Full Practice Exam 3 — Module 2

Questions in this quiz (22)

1. For a particular factory that makes light bulbs, $$7$$ out of every $$250$$ light bulbs produced are defective. A light bulb from the factory is selected at random. What is the probability that the selected light bulb is defective?

   • $$\frac{1}{250}$$
   • $$\frac{7}{250}$$
   • $$\frac{1}{25}$$
   • $$\frac{1}{4}$$

2. The total cost $$g(x)$$, in dollars, to lease a laptop for $$24$$ months from a tech company is given by:$$g(x)=24x+750$$where $$x$$ is the monthly payment, in dollars. What is the total cost to lease the laptop when the monthly payment is $$320$$?

   • 8430

3. Each side of a square has a length of $$32$$ units. What is the perimeter of this square?

   • $$128$$
   • $$96$$
   • $$120$$
   • $$90$$

4. $$\frac{42}{x+5}=x$$What is the positive solution to the given equation?

   • $$\frac{5}{2}$$
   • $$\frac{\sqrt{5}}{2}$$
   • $$\frac{\sqrt{193}}{5}$$
   • $$\frac{-5+\sqrt{193}}{2}$$

5. A robot moves at a constant speed of $$15$$ centimeters per second. At this speed, how long, in seconds, will it take the robot to travel $$180$$ centimeters?

   • $$12$$
   • $$10$$
   • $$15$$
   • $$9$$

6. Data set $$A$$: $$4,8,8,12$$Data set $$B$$: $$4,8,8,12,20$$The lists give the values in data sets $$A$$ and $$B$$. Which statement correctly compares the mean of data set $$A$$ and the mean of data set $$B$$?

   • The mean of data set A is less than the mean of data set B.
   • The mean of data set A is less than the mean of data set B.
   • The means of data set A and data set B are equal.
   • There is not enough information to compare the means.

7. A spacecraft carried $$520000$$ kilograms of fuel at launch. After $$18$$ seconds, $$388400$$ kilograms of fuel remained. On average, approximately how many kilograms of fuel did the spacecraft burn per second during those $$18$$ seconds?

   • $$2300$$
   • $$4200$$
   • $$7311$$
   • $$9200$$

8. If $$3x-7=5$$ what is the value of $$27x^2-126x+147$$?

   • $$36$$
   • $$75$$
   • $$81$$
   • $$147$$

9. An object is thrown upward from a cliff. The equation:$$h=-5t^2+8t+12$$represents this situation, where $$h$$ is the height of the object above the ground, in meters, $$t$$ seconds after it is thrown. Which number represents the height, in meters, from which the object was thrown?

   • $$0$$
   • $$5$$
   • $$8$$
   • $$12$$

10. The function is given by $$g(x)=3x^2-24x+10$$. For what value of $$x$$ does $$g(x)$$ reach its minimum?

    • $$3$$
    • $$4$$
    • $$-3$$
    • $$-24$$

11. A florist has a budget of $$3150$$ dollars to buy roses and tulips. Each rose costs $$7.25$$ dollars and each tulip costs $$3.80$$ dollars. The florist must buy at least $$300$$ flowers in total. What is the maximum number of roses that can be purchased while staying within the $$3150$$ dollar budget and still buying at least $$300$$ flowers?

    • 434

12. In the linear function $$g$$, $$g(0)=-3$$ and $$g(2)=5$$. Which equation defines $$g$$?

    • $$g(x)=5x+4$$
    • $$g(x)=4x-3$$
    • $$g(x)=3x+4$$
    • $$g(x)=8x+3$$

13. The function $$g(r)=8r^2$$ gives the area, in square meters $$m^2$$, of a garden if each side of the garden has length $$r$$ meters. Which of the following is the best interpretation of $$g(10)=800$$?

    • If the side length of the garden is 10 m, then the perimeter of the garden is $$800$$ $$m$$.
    • If the side length of the garden is $$10$$ meters, then the area of the garden is $$800$$ $$m^2$$.
    • If the area of the garden is $$800$$ $$m^2$$, then the side length of the garden is $$8$$ $$m$$.
    • If the perimeter of the garden is $$800$$ $$m$$, then the side length of the garden is $$10$$ $$m$$.

