Full Practice Exam 12 — Module 1
Questions in this quiz (22)
A cylindrical tank initially contains $$4,800$$ liters of water. Water drains from the tank at a rate proportional to the amount of water remaining, such that every $$12$$ minutes the amount of water decreases by $$25\%$$. Which function best models the amount of water, in liters, remaining in the tank after $$t$$ minutes?
- $$W(t)=4800(0.75)^{12t}$$
- $$W(t)=4800(0.25)^{t/12}$$
- $$W(t)=4800(0.75)^{t/12}$$
- $$W(t)=4800-0.25t$$
The price of a computer was decreased by $$15\%$$ during a sale. One week later, the sale price was increased by $$20\%$$. After that, the new price was discounted by another $$10\%$$. What is the final price as a percentage of the original price?
- $$91.8\%$$
- $$92\%$$
- $$95\%$$
- $$102\%$$
In the $$xy$$-plane, the line defined by $$(2k-3)x+(k+4)y=30$$ has slope $$\frac{3}{2}$$. What is the $$x$$-intercept of the line?
- $$3$$
- $$5$$
- $$6$$
- $$-\frac{70}{11}$$
A company manufactures a specialized device. The company incurs a fixed monthly cost of $$24,000$$. For the first $$300$$ devices produced, the manufacturing cost is $$80$$ per device. For every device beyond the first $$300$$, the manufacturing cost decreases to $$60$$ per device. Each device sells for $$140$$. If the company wants a monthly profit of exactly $$54,000$$, how many devices must it sell?
- $$900$$
- $$950$$
- $$1000$$
- $$1050$$
Which expression is equivalent to $$\frac{x^2-9}{x-3}+\frac{x^2+7x+10}{x+5}$$ for all values of $$x$$ for which the expression is defined?
- $$2x+2$$
- $$2x+5$$
- $$x^2+4x+1$$
- $$x^2+7x+1$$
A random sample of $$800$$ voters is surveyed before an election. Of those surveyed, $$472$$ say they support Candidate A. The survey has a margin of error of $$3.5\%$$. Which statement is most plausible?
- Exactly $$59\%$$ of all voters support Candidate A.
- Between $$55.5\%$$ and $$62.5\%$$ of all voters support Candidate A.
- Less than $$55.5\%$$ of all voters support Candidate A.
- More than $$62.5\%$$ of all voters support Candidate A.
A factory uses Machine A and Machine B to manufacture computer chips. Machine A produces $$65\%$$ of all chips and has a defect rate of $$2\%$$. Machine B produces the remaining chips and has a defect rate of $$6\%$$. If a randomly selected chip is defective, what is the probability that it came from Machine B?
- $$\frac{21}{34}$$
- $$\frac{9}{17}$$
- $$\frac{3}{10}$$
- $$\frac{7}{20}$$
In the $$xy$$-plane, the graphs of $$y=x^2-8x+20$$ and $$y=4x+k$$ intersect at exactly one point. What is the value of $$k$$?
- $$-16$$
- $$0$$
- $$4$$
- $$8$$
The function $$f$$ is defined by $$f(x)=3x-7$$ The function $$g$$ is linear and satisfies $$g(x)=f(ax+b)$$ for constants $$a$$ and $$b$$. If $$g(2)=11$$ and $$g(5)=38$$, what is the value of $$a+b$$?
- $$2$$
- $$3$$
- $$4$$
- $$5$$
The daily revenue, in dollars, for a company is modeled by $$R(p)=-8p^2+640p-3200$$ where $$p$$ is the price, in dollars, of the product. What is the maximum possible daily revenue?
- $$9600$$
- $$96000$$
- $$12800$$
- $$16000$$
In right triangle $$\triangle ABC$$, angle $$C$$ is a right angle. If $$\sin(A)=\frac{12}{13}$$ and the hypotenuse has length $$39$$, what is the area of the triangle?
- $$270$$
- $$378$$
- $$420$$
- $$486$$
For all real numbers $$x$$ satisfying $$\sqrt{2x+9}=x-3$$ what is the value of $$x$$?
