Inequalities — Quiz 5

Questions in this quiz (8)

1. The ideal storage temperature for a chemical solution is between $$50^\circ F$$ and $$77^\circ F$$. Using the formula:$$T = \frac{5}{9}(F - 32)$$where $$T$$ represents the temperature in degrees Celsius and $$F$$ represents the temperature in degrees Fahrenheit, determine the corresponding temperature range in degrees Celsius for storing the chemical solution.

   • $$10^\circ \leq T \leq 45^\circ$$
   • $$5^\circ \leq C \leq 25^\circ $$
   • $$10^\circ \leq C \leq 25^\circ $$
   • $$9^\circ \leq C \leq 25^\circ$$

2. Adam's workplace is a 45-minute walk or a 10-minute bus ride away from his house. The bus runs once every 40 minutes, and the number of minutes, $$w$$, that Adam waits for the bus varies between 0 and 40. In addition, Adam takes 3 minutes to reach the bus stop and 2 minutes to walk from the bus stop to his workplace after the ride.Which of the following inequalities gives the values of $$w$$ for which it would be faster for Adam to walk to work?

   • $$w + 10$$ > $$45$$
   • $$w + 15$$ > $$45$$
   • $$w + 10$$ > $$15$$
   • $$w + 15$$ > $$30$$

3. If $$c$$ < $$\frac{30}{5y}$$ < $$d$$, and $$c=3$$ and $$d=7$$, which of the following could be true?

   • $$y$$ < $$c$$
   • $$y$$>$$d$$
   • $$c$$ < $$y$$ < $$d$$
   • $$y=c$$

4. Consider fractions of the form $$\frac{9}{m}$$, where $$m$$ is an integer. How many integer values of $$m$$ make this fraction greater than 0.6 and less than 1.2?

   • 5
   • 6
   • 7
   • 8

5. Solve the inequality: $$(2x-3)(x+4)$$ < $$0$$

   • $$(-4,\frac{3}{2})$$
   • $$(-4,\infty)$$
   • $$(-\infty, \frac{3}{2})$$
   • $$(\frac{3}{2}, \infty)$$

6. Solve the inequality: $$x^2-2x+5$$ > $$0$$

   • $$(-2, 2)$$
   • $$(-2, \infty)$$
   • $$(2, \infty)$$
   • $$(-\infty, \infty)$$

7. If $$\frac{-2|x|}{3y}$$ > $$-1$$, which of the following MUST be true?

   • $$y$$ > $$0$$
   • $$|x|$$ < $$3$$
   • $$y$$ < $$0$$
   • $$xy$$ > $$0$$

8. If $$a^3bc^2$$ < $$0$$, which of the following must be correct?

   • $$a$$ > $$0$$ and $$b$$ > $$0$$
   • $$a$$ > $$0$$ and $$c$$ > $$0$$
   • $$a$$ < $$0$$ or $$b$$ < $$0$$
   • $$b$$ > $$0$$ and $$c$$ > $$0$$