Advanced Quizzes — Quiz 24

Questions in this quiz (10)

1. The kinetic energy $$K$$ of an object is given by the formula $$K=\frac{1}{2}mv^2$$ where $$m$$ is the mass of the object and $$v$$ is its speed. A scientist compares two drones. Drone A has mass $$m$$ and speed $$v$$. Drone B has mass that is one-fourth the mass of Drone A and speed that is eight times the speed of Drone A. What is the ratio of the kinetic energy of Drone B to the kinetic energy of Drone A?

   • $$8:1$$
   • $$16:1$$
   • $$24:1$$
   • $$32:1$$

2. The graph of the quadratic function $$f(x)=ax^2+bx+c$$ has $$x$$-intercepts at $$(-3,0)$$ and $$(7,0)$$. The minimum value of the function is $$-40$$. What is the value of $$c$$?

   • $$-\frac{168}{5}$$
   • $$-\frac{7}{5}$$
   • $$\frac{7}{5}$$
   • $$\frac{8}{5}$$

3. A research team investigated the relationship between average nightly sleep and standardized test performance among high school students. They surveyed $$500$$ students from several schools and asked each student to self-report their average hours of sleep during the school year. The researchers then compared the reported sleep averages with the students' SAT scores and found that students who reported sleeping at least $$8$$ hours per night tended to have higher SAT scores on average than students who reported sleeping fewer than $$8$$ hours. Based on the design and findings of this study, which conclusion is most appropriate?

   • Sleeping at least $$8$$ hours per night directly causes higher SAT scores in high school students.
   • High school students should sleep at least $$8$$ hours per night to guarantee higher SAT scores.
   • There is an association between higher reported sleep duration and higher SAT scores among the students observed in the study.
   • Sleep duration is the primary factor that determines SAT performance in high school students.

4. A recent national poll surveyed $$2,400$$ likely voters and found that $$54\%$$ of respondents planned to vote for Candidate X in an upcoming election. The poll reported a margin of error of $$2$$ percentage points. If there are an estimated $$180$$ million likely voters nationwide, which of the following could plausibly represent the number of likely voters who plan to vote for Candidate X?

   • $$86,400,000$$
   • $$90,000,000$$
   • $$100,800,000$$
   • $$108,000,000$$

5. A data set consists of $$17$$ distinct positive integers. The mean of the data set is $$52$$, and the median is $$47$$. A new integer, $$k$$, is added to the data set, and the mean of the $$18$$ integers becomes $$55$$. Which of the following statements must be true?

   • The new median is greater than $$47$$, and the new standard deviation is greater than the original standard deviation.
   • The new median is less than $$47$$, and the new standard deviation is greater than the original standard deviation.
   • The new median is greater than $$47$$, and the new standard deviation is less than the original standard deviation.
   • The new median is greater than $$47$$, but the change in standard deviation cannot be determined.

6. In the system of equations below, $$a$$ and $$c$$ are constants.$$\frac{3}{4}x-3y=9-\frac{9}{4}x$$$$ax+8y=c+2y$$If the system has infinitely many solutions, what is the value of $$a-c$$?

   • $$-24$$
   • $$-12$$
   • $$12$$
   • $$24$$

7. In $$\triangle ABC$$, $$AD$$ is the angle bisector of $$\angle BAC$$, with point $$D$$ on $$BC$$. A line segment through $$D$$ is drawn parallel to $$AB$$, intersecting $$AC$$ at point $$E$$. If the measure of $$\angle ABC$$ is $$80^\circ$$ and the measure of $$\angle ACB$$ is $$40^\circ$$, what is the measure of $$\angle CED$$?

   • $$40^\circ$$
   • $$50^\circ$$
   • $$60^\circ$$
   • $$80^\circ$$

8. The polynomial $$P(x)=64x^3-nk^3$$ has a factor of $$4x-k$$, where $$n$$ and $$k$$ are constants and $$k$$ > $$0$$. What is the value of $$n$$?

   • 1

9. A manufacturing company uses three conveyor systems, $$A$$, $$B$$, and $$C$$, to package products. Conveyor $$A$$ packages items at a rate that is $$p$$ times the rate of Conveyor $$B$$. Conveyor $$C$$ packages items at a rate that is $$q$$ times the rate of Conveyor $$A$$. If Conveyor $$B$$ packages $$R$$ items in $$T$$ minutes, which of the following expressions represents the total number of items all three conveyors can package together in $$W$$ minutes?

   • $$\frac{RW}{T}(1+p+q)$$
   • $$\frac{RW}{T}(1+p+pq)$$
   • $$\frac{RW}{T}(p+q+pq)$$
   • $$\frac{RW}{T}(1+pq)$$

10. In the figure shown, two concentric circles are centered at point $$O$$. A chord of the larger circle is tangent to the smaller circle. If the area of the larger circle is $$100\pi$$ square units and the length of the chord is $$16$$ units, what is the area of the smaller circle?

    • $$16\pi$$
    • $$25\pi$$
    • $$36\pi$$
    • $$64\pi$$