Mini Exam 18 — Timed Mini Exams

Questions in this quiz (10)

1. How many solutions does the given equation have?$$12y = 6y$$

   • Zero
   • Exactly one
   • Exactly two
   • Infinitely many

2. A race consisted of five different stages. One runner completed the third stage with an average speed of $$18.750$$ miles per hour. What was this average speed, in yards per hour?$$(1\text{ mile}=1760\text{ yards})$$

   • $$18750$$
   • $$17600$$
   • $$33000$$
   • $$17500$$

3. Which expression is equivalent to $$(m^3q^{-2}z^4)(m^{-5}q^7z^{-3})(m^2q^4z)$$, where $$m, q,$$ and $$z$$ are positive?

   • $$m^{-2}q^5z$$
   • $$m^2q^5z$$
   • $$m^2q^5z^2$$
   • $$q^9z^2$$

4. The formula $$C = F - \frac{7}{20}(120 - R)$$ can be used to approximate the cloud base height $$C$$, in meters, given the air temperature $$F$$ in degrees Celsius, and the relative humidity $$R$$ percent, where $$R$$ > $$40$$. Which of the following expresses the relative humidity $$R$$ in terms of the temperature $$F$$ and the cloud base height $$C$$?

   • $$R = 120 - \frac{20}{7}(F - C)$$
   • $$R = 120 - \frac{20}{7}(C - F)$$
   • $$R = \frac{20}{7}(F - C) + 120$$
   • $$R = -120 - \frac{20}{7}(C - F)$$

5. The graph of the equation $$15x+20y=160$$ is shifted up $$7$$ units in the xy-plane. What is the y-intercept of the resulting graph?

   • $$(0,8)$$
   • $$(0,15)$$
   • $$(7,8)$$
   • $$(8,7)$$

6. The floor of a rectangular gymnasium has an area of $$800$$ square meters. A designer makes a scale drawing of the gym floor, where the length of each side in the drawing is $$\frac{1}{20}$$ of the length of the corresponding side of the actual gym floor. What is the area, in square meters, of the scale drawing?

   • $$2$$
   • $$3$$
   • $$4$$
   • $$6$$

7. Triangle $$ABC$$ is a right triangle with a right angle at $$B$$. The two legs satisfy $$AB = BC = 18$$. What is the measure of angle $$A$$ in Triangle $$ABC$$?

   • $$30^\circ$$
   • $$45^\circ$$
   • $$60^\circ$$
   • $$65^\circ$$

8. Function $$g$$ is a quadratic function where $$g(5)=0$$ and $$g(-11)=0$$. The graph of $$y=g(x)$$ in the $$xy$$-plane has a vertex at $$(s,-36)$$. What is the value of $$s$$?

   • $$-3$$
   • $$2$$
   • $$5$$
   • $$-11$$

9. The average annual water bill for a home is $$1,280$$. A homeowner plans to spend $$18,000$$ to install a rainwater harvesting system. After installation, the homeowner estimates the average annual water bill will be $$640$$. Which of the following inequalities can be solved to find $$t$$, the number of years after installation at which the total amount of water bill savings will exceed the installation cost?

   • $$18,000−1,280$$ > $$640t$$
   • $$18,000$$ < $$(1,280 - 640)t$$
   • $$640$$ < $$(1,280 + 18,000)t$$
   • $$18,000$$ > $$(1,280−640)t$$

10. The first term of a sequence is $$9$$. Each term after the first is $$4$$ times the preceding term. If $$w$$ represents the $$n$$th term of the sequence, which equation gives $$w$$ in terms of $$n$$?

    • $$w=4(9^{n})$$
    • $$w=9(4^{n+1})$$
    • $$w=4(9^{n-1})$$
    • $$w=9(4^{n-1})$$