Mini Exam 6 — Timed Mini Exams

Questions in this quiz (10)

1. $$b\ge a+4$$$$a\lt25$$For which of the following tables are all the values of a and their corresponding values of b solutions to the given system of inequalities?

2. The frequency table below shows the number of movies watched by each of the $$50$$ students in a film club. A new student, who watched $$8$$ movies, joins the club. How do the mean and median of the number of movies watched by the new group of students compare to the mean and median of the original group?

   • Mean increases, median stays the same.
   • Mean decreases, median remains the same.
   • Mean remains the same, and the median increases.
   • Both the mean and the median will increase.

3. A local middle school surveyed $$300$$ students on their participation in after-school activities. The table below summarizes the data on whether a student is a member of a sports team, a music club, both, or neither. Based on the data in the table, what is the probability that a student selected at random is a member of a music club?

   • $$\frac{43}{60}$$
   • $$\frac{7}{17}$$
   • $$\frac{5}{17}$$
   • $$\frac{17}{60}$$

4. The value of a certain investment doubles every 5 years. The function $$V(t)=1200(2)^{t/5}$$ gives the approximate value of the investment in dollars, where $$t$$ is the number of years after the initial investment of $$1200$$ dollars. Which statement is the best interpretation of $$V(10)=4800$$ in this context?

   • Approximately $$4800$$ dollars is the value of the investment $$10$$ years after the initial investment.
   • The value of the investment has increased by approximately $$4800$$ dollars after $$10$$ years.
   • The value of the investment has increased by approximately $$10$$ dollars after $$4800$$ years.
   • Approximately $$10$$ dollars is the value of the investment $$4800$$ years after the initial investment.

5. $$\frac{4}{a}=\frac{5}{b}-\frac{2}{c}$$The given equation relates the variables $$a$$, $$b$$, and $$c$$, where $$a\gt0$$, $$b\gt0$$, and $$5c\gt2b$$. Which expression is equivalent to $$a$$?

   • $$4bc$$
   • $$4(5c-2b)$$
   • $$\frac{5c-2b}{2bc}$$
   • $$\frac{4bc}{5c-2b}$$

6. $$f(x)=x^2+bx$$$$g(x)=3x^2+6x$$Functions $$f$$ and $$g$$ are given, and in function $$f$$, $$b$$ is a constant. If $$f(x)\cdot g(x)=3x^4+12x^3+18x^2$$, what is the value of $$b$$?

   • $$2$$
   • $$4$$
   • $$6$$
   • $$8$$

7. In the $$xy$$-plane, the graphs of the equations $$y=x^2-4x+7$$ and $$y=2x+1$$ intersect at two points, $$(x_1,y_1)$$ and $$(x_2,y_2)$$. What is the value of $$y_1+y_2$$?

   • $$10$$
   • $$14$$
   • $$18$$
   • $$26$$

8. The equation $$(x-3)^2+(y+4)^2=81$$ represents a circle in the $$xy$$-plane. What is the length of the diameter of this circle?

   • $$81$$
   • $$9$$
   • $$27$$
   • $$18$$

9. Jordan is buying snacks for a trip. He buys one water bottle for $$8$$ dollars and a number of granola bars that cost $$2$$ dollars each. If he can spend no more than $$26$$ dollars on these items, what is the maximum number of granola bars he can buy?

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

10. $$V(t)=-4t^2+60t+180$$The function above models the value $$V$$, in dollars, of a collectible item $$t$$ years after it was purchased. What does the number $$180$$ represent in the function?

    • The initial value, in dollars, of the item
    • The maximum value, in dollars, of the item
    • The initial rate of increase in value, in dollars per year
    • The number of years after which the item reaches its maximum value