- $$5$$
- $$8$$
- $$9$$
- $$11$$
A sphere is inscribed in a right circular cylinder. The total surface area of the cylinder is $$216\pi$$ square units. What is the volume of the sphere?
- $$144\pi$$
- $$192\pi$$
- $$256\pi$$
- $$288\pi$$
$$4x-3y=29$$$$7x+5y=1$$What is the value of $$43x-6y$$?
- $$145$$
- $$173$$
- $$\frac{7558}{41}$$
- $$203$$
$$y=x^2-8x+k$$$$y=4x-7$$The system has exactly one real solution. What is the value of $$k$$?
- $$21$$
- $$25$$
- $$29$$
- $$33$$
A line passes through the points $$(1,4)$$ and $$(5,16)$$. Another line is perpendicular to this line and passes through $$(0,10)$$. What is the $$y$$-coordinate of the intersection point of the two lines?
- $$\frac{34}{5}$$
- $$7$$
- $$\frac{38}{5}$$
- $$\frac{91}{10}$$
A company's revenue came from two divisions in $$2024$$:What was the approximate overall percent change in total revenue?
- $$5\%$$ increase
- $$7\%$$ increase
- $$9\%$$ increase
- $$12\%$$ increase
If $$(3m-x)$$ is a factor of $$(x^3-31pm^3)$$, where $$p$$ and $$m$$ are constants and $$m$$ > $$0$$, what is the value of $$p$$? Round your answer to the nearest hundredth.
- 0.87
The dot plots show the distributions of two different data sets, Data Set A and Data Set B. Which of the following statements about the standard deviations of Data Set A and Data Set B is true?
- The standard deviation of Data Set A is less than the standard deviation of Data Set B.
- The standard deviation of Data Set A is greater than the standard deviation of Data Set B.
- The standard deviation of Data Set A is equal to twice the standard deviation of Data Set B.
- The standard deviation of Data Set A is less than the standard deviation of Data Set B.
In the figure, $$\triangle ABC$$ is shown. Point $$D$$ is on $$\overline{AB}$$ and point $$E$$ is on $$\overline{AC}$$ such that $$\overline{DE}\parallel\overline{BC}$$. Point $$F$$ is on $$\overline{AD}$$ and point $$G$$ is on $$\overline{AE}$$ such that $$\overline{FG}\parallel\overline{DE}$$. Suppose $$AB=3\cdot AD$$ and $$AF=\frac{2}{3}AD$$ If the area of trapezoid $$FGED$$ is $$56$$ square units, what is the area of trapezoid $$DECB$$?
- $$98.3$$
- $$112.7$$
- $$126.8$$
- $$806.4$$
A survey was conducted among $$140$$ pet owners to determine their primary pet type and their preference for indoor or outdoor pets. The results are summarized in the table below.Among the pet owners surveyed, if a pet owner is selected at random and it is found that they either own a cat or prefer outdoor pets, what is the probability that this selected owner is a dog owner?
- $$\frac{5}{14}$$
- $$\frac{3}{13}$$
- $$\frac{5}{11}$$
- $$\frac{8}{11}$$
A bakery produces two types of cakes: vanilla and chocolate. Each vanilla cake requires $$2$$ cups of flour and $$1$$ cup of sugar. Each chocolate cake requires $$3$$ cups of flour and $$2$$ cups of sugar. The bakery has a daily supply of no more than $$30$$ cups of flour and no more than $$20$$ cups of sugar. If $$v$$ represents the number of vanilla cakes and $$c$$ represents the number of chocolate cakes the bakery produces daily, which system of inequalities accurately describes the constraints on the number of cakes that can be produced?
- $$2v+3c\le30,\ v+2c\le20,\ v\ge0,\ c\ge0$$
- $$2v+3c\ge30,\ v+2c\ge20,\ v\ge0,\ c\ge0$$
- $$3v+2c\le30,\ 2v+c\le20,\ v\ge0,\ c\ge0$$
- $$2v+3c\le20,\ v+2c\le30,\ v\ge0,\ c\ge0$$