Mini Exam 15 — Timed Mini Exams

Questions in this quiz (10)

1. A company sells $$200$$ headphones per month at a price of $$180$$ dollars each. Market research indicates that for each $$10$$ dollar price reduction, the company will sell $$20$$ more headphones per month. The company's monthly revenue, $$R$$, in dollars, can be modeled by the equation$$R=-200x^2+4000x+36000$$where $$x$$ represents the number of $$10$$ dollar price reductions. If this equation is graphed in the $$xy$$-plane, what value of $$x$$ corresponds to the maximum monthly revenue?

   • $$12$$
   • $$10$$
   • $$8$$
   • $$6$$

2. A polling organization conducted two surveys to estimate the proportion of voters in a county who support a new recycling program. The results from two random samples are shown in the table. The samples were selected from the same population of voters, and the margins of error were determined using the same method.Which of the following is the most likely reason that the margin of error for survey $$1$$ is greater than the margin of error for survey $$2$$?

   • Survey $$1$$ had a lower percentage of supporters.
   • Survey $$1$$ had a larger sample size.
   • Survey $$1$$ had a smaller sample size.
   • The voters were selected from the same county.

3. Two rectangles, $$ABCD$$ and $$EFGH$$, are similar. The length of each side of $$EFGH$$ is $$5$$ times the length of the corresponding side of $$ABCD$$. The area of $$ABCD$$ is $$12$$ square units. What is the area, in square units, of $$EFGH$$?

   • $$300$$
   • $$240$$
   • $$120$$
   • $$60$$

4. How many distinct real solutions does the equation $$(x^2+4)^2=-16$$ have?

   • $$2$$
   • $$4$$
   • $$6$$
   • $$0$$

5. The table above shows the number of attendees at a local music festival in $$2022$$ and $$2023$$. The organizer projected that the percent increase in the number of attendees from $$2022$$ to $$2023$$ was one-half of the projected percent increase from $$2023$$ to $$2024$$. How many attendees were projected to attend the festival in $$2024$$?

   • $$6500$$
   • $$6100$$
   • $$5600$$
   • $$5980$$

6. Function $$f$$ is defined by $$f(x)=-a^x+b$$, where $$a$$ and $$b$$ are constants. In the $$xy$$-plane, the graph of $$y=f(x)+2$$ has a $$y$$-intercept at $$(0,\frac{10}{3})$$. The product of $$a$$ and $$b$$ is $$12$$. What is the value of $$a$$?

   • $$\frac{48}{7}$$
   • $$\frac{42}{7}$$
   • $$\frac{36}{7}$$
   • $$\frac{21}{7}$$

7. Two identical right rectangular prisms each have a height of $$40$$ centimeters. The base of each prism is a square, and the surface area of each prism is $$S$$ square centimeters. If the prisms are glued together along a square base, the resulting prism has a surface area of $$\frac{9}{5}S$$ square centimeters. What is the side length, in centimeters, of each square base?

   • $$20$$
   • $$25$$
   • $$10$$
   • $$15$$

8. Which of the following is equivalent to $$(a+b)^{-1}(a^{-1}+b^{-1})$$ for all positive values of $$a$$ and $$b$$?

   • $$\frac{1}{a^2b^2}$$
   • $$\frac{a+b}{ab}$$
   • $$\frac{1}{a+b}$$
   • $$\frac{1}{ab}$$

9. A tank contains $$90000$$ gallons of water. Water is drained at a constant rate. If $$72000$$ gallons remain after $$6$$ hours, how many total hours will it take until $$18000$$ gallons of water remain in the tank?

   • $$30$$
   • $$24$$
   • $$18$$
   • $$12$$

10. Which of the following is equivalent to $$(m+n)^{-1}(m^{-1}+n^{-1})$$ for all positive values of $$m$$ and $$n$$?

    • $$\frac{1}{m^2n^2}$$
    • $$\frac{m+n}{mn}$$
    • $$\frac{1}{mn}$$
    • $$\frac{1}{m+n}$$