Mini Exam 11 — Timed Mini Exams

Questions in this quiz (10)

1. In the given equation, $$m$$ is an integer constant. If the equation has no real solution, what is the least possible value of $$m$$?$$y(my-48)=-9$$

   • $$66$$
   • $$64$$
   • $$62$$
   • $$65$$

2. A circle in the $$xy$$-plane has its center at $$(-8,12)$$. Line $$\ell$$ is tangent to this circle at the point $$(4,-6)$$. What is the slope of line $$\ell$$?

   • $$\frac{2}{3}$$
   • $$-\frac{3}{2}$$
   • $$\frac{3}{2}$$
   • $$-\frac{2}{3}$$

3. A painter can paint $$25$$ walls in $$1$$ hour. A large project requires a total of $$w$$ walls, and each wall must receive $$2$$ coats of paint. Which equation represents the total time $$T$$, in hours, the painter will need to complete the painting for this project?

   • $$T=\frac{w}{50}$$
   • $$T=\frac{2w}{25}$$
   • $$T=\frac{25}{2w}$$
   • $$T=\frac{w}{25}$$

4. Data set $$A$$ consists of the test scores of $$18$$ students and has a mean of $$92$$. Data set $$B$$ consists of the test scores of $$27$$ students and has a mean of $$76$$. Data set $$C$$ consists of the test scores of the $$45$$ students from data sets $$A$$ and $$B$$. What is the mean score of data set $$C$$?

   • $$83.1$$
   • $$81.2$$
   • $$80.6$$
   • $$82.4$$

5. A number $$m$$ is at most $$7$$ less than $$3$$ times the value of $$n$$. What is the greatest possible value of $$m$$, if the value of $$n$$ is $$-4$$?

   • $$-16$$
   • $$-19$$
   • $$-18$$
   • $$-21$$

6. The volume of right circular cone $$M$$ is $$24$$ cubic centimeters. What is the volume, in cubic centimeters, of a right circular cone with one-half the radius and $$8$$ times the height of cone $$M$$?

   • $$72$$
   • $$54$$
   • $$48$$
   • $$36$$

7. The function $$h$$ is defined by $$h(x)=a^x+b$$, where $$a$$ and $$b$$ are constants and $$a$$>$$0$$. In the $$xy$$-plane, the graph of $$y=h(x)$$ has a $$y$$-intercept at $$(0,-3)$$ and passes through the point $$(3,13)$$. What is the value of $$a+b$$?

   • $$\sqrt[3]{18}-4$$
   • $$\sqrt[3]{16}-4$$
   • $$\sqrt[3]{17}+4$$
   • $$\sqrt[3]{17}-4$$

8. In triangle $$PQR$$, angle $$Q$$ is a right angle. Point $$S$$ lies on $$PR$$ and point $$T$$ lies on $$QR$$ such that $$ST$$ is parallel to $$PQ$$. If the measure of angle $$QRP$$ is $$64$$, what is the measure, in degrees, of angle $$RST$$?

   • $$32$$
   • $$26$$
   • $$28$$
   • $$24$$

9. Which system of linear equations has no solution?

   • $$3x+5y=18$$$$3x-5y=18$$
   • $$3x+5y=18$$$$4x+6y=20$$
   • $$3x+5y=18$$$$-6x-10y=-36$$
   • $$3x+5y=18$$$$6x+10y=40$$

10. Two identical rectangular prisms, each with a height of $$30$$ cm and a square-shaped base, have a surface area of $$S$$ cm$$2$$ when considered separately. When these prisms are attached base to base, the total surface area is reduced to $$\frac{28}{15}S$$ cm$$2$$. What is the length of one side of the square base?

    • $$\frac{130}{13}$$
    • $$\frac{100}{13}$$
    • $$\frac{90}{13}$$
    • $$\frac{120}{13}$$