle $$\triangle ABC$$, point $$D$$ lies on side $$BC$$ such that $$AD$$ bisects $$\angle BAC$$. If $$AB=8$$, $$AC=12$$, and the area of $$\triangle ABD$$ is $$20$$, what is the area of $$\triangle ACD$$?

   • $$24$$
   • $$30$$
   • $$36$$
   • $$40$$

4. Which of the following expressions is equivalent to $$\frac{1}{x-1}-\frac{1}{x+1}-\frac{2}{x^2+1}-\frac{4}{x^4+1}-\frac{8}{x^8+1}$$ for all $$x$$ > $$1$$?

   • $$\frac{16}{x^{16}-1}$$
   • $$\frac{16}{x^{16}+1}$$
   • $$\frac{8}{x^{16}-1}$$
   • $$\frac{1}{x-1}-\frac{8}{x^8+1}$$

5. The graph of the quadratic equation $$y=x^2+ax+b$$ intersects the graph of the line $$y=4x-5$$ at exactly one point. If this point of intersection is $$(p,q)$$, and it is given that $$a^2-4b=36$$, what is the value of $$p$$?

   • $$-3$$
   • $$0$$
   • $$3$$
   • $$6$$

6. Quantity $$A$$ is $$60\%$$ greater than quantity $$B$$. Quantity $$C$$ is $$30\%$$ less than quantity $$A$$. Quantity $$D$$ is $$35\%$$ of quantity $$B$$. To the nearest whole percent, what percentage of quantity $$C$$ is quantity $$D$$?

   • $$24\%$$
   • $$28\%$$
   • $$31\%$$
   • $$35\%$$

7. The numbers $$x$$, $$y$$, and $$z$$ are positive constants, where $$y$$ > $$z$$. The number $$x$$ is $$1,400\%$$ more than the positive difference between $$y$$ and $$z$$, and $$z$$ is $$72\%$$ of $$y$$. If $$x$$ is $$p\%$$ greater than $$z$$, and $$z$$ is $$w\%$$ of $$x$$, what is the value of $$pw$$ to the nearest integer?

   • 8286

8. In a circle with center $$O$$, chord $$AB$$ has length $$12$$. The perpendicular distance from the center $$O$$ to chord $$AB$$ is $$5$$. Another chord $$CD$$ is parallel to $$AB$$, and the distance between $$AB$$ and $$CD$$ is $$2$$. Both chords lie on the same side of the center $$O$$. What is the length of chord $$CD$$?

   • $$4\sqrt{7}$$
   • $$2\sqrt{39}$$
   • $$8\sqrt{2}$$
   • $$4\sqrt{13}$$

9. In right triangle $$ABC$$, $$\angle C$$ is a right angle. Point $$D$$ lies on side $$AB$$, and point $$E$$ lies on side $$BC$$ such that $$DE\parallel AC$$. The length of $$BC$$ is $$24$$ units, the length of $$BE$$ is $$15$$ units, and the area of $$\triangle BDE$$ is $$75$$ square units. What is the area of trapezoid $$ACED$$, in square units?

   • 117

10. A linear function $$f$$ has the property that for every increase of $$3$$ in the value of $$x$$, the value of $$f(x)$$ decreases by $$8$$. If $$f(6)=11$$, what is the $$x$$-intercept of the graph of $$y=f(x)$$?

    • $$\frac{33}{8}$$
    • $$\frac{81}{8}$$
    • $$\frac{57}{8}$$
    • $$\frac{99}{8}$$