Advanced Quizzes — Quiz 12

Questions in this quiz (10)

1. The graph of $$2x-3y=6$$ is translated down $$3$$ units in the $$xy$$-plane. If the resulting graph crosses the $$x$$-axis at a certain point, what is the $$x$$-coordinate of the point?

   • $$\frac{7}{2}$$
   • $$\frac{15}{2}$$
   • $$\frac{3}{2}$$
   • $$\frac{3}{5}$$

2. In the $$xy$$-plane, the graph of $$2x^2-6x+2y^2+2y=45$$ is a circle. What is the radius of the circle?

   • $$5$$
   • $$6.5$$
   • $$\sqrt{40}$$
   • $$\sqrt{50}$$

3. A three-digit number, $$XYZ$$, is formed of three different nonzero digits $$X$$, $$Y$$, and $$Z$$. A new number is formed by rearranging the same three digits. What is the greatest possible difference between the two numbers?

   • 792

4. On the number line above, the tick marks correspond to consecutive integers. What is the value of $$x$$?

   • 96

5. In the figure shown, $$AB=\sqrt{185}$$ units, $$AC=4$$ units, and $$CE=10$$ units. What is the area, in square units, of triangle $$ADE$$?

   • $$\frac{91}{2}$$
   • $$\frac{13}{2}$$
   • $$\frac{637}{2}$$
   • $$\frac{\sqrt{185}}{2}$$

6. A motorcycle can travel $$240$$ miles on a full tank of fuel and has a fuel efficiency of $$40$$ miles per gallon. Motorcycle B has a fuel tank that is geometrically similar to Motorcycle A's tank, but each linear dimension is doubled. Additionally, Motorcycle B's fuel efficiency is $$25%$$ less than Motorcycle A's. What is the range of Motorcycle B, in miles?

   • 1440

7. A research company surveys $$2400$$ randomly selected adults about support for a proposed law. The survey reports that $$54\%$$ of respondents support the law, with a margin of error of $$pm1.5%\$$. Which of the following is the most appropriate conclusion based on these results?

   • It is certain that between $$52.5\%$$ and $$55.5\%$$ of all adults support the law.
   • If another sample of $$2400$$ adults were surveyed, exactly $$54\%$$ would support the law.
   • The survey suggests that the true percentage of all adults who support the law is likely between $$52.5\%$$ and $$55.5\%$$.
   • The law definitely has majority support among all adults.

8. The equation below is true for all values of $$x$$ where $$x \ne3$$ and $$x \ne-4$$, and $$M$$ and $$N$$ are constants.$$\frac{M}{x-3}+\frac{N}{x+4}=\frac{7x+2}{(x-3)(x+4)}$$What is the value of $$MN$$?

   • $$\frac{7}{2}$$
   • $$10$$
   • $$12$$
   • $$\frac{598}{49}$$

9. A company produces computer chips at three factories: Factory A, Factory B, and Factory C. Factory A produces $$50\%$$ of the chips, Factory B produces $$30\%$$, and Factory C produces the remaining $$20\%$$. Historical data shows that $$4\%$$ of the chips from Factory A are defective, $$8\%$$ from Factory B are defective, and $$12\%$$ from Factory C are defective. If a randomly selected chip is defective, what is the probability that it came from Factory C?

   • $$\frac{3}{14}$$
   • $$\frac{2}{7}$$
   • $$\frac{3}{7}$$
   • $$\frac{6}{17}$$

10. The table below summarizes the results of a survey asking $$300$$ people about their favorite type of music, categorized by age group.If a person surveyed is chosen at random from those who prefer either Rock or Hip-Hop music, what is the probability that the person is between ages $$25$$ and $$50$$?

    • $$\frac{4}{7}$$
    • $$\frac{8}{15}$$
    • $$\frac{16}{35}$$
    • $$\frac{5}{11}$$