Advanced Quizzes — Quiz 13

Questions in this quiz (10)

1. In right triangle $$\triangle ABC$$, $$\angle C=90^\circ$$. If $$\sin A=\frac{8}{17}$$ and the perimeter of the triangle is $$180$$ units, what is the area of $$\triangle ABC$$ in square units?

   • 720
   • 840
   • 1080
   • 1215

2. In right triangle $$ABC$$, the right angle is at vertex $$C$$. Point $$D$$ is on $$\overline{AB}$$ and point $$E$$ is on $$\overline{BC}$$ such that $$\overline{DE}\parallel\overline{AC}$$. The length of $$\overline{BC}$$ is $$40$$ units, and the length of $$\overline{CE}$$ is $$24$$ units. The area of trapezoid $$ACED$$ is $$336$$ square units. What is the length of $$\overline{DE}$$?

   • 8

3. A right circular cylinder has radius $$r$$ and height $$h$$. A right circular cone has radius $$3r$$ and height $$H$$. If the volume of the cone is four times the volume of the cylinder, what is $$H$$ in terms of $$h$$?

   • $$\frac{4}{3}h$$
   • $$\frac{3}{2}h$$
   • $$\frac{4}{9}h$$
   • $$\frac{12}{9}h$$

4. The graph of the quadratic function $$f(x)=x^2+bx+c$$ in the $$xy$$-plane has its vertex on the line $$y=-3x+5$$. If the graph intersects the $$x$$-axis at exactly one point, what is the value of $$b+c$$?

   • $$-\frac{5}{4}$$
   • $$\frac{3}{4}$$
   • $$\frac{5}{4}$$
   • $$-\frac{5}{9}$$

5. Researchers conducted a clinical trial to evaluate the effectiveness of a new dietary supplement designed to improve concentration. They recruited $$500$$ participants and randomly assigned them to two groups. Group A received the supplement, while Group B received a placebo. After $$10$$ weeks, Group A showed significantly greater improvement on concentration tests than Group B. However, investigators later discovered that Group A participants also averaged substantially more sleep per night during the study period. Based on this information, which of the following is the most significant limitation in concluding that the supplement caused the improvement in concentration?

   • The sample size may not be large enough.
   • The placebo effect may still influence results.
   • Increased sleep acts as a confounding variable.
   • The study lasted too few weeks.

6. Two manufacturing plants, Plant A and Plant B, produce identical batteries. Plant A produces batteries at a rate that is $$40\%$$ greater than Plant B. Historical data shows that $$3\%$$ of batteries from Plant A are defective, while $$8\%$$ of batteries from Plant B are defective. The two plants operate for the same amount of time. If the plants produce a combined total of $$4,556$$ non-defective batteries on a certain day, how many batteries did Plant A produce?

   • 2800

7. $$x^2+y^2=50$$$$y=2x-5$$The system of equations has two solutions $$(x_1,y_1)$$ and $$(x_2,y_2)$$. What is the product of the $$y$$-coordinates of the two solutions?

   • $$-25$$
   • $$-35$$
   • $$0$$
   • $$25$$

8. In the given system of equations, $$k$$ and $$m$$ are constants. $$\frac{5}{6}x-\frac{7}{4}y=3x+2$$ $$ky+mx=5m-\frac{3}{2}y$$ I. $$10m-3k=0$$ II. $$m\ne0$$ III. $$k=-\frac{3}{2}$$ If the system has no solution, which of the following must be true?

   • I only
   • II only
   • I and II only
   • I, II, and III

9. The population of a certain species of birds in a wildlife reserve can be modeled by an exponential function of the form $$P(t)=P_0(1+r)^t$$, where $$P(t)$$ is the population after $$t$$ years. In the year $$2012$$, the population was estimated to be $$1,600$$ birds. In the year $$2018$$, the population was estimated to be $$2,560$$ birds. If the population continues to grow according to this model, what is the predicted population in the year $$2030$$?

   • 4,096
   • 5,120
   • 6,553.6
   • 10,485.76

10. In the $$xy$$-plane, the graph of the line with equation $$y=4x+k$$ is tangent to the graph of the parabola with equation $$y=x^2-6x+11$$, where $$k$$ is a constant. What is the value of $$k$$?

    • -14