Mini Exam 20 — Timed Mini Exams

Questions in this quiz (10)

1. Carlos mixed $$4$$ ounces of red paint with $$6$$ ounces of white paint to make a light-red shade. He needs to make a second batch using the same ratio of red to white paint as the first batch. If he uses $$10$$ ounces of red paint in the second batch, how much white paint should he use?

   • $$10$$
   • $$15$$
   • $$18$$
   • $$20$$

2. Jamal is organizing a conference that requires hiring at least $$15$$ volunteers. He can hire student volunteers, who will be paid $$120$$ dollars per day, and professional volunteers, who will be paid $$180$$ dollars per day. He must hire at least $$5$$ student volunteers and at least $$2$$ professional volunteers. His budget for paying volunteers is no more than $$2700$$ dollars per day. If $$x$$ is the number of student volunteers and $$y$$ is the number of professional volunteers, which system of inequalities represents the situation?

   • $$120x + 180y \le 2700$$ $$x + y \le 15$$ $$x \le 5$$ $$y \ge 2$$
   • $$120x + 180y \le 2700$$ $$x + y \ge 15$$ $$x \ge 5$$ $$y \ge 2$$
   • $$120x + 180y \ge 2700$$ $$x + y \le 15$$ $$x \ge 5$$ $$y \ge 2$$
   • $$120x + 180y \ge 2700$$$$x + y \ge 15$$$$x \ge 5$$$$y \le 2$$

3. In $$2020$$, Victor earned $$12\%$$ more than in 2019, and in 2021 Victor earned $$5\%$$ more than in 2020. If Victor earned $$y$$ times as much in 2021 as in 2019, what is the value of $$y$$?

   • $$1.122$$
   • $$1.115$$
   • $$1.250$$
   • $$1.176$$

4. Marcus measured the temperature of a bowl of soup cooling in a kitchen with a constant temperature of $$65^\circ \!F$$. The soup’s temperature was $$200^\circ \!F$$ at $$7{:}00$$ p.m. when it started cooling. The temperature of the soup was $$170^\circ \!F$$ at $$7{:}05$$ p.m. and $$144.5^\circ \!F$$ at $$7{:}10$$ p.m. The soup continued to cool. Which of the following functions best models the temperature $$S(t)$$, in degrees Fahrenheit, of the soup $$t$$ minutes after it started cooling?

   • $$S(t)=200(1.15)^t$$
   • $$S(t)=200(0.85)^t$$
   • $$S(t)=(200-65)(0.85)^{\frac{t}{5}}$$
   • $$S(t)=65+135(0.85)^{\frac{t}{5}}$$

5. For the function $$f,$$ $$f(kx)=2x+7$$ for all values of $$x,$$ where $$k$$ is a positive constant. If $$f(4)=23,$$ what is the value of $$k$$?

   • $$\frac{1}{4}$$
   • $$\frac{4}{7}$$
   • $$\frac{1}{2}$$
   • $$\frac{4}{23}$$

6. The function is $$y=3(5^x).$$ Which of the following shows the correct graph of this equation in the $$xy$$-plane?

7. The coordinates of one of the legs of a right triangle in the $$xy$$-plane are $$(-6,4)$$ and $$(3,10)$$. The area of this triangle is $$48\sqrt{5}$$ square units. What is the length, in units, of the other leg of the triangle?

   • $$\frac{32\sqrt{65}}{13}$$
   • $$32\sqrt{5}$$
   • $$\frac{\sqrt{5}}{2}$$
   • $$\frac{3\sqrt{5}}{2}$$

8. $$\frac14 x^2 - 5$$ can be rewritten as $$\frac14 (x-k)(x+k),$$ where $$k$$ is a positive constant. What is the value of $$k?$$

   • $$5$$
   • $$\sqrt{5}$$
   • $$2\sqrt{5}$$
   • $$10$$

9. $$|18-x|+|42-x|=30$$What is the greatest possible value of $$x$$?

   • $$15$$
   • $$25$$
   • $$30$$
   • $$45$$

10. In the system of equations below, $$a$$ and $$c$$ are constants:$$\frac34 x+\frac25 y=1$$$$ax+y=c$$If the system has an infinite number of solutions $$(x,y)$$, what is the value of $$a$$?

    • $$\frac{15}{8}$$
    • $$\frac{3}{4}$$
    • $$\frac{2}{5}$$
    • $$-\frac{3}{4}$$