Mini Exam 3 — Timed Mini Exams

Questions in this quiz (10)

1. A bag contains $$3$$ red, $$5$$ blue, and $$2$$ green balls. Two balls are drawn without replacement. What is the probability that both balls are blue?

   • $$\frac{2}{9}$$
   • $$\frac{1}{5}$$
   • $$\frac{5}{18}$$
   • $$\frac{5}{9}$$

2. A car travels $$180$$ miles at an average speed of $$60$$ mph, then stops for $$30$$ minutes, and continues another $$60$$ miles at an average speed of $$40$$ mph. What is the car’s average speed for the entire trip, including the stop?

   • $$40$$
   • $$42$$
   • $$45$$
   • $$48$$

3. A car’s value decreases by $$10\%$$ each year. After $$2$$ years, the car is worth $$16200$$ dollars. What was the car’s original value?

   • $$18,000$$
   • $$19,000$$
   • $$20,000$$
   • $$22,000$$

4. A trapezoid has bases of lengths $$x$$ and $$x+4$$ and a height of $$8$$. If the area of the trapezoid is $$96$$ square units, what is the value of $$x$$?

   • $$8$$
   • $$10$$
   • $$12$$
   • $$14$$

5. In a right triangle, the hypotenuse is $$15$$, and one leg is $$9$$. Let $$\theta$$ be the angle opposite the leg of length $$9$$. If $$\sin\theta+\cos\theta=\frac{m}{n},$$ where $$m$$ and $$n$$ are relatively prime positive integers, what is the value of $$m+n$$?

   • $$5$$
   • $$7$$
   • $$12$$
   • $$15$$

6. A line has slope $$-\frac{3}{2}$$ and passes through the point $$(2,1)$$. Which of the following equations represents a line parallel to this line and passing through the point $$(4,-2)$$?

   • $$y+2=-\frac{3}{2}(x-4)$$
   • $$y-1=-\frac{2}{3}(x-2)$$
   • $$y+2=\frac{3}{2}(x-4)$$
   • $$y=-\frac{3}{2}x+4$$

7. $$|2x-5|\le|x+1|$$Which of the following describes the solution set?

   • $$\left(\frac{5}{2},\infty\right)$$
   • $$[\frac{4}{3},6]$$
   • $$\left(-\infty,6\right)$$
   • $$\left[6,\infty\right)$$

8. $$|x-3|+|x+1|=8$$How many distinct solutions does this equation have?

   • $$1$$
   • $$2$$
   • Infinitely many solutions
   • No Solution

9. $$4x+7y=18$$$$20x+35y=90$$A system of equations is shown. For each real number $$r,$$ which of the following points lies on the graph of each equation in the $$xy$$-plane for the given system?

   • $$(r,-\frac{4r}{7}+\frac{18}{7})$$
   • $$(r,-\frac{7r}{4}+\frac{18}{4})$$
   • $$(r,\frac{4r}{7}+\frac{18}{7})$$
   • $$(\frac{7r}{4}+\frac{18}{4},r)$$

10. Circle $$P$$ has equation $$\left(x+3\right)^2+\left(y-4\right)^2=25$$. In the $$xy$$-plane, circle $$Q$$ is obtained by translating circle $$P$$ left $$5$$ units. Which equation represents circle $$Q$$?

    • $$\left(x+8\right)^2+\left(y-4\right)^2=25$$
    • $$\left(x-2\right)^2+\left(y-4\right)^2=25$$
    • $$\left(x+3\right)^2+\left(y+1\right)^2=25$$
    • $$\left(x+3\right)^2+\left(y-9\right)^2=25$$