Timed Mini Exam 15 — Timed Mini Exams

Questions in this quiz (10)

1. Which function is represented by the graph shown?

   • $$f(x)=\frac{x^2}{x^2+25}$$
   • $$f(x)=\frac{x^2}{x^2-25}$$
   • $$f(x)=\frac{5x^2}{x^2-1}$$
   • $$f(x)=\frac{5x^2}{x^2+1}$$

2. A rectangular parking lot measures 40 m by 60 m. Only 75% of the area is usable for parking. Each motorcycle uses $$4$$ $$m^2$$, each truck uses $$24$$ $$m^2$$. At most $$120$$ vehicles can be parked. The fee is 3 dollars per motorcycle and 18 dollars per truck. What is the maximum possible income if the lot is filled optimally?

   • $$900$$
   • $$1350$$
   • $$1440$$
   • $$1800$$

3. Which of the following is a solution to the equation $$\sin(x\sqrt{3})=1$$?

   • $$\frac{7\pi}{2\sqrt{3}}$$
   • $$\frac{\pi}{\sqrt{3}}$$
   • $$\frac{5\pi}{2\sqrt{3}}$$
   • $$\frac{\pi}{2\sqrt{3}}$$

4. The population of bacteria is modeled by $$P=3e^{0.4t}$$, where $$t$$ is in days. How long does it take for the population to be 6 times its initial size?

   • 4 days, 6 hours
   • 1 day, 4 hours
   • 3 days, 1 hour
   • 2 days, 3 hours

5. The first term of an arithmetic sequence is $$-10$$ with common difference $$d_1$$. Another arithmetic sequence has first term $$60$$ with common difference $$d_2$$. If the $$8th$$ terms of both sequences are equal, what relationship must hold between $$d_1$$ and $$d_2$$?

   • $$d_1-d_2=7$$
   • $$d_1+d_2=10$$
   • $$d_1-d_2=10$$
   • $$d_1+d_2=7$$

6. An AC source has peak-to-peak voltage 20 volts and frequency $$\frac{2}{\pi}$$ hertz. A constant direct voltage of 6 volts is added, shifting the waveform vertically. Find the voltage function $$v(t)$$.

   • $$v(t)=10\sin(4t)+6$$
   • $$v(t)=10\sin(\frac{4t}{\pi})+6$$
   • $$v(t)=10\sin(\frac{t}{2\pi})+6$$
   • $$v(t)=10\sin(\frac{t}{\pi})+6$$

7. Two vectors are given: $$a=-4\hat{\imath}+2\hat{\jmath}+\hat{k}$$ and $$b=\hat{\imath}+3\hat{\jmath}-\hat{k}$$. Find the cosine of the angle between the vectors $$a+b$$ and $$a$$.

   • $$\frac{4}{\sqrt{7}}$$
   • $$\frac{22}{\sqrt{714}}$$
   • $$\frac{\sqrt{7}}{4}$$
   • $$\frac{1}{7}$$

8. Given $$2≤a≤5$$, $$5≤b≤7$$, and $$6≤c≤9$$, find the greatest possible value of $$(a/b)$$ $$(1/c)$$.

   • $$\frac{2}{35}$$
   • $$\frac{1}{18}$$
   • $$\frac{2}{21}$$
   • $$\frac{5}{30}$$

9. Given the equation $$\sqrt[3]{x}=y$$, where $$y$$ is a real number, what must be true of $$x$$?

   • $$x$$ is even
   • $$x$$ is a rational number
   • $$x$$ is an integer
   • $$x$$ is a real number

10. Sophia tracked the number of books she read each month over 12 months. The table shows how many months she read each number of books.What is the median number of books read in a month?

    • $$3$$
    • $$3.5$$
    • $$4$$
    • $$4.5$$