Mini Exam 35 — Timed Mini Exams

Questions in this quiz (10)

1. Two positive numbers $$a$$ and $$b$$ satisfy $$\sqrt[3]{a}=\sqrt{b}$$. For what value of $$x$$ is $$a^{6x-1}=b^2$$?

   • $$\frac14$$
   • $$\frac38$$
   • $$\frac{7}{18}$$
   • $$\frac49$$

2. The function $$f(t)=60,000\cdot2^{t/410}$$ gives the number of bacteria in a population $$t$$ minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?

   • 410

3. Define $$f(x)=|x-8|$$. If $$f(3)-f(a)=-30$$, which of the following is the positive solution for $$a$$?

   • $$-27$$
   • $$35$$
   • $$42$$
   • $$43$$

4. What is the center of the circle defined by $$(x-2)^2+(y+9)^2=1$$?

   • $$(2,-9)$$
   • $$(2,9)$$
   • $$(-2,-9)$$
   • $$(-2,9)$$

5. The quantity $$L$$ is given by $$L=\frac{100}{m}+40n,$$ where $$m$$ and $$n$$ are variables. Which equation correctly expresses $$n$$ in terms of $$L$$ and $$m$$?

   • $$n=\frac{L-100}{40m}$$
   • $$n=\frac{100+L}{40m}$$
   • $$n=\frac{L-\frac{100}{m}}{40}$$
   • $$n=\frac{mL-100}{40}$$

6. A scientist analyzed a soil sample with a mass of $$1,000$$ grams and determined that it contained $$220$$ grams of water. What is the percentage of water, by mass, in this soil sample?

   • $$10\%$$
   • $$18.9\%$$
   • $$22\%$$
   • $$24\%$$

7. A school club has $$40$$ members, consisting of $$24$$ juniors and $$16$$ seniors. Among the juniors, $$10$$ are on the debate team, while among the seniors, $$6$$ are on the debate team. If a club member is selected at random, what is the probability that the member is a junior, given they are not on the debate team?

   • $$\frac{14}{34}$$
   • $$\frac{14}{20}$$
   • $$\frac{14}{24}$$
   • $$\frac{14}{40}$$

8. An object travels at a constant speed of $$16$$ centimeters per second. At this speed, what is the time, in seconds, that it would take for the object to travel $$144$$ centimeters?

   • $$9$$
   • $$96$$
   • $$160$$
   • $$230$$

9. An object moves at a speed of $$\frac{3}{20}$$ feet per second. $$(3\text{ feet}=1\text{ yard})$$ What is this speed, in yards per second?

   • $$20$$
   • $$\frac{3}{20}$$
   • $$\frac{9}{20}$$
   • $$\frac{1}{20}$$

10. An environmental scientist is investigating the volatility of $$200$$ organic compounds by finding the boiling point of each compound. The mean boiling point of all $$200$$ compounds is $$185$$ degrees Celsius. The scientist classifies each compound as either semivolatile or volatile. Of the $$200$$ compounds, $$60$$ compounds were classified as semivolatile, and these $$60$$ compounds have a mean boiling point of $$340$$ degrees Celsius. The remaining $$140$$ compounds were classified as volatile. What is the mean boiling point, in degrees Celsius, of the $$140$$ compounds classified as volatile?

    • $$102.36$$
    • $$112.5$$
    • $$118.6$$
    • $$120.3$$