14. A boat tour company takes groups of $$24$$ people at a time. The company charges $$75$$ per adult and $$50$$ per child. For one tour, the total revenue from the group was $$1500$$. How many people in the group were children?

    • $$4$$
    • $$6$$
    • $$10$$
    • $$12$$

15. The function $$g(x)=-5x+35$$. The graph of $$y=g(x)$$ in the $$xy$$-plane has an $$x$$-intercept at $$(a,0)$$ and a $$y$$-intercept at $$(0,b)$$, where $$a$$ and $$b$$ are constants. What is the value of $$a+b$$?

    • $$14$$
    • $$21$$
    • $$28$$
    • $$42$$

16. $$y=2$$$$y=x^2-6x+b$$In the given system of equations, $$b$$ is a positive constant. The system has exactly one distinct real solution. What is the value of $$b$$?

    • $$4$$
    • $$6$$
    • $$8$$
    • $$11$$

17. For the function $$f$$, the value of $$f(x)$$ decreases by $$30\%$$ for every increase in the value of $$x$$ by $$1$$. If $$f(0)=20$$, which equation defines $$f$$?

    • $$f(x)=0.7(20)^x$$
    • $$f(x)=1.3(20)^x$$
    • $$f(x)=20(0.7)^x$$
    • $$f(x)=20(1.3)^x$$

18. The side lengths of right triangle $$ABC$$ are given. Triangle $$ABC$$ is similar to triangle $$DEF$$, where $$B$$ corresponds to $$E$$ and $$C$$ corresponds to $$F$$. The side lengths are $$AB=15$$, $$BC=36$$, $$AC=39$$. What is the value of $$\tan F$$?

    • $$\frac{5}{12}$$
    • $$\frac{4}{3}$$
    • $$\frac{3}{4}$$
    • $$\frac{7}{12}$$

19. From a point on the ground, the angle of elevation to the top of a building is $$30^\circ$$. From the same point, the angle of elevation to the top of a flagpole standing on top of the building is $$45^\circ$$. If the flagpole is $$20$$ feet tall, what is the height, in feet, of the building?

    • $$10(\sqrt{3}-1)$$
    • $$10\sqrt{3}$$
    • $$10(\sqrt{3}+1)$$
    • $$20\sqrt{3}$$

20. A right cylindrical tank has an inner radius of $$6$$ inches. The tank initially contains water to a height of $$8$$ inches. A solid metal sphere is completely submerged in the tank, causing the water level to rise. The volume of the sphere is $$288\pi$$ cubic inches. What is the new height, in inches, of the water in the tank after the sphere is submerged?

    • $$12$$
    • $$14$$
    • $$16$$
    • $$18$$

21. A large cylindrical water tank is initially empty. Pipe 1 fills the tank at a constant rate of $$150$$ gallons per minute. Pipe 2 fills the tank at a constant rate of $$30$$ cubic feet per minute. Pipe 3 drains the tank at a constant rate of $$60$$ gallons per minute. If Pipe 1 and Pipe 2 are turned on simultaneously for $$10$$ minutes, and then Pipe 3 is also turned on, and all three pipes operate until the tank is full in an additional $$20$$ minutes, what is the total capacity of the tank in gallons?Use: $$1\text{ cubic foot}=7.48\text{ gallons}$$

    • $$9432$$
    • $$10032$$
    • $$10050$$
    • $$11232$$

22. A biologist is studying the relationship between the average daily sunlight hours $$S$$ and the average growth rate $$G$$, in centimeters per week, of a certain plant species. A scatterplot of the data suggests a positive linear association. The least-squares regression line that models this relationship is given by:$$G=2.5S+4$$For one particular week, the average daily sunlight was $$8$$ hours, and the actual average plant growth rate was $$27$$ centimeters per week. What is the residual for the average plant growth rate for this particular week, according to the model?

    • $$3\text{ cm/week}$$
    • $$-3\text{ cm/week}$$
    • $$24\text{ cm/week}$$
    • $$27\text{ cm/week}$$