Advanced Quizzes — Quiz 2

Questions in this quiz (10)

1. The diagram on the left shows a wheel with a point marked on its rim. The wheel rolls along a flat, straight surface at a constant speed, moving from a starting location to an ending location. The graph on the right shows a function $$y=d(t)$$ plotted against time. Which of the following quantities could be represented by the graph of $$d(t)$$ as a function of time, beginning at the moment the wheel starts rolling?

   • The constant speed of the rolling wheel
   • The distance the wheel has traveled from its starting point
   • The distance between the marked point on the rim and the center of the wheel
   • The distance between the marked point on the rim and the ground

2. In the $$xy$$-plane, a circle has center $$(h,k)$$ and radius $$10$$. The circle intersects the $$x$$-axis at the points $$(2,0)$$ and $$(8,0)$$. In addition, the point $$(5,3)$$ lies inside the circle. What is the value of $$k$$?

   • $$\sqrt{91}$$
   • $$9$$
   • $$5$$
   • $$10$$

3. The polynomial function $$P(x)$$ has three distinct real roots. The sum of these roots is $$12$$. A new function $$Q(x)$$ is defined by $$Q(x)=P(3x-6)$$. What is the sum of the roots of $$Q(x)$$?

   • $$6$$
   • $$8$$
   • $$10$$
   • $$12$$

4. The system of linear equations below has infinitely many solutions.$$5x-2y=14$$$$ax+by=42$$What is the value of $$a+b$$?

   • $$3$$
   • $$6$$
   • $$9$$
   • $$12$$

5. In the $$xy$$-plane, a circle has center $$(5,k)$$ and radius $$13$$. The circle intersects the $$x$$-axis at the points $$(0,0)$$ and $$(10,0)$$. In addition, the point $$(5,6)$$ lies inside the circle. What is the value of $$k$$?

   • 12

6. A chemist has two salt solutions. The first solution is 15% salt by volume, and the second solution is 55% salt by volume. The chemist wants to mix the two solutions to obtain 200 milliliters of a new solution that is 31% salt by volume. How many milliliters of the 15% salt solution should be used?

   • $$80$$ mL
   • $$100$$ mL
   • $$120$$ mL
   • $$140$$ mL

7. A data set has a mean of $$24$$, a median of $$21$$, and a standard deviation of $$6$$. A new data set is created by multiplying each number in the original data set by $$4$$ and then subtracting $$9$$. Which statement accurately describes the new data set?

   • Mean $$87$$, median $$75$$, standard deviation $$6$$
   • Mean $$87$$, median $$75$$, standard deviation $$24$$
   • Mean $$96$$, median $$84$$, standard deviation $$24$$
   • Mean $$96$$, median $$75$$, standard deviation $$6$$

8. The function $$P(t)=24000(0.87)^t$$ models the population of a certain bird species in a forest, where $$t$$ is the number of years after monitoring began. Which is the best interpretation of $$0.87$$ in this context?

   • The initial population was $$87\%$$ of $$24000$$.
   • The population decreases by $$13\%$$ each year.
   • The population decreases by $$87\%$$ each year.
   • The population is $$13\%$$ of the previous year's population.

9. A company has two machines, Machine A and Machine B. Machine A produces 1500 parts per day, and 4% of its parts are defective. Machine B produces 2500 parts per day, and 2% of its parts are defective. All parts are combined into one daily shipment. If a part is selected at random and is found to be defective, what is the probability that it was produced by Machine B?

   • $$\frac{5}{11}$$
   • $$\frac{6}{11}$$
   • $$\frac{1}{40}$$
   • $$\frac{1}{2}$$

10. Triangles $$ABC$$ and $$DEF$$ are similar. The lengths of some sides are given by $$AB=x+2$$, $$BC=4x-1$$, $$DE=x-4$$, and $$EF=x+5$$. All side lengths are positive. What is the length of side $$BC$$?

    • $$11$$
    • $$19$$
    • $$27$$
    • $$15+12\sqrt{2}$$