Mini Exam 18 — Timed Mini Exams

Questions in this quiz (10)

1. The function $$P(t)=22000(1.03)^t$$ gives the predicted population of a city $$t$$ years after the year $$2015$$. What is the best interpretation of the statement "$$P(4)$$ is approximately equal to $$24,762$$"?

   • In the year $$2015$$, the predicted population was approximately $$24,762$$.
   • Four years after $$2015$$, the predicted population was approximately $$24,762$$.
   • In the year $$2019$$, the predicted population was approximately $$22,000$$.
   • The population increased by approximately $$24,762$$ people in four years.

2. $$x=7$$$$y=x^2-4x+3$$The graphs of the given equations intersect at the point $$(x,y)$$ in the $$xy$$-plane. What is the value of $$y$$?

   • $$24$$
   • $$28$$
   • $$35$$
   • $$40$$

3. Lines $$m$$ and $$n$$ are parallel. A transversal intersects line $$m$$ at point $$P$$ and line $$n$$ at point $$Q$$. Point $$R$$ lies on line $$n$$, forming triangle $$PQR$$. A ray extending left from $$P$$ along line $$m$$ forms an angle of $$80^\circ$$ with $$PQ$$. If $$\angle QPR=45^\circ$$, what is the measure of $$\angle PRQ$$?

   • $$45^\circ$$
   • $$55^\circ$$
   • $$65^\circ$$
   • $$80^\circ$$

4. A machine produces $$72$$ parts in $$3$$ hours. At this constant rate, how many parts can the machine produce in $$8$$ hours?

   • $$144$$
   • $$168$$
   • $$192$$
   • $$216$$

5. $$\frac{3}{4}(x-6)=\frac{1}{2}x+3$$What is the solution to the equation?

   • $$12$$
   • $$16$$
   • $$24$$
   • $$30$$

6. $$(3x-4)(x+6)-(x^2-8x+12)$$Which of the following expressions is equivalent to the expression shown above?

   • $$2x^2+22x-36$$
   • $$2x^2+14x-36$$
   • $$x^2+22x-36$$
   • $$x^2+14x-36$$

7. A researcher wants to determine whether a new study app improves students' science scores. Students choose whether or not to download and use the app. At the end of the semester, the researcher compares the science scores of students who used the app with those who did not. Which of the following is the most significant limitation of this study?

   • The students who used the app may have been more motivated to improve their scores.
   • The researcher did not collect enough data.
   • The study should have included students from other schools.
   • Science scores are not useful measures of performance.

8. A circle in the $$xy$$-plane has center $$(0,0)$$. A line is tangent to the circle at the point $$(5,12)$$. Which of the following is an equation of the tangent line?

   • $$5x+12y=169$$
   • $$12x+5y=169$$
   • $$5x-12y=-119$$
   • $$12x-5y=0$$

9. $$H(t)=8(1.06)^t$$The function $$H$$ gives the predicted height, in centimeters, of a plant $$t$$ weeks after it was planted. What is the best interpretation of $$H(0)=8$$?

   • The predicted height of the plant was $$8$$ centimeters when it was planted.
   • The plant grows $$8$$ centimeters every week.
   • The plant grows $$6$$ centimeters every week.
   • After $$8$$ weeks, the plant is $$0$$ centimeters tall.

10. A theater sells student tickets for $$8$$ dollars and adult tickets for $$12$$ dollars. The theater wants to earn at least $$1,200$$ dollars from ticket sales. Due to seating limitations, no more than $$150$$ tickets can be sold. Let $$x$$ represent the number of student tickets sold and $$y$$ represent the number of adult tickets sold. Which system of inequalities models the situation?

    • $$8x+12y\ge1200$$ $$x+y\le150$$
    • $$8x+12y\le1200$$ $$x+y\ge150$$
    • $$12x+8y\ge1200$$ $$x+y\le150$$
    • $$8x+12y\ge1200$$$$x+y\ge150$$