Mini Exam 16 — Timed Mini Exams

Questions in this quiz (10)

1. $$510$$ is $$85\%$$ of what number?

   • $$433.5$$
   • $$600$$
   • $$76.5$$
   • $$423.5$$

2. $$\frac{3(x-2)}{x+4}=2-\frac5{x+4}$$What is the solution to the equation above?

   • $$4$$
   • $$9$$
   • $$2$$
   • $$11$$

3. Data set $$A$$ consists of $$60$$ integers between $$300$$ and $$500$$. Data set $$B$$ consists of all the integers in data set $$A$$ as well as the integer $$50$$. Which of the following must be greater for data set $$B$$ than for data set $$A$$?I. The meanII. The median

   • I only
   • II only
   • I and II
   • Neither I nor II

4. The solutions to $$x^2 + 4x + 5 = 0$$ are $$a$$ and $$b$$, where $$a$$ < $$b$$. The solutions to $$x^2 + 10x + 21 = 0$$ are $$c$$ and $$d$$, where $$c$$ < $$d$$. The solutions to $$x^2 + 14x + k = 0$$, where $$k$$ is a constant, are $$a + c$$ and $$b + d$$. What is the value of $$k$$?

   • $$40$$
   • $$21$$
   • $$66$$
   • $$60$$

5. A wildlife reserve covers $$310$$ acres. To estimate how many shrubs grow in the reserve, a botanist randomly selects $$6$$ different $$1$$-acre plots and counts the number of shrubs in each one. The numbers of shrubs in the sample plots are $$38, 42, 55, 47, 61,$$ and $$50$$. Based on the mean of the sample, which of the following ranges is the best estimate for the total number of shrubs in the entire reserve?

   • $$11,000$$ to $$12,000$$
   • $$12,000$$ to $$13,500$$
   • $$14,000$$ to $$15,500$$
   • $$18,000$$ to $$19,500$$

6. In $$1804$$, Lewis and Clark began their expedition across the western territories of the United States. Suppose one member of the expedition rode on horseback from one camp to another. If the rider had traveled straight without stopping, he would have covered $$15$$ miles in $$40$$ minutes. In such a ride, what would the average speed of his horse have been, to the nearest tenth of a mile per hour?

   • $$15.5$$
   • $$21.5$$
   • $$22.5$$
   • $$19.5$$

7. Which of the following functions has a maximum value at $$5$$?I. $$f(x) = -4(2)^x + 5$$II. $$g(x) = 5(0.5)^x + 5$$

   • I only
   • II only
   • I and II
   • Neither I nor II

8. A conical cup is shown above. Its volume (in cubic centimeters) is given by $$V=\frac{5\pi h^3}{54}$$, where $$h$$ represents the height of the cup in centimeters. The cup can hold a maximum volume of $$360$$ cubic centimeters. What is the approximate value of $$h$$ in centimeters?

   • $$8.50$$
   • $$10.74$$
   • $$12.00$$
   • $$15.75$$

9. In the $$xy$$-plane, a line with equation $$3y=k$$ for some constant $$k$$ intersects a parabola at exactly one point. If the parabola has equation $$y=-x^2+8x$$, what is the value of $$k$$?

   • 12
   • 24
   • 48
   • 16

10. At a science fair, there are a total of $$320$$ participants. Each participant is assigned to either Team $$X$$, Team $$Y$$, or Team $$Z$$. If one of these participants is selected at random, the probability that the participant is assigned to Team $$X$$ is $$0.37$$, and the probability that the participant is assigned to Team $$Y$$ is $$0.28$$. How many participants are assigned to Team Z?

    • $$112$$
    • $$118$$
    • $$90$$
    • $$208$$