Mini Exam 24 — Timed Mini Exams

Questions in this quiz (10)

1. Line $$p$$ is parallel to line $$q$$. A transversal line $$r$$ intersects line $$p$$ at point $$C$$ and line $$q$$ at point $$D$$. The measure of the angle formed above line $$p$$ and to the right of transversal $$r$$ is $$(2x+30)^\circ$$. The measure of the angle formed below line $$q$$ and to the left of transversal $$r$$ is $$(x+80)^\circ$$. What is the value of $$x$$?

   • $$20$$
   • $$30$$
   • $$40$$
   • $$50$$

2. In a circle, a chord has a length of $$30$$ units. The radius of the circle is $$17$$ units. What is the distance from the center of the circle to the chord?

   • $$7$$
   • $$8$$
   • $$9$$
   • $$10$$

3. Which of the following expressions is equivalent to $$(x-6)^2-16$$?

   • $$(x-10)(x-2)$$
   • $$(x-8)(x-4)$$
   • $$(x-6)(x+6)$$
   • $$(x-4)(x+4)$$

4. A random sample of $$600$$ middle school students was surveyed about their favorite type of extracurricular activity. Based on the survey results, it was estimated that $$55\%$$ of all middle school students prefer sports activities, with an associated margin of error of $$4\%$$. Based on the estimate and associated margin of error, which of the following is the most appropriate conclusion about all middle school students?

   • Exactly $$55\%$$ of all middle school students prefer sports activities.
   • It is plausible that between $$51\%$$ and $$59\%$$ of all middle school students prefer sports activities.
   • More than $$59\%$$ of all middle school students prefer sports activities.
   • Less than $$51\%$$ of all middle school students prefer sports activities.

5. The equation $$\frac{1}{a}+\frac{1}{b}=\frac{1}{c}$$ relates the positive numbers $$a$$, $$b$$, and $$c$$. Which equation correctly expresses $$c$$ in terms of $$a$$ and $$b$$?

   • $$c=a+b$$
   • $$c=ab$$
   • $$c=\frac{a+b}{ab}$$
   • $$c=\frac{ab}{a+b}$$

6. $$\sqrt{x+y}=6$$ $$x^2-y^2=132$$ Consider the system of equations, where $$x$$ and $$y$$ are real numbers. If $$(x,y)$$ is a solution to the system, what is the value of $$x$$?

   • $$18$$
   • $$\frac{132}{7}$$
   • $$22$$
   • $$\frac{119}{6}$$

7. Two cubes are such that the surface area of the larger cube is $$16$$ times the surface area of the smaller cube. What is the ratio of the volume of the larger cube to the volume of the smaller cube?

   • $$16$$
   • $$32$$
   • $$64$$
   • $$128$$

8. A factory produces $$M$$ items in $$T$$ hours. If the factory increases its production rate by $$50\%$$, how many hours will it take to produce $$2M$$ items?

   • $$\frac{2}{3}T$$
   • $$\frac{4}{3}T$$
   • $$\frac{3}{2}T$$
   • $$2T$$

9. A factory produces two types of devices, Device A and Device B. Manufacturing Device A requires $$2$$ hours of machine time and $$3$$ kg of raw material. Manufacturing Device B requires $$5$$ hours of machine time and $$1$$ kg of raw material. The factory has a maximum of $$120$$ machine hours available per day and $$60$$ kg of raw material available per day. The factory must produce at least $$12$$ devices in total each day. What is the maximum number of Device B units that the factory can produce in a day?

   • $$18$$
   • $$20$$
   • $$22$$
   • $$24$$

10. A large cylindrical water tank with a maximum capacity of $$8000$$ liters is initially empty. Water is pumped into the tank at a rate of $$250$$ liters per minute for the first $$20$$ minutes. Then the rate is increased to $$400$$ liters per minute for the next $$15$$ minutes. Finally, the rate is reduced to $$200$$ liters per minute for the next $$25$$ minutes. Based on the graph, what is the total time, in minutes, it will take to fill the tank to its maximum capacity?

    • $$45$$
    • $$55$$
    • $$65$$
    • $$60$$