Advanced Quizzes — Quiz 10

Questions in this quiz (10)

1. In the figure, a square is inscribed in a circle. If the area of the square is $$36$$, what is the perimeter of the shaded region?

   • $$6+\frac{3\sqrt{2}}{2}\pi$$
   • $$6+3\pi$$
   • $$6+3\sqrt{2}\pi$$
   • $$36+6\sqrt{2}\pi$$

2. What is the solution set for the equation $$\sqrt{x+22}-2=x$$?

   • $$\{-6,3\}$$
   • $$\{-6\}$$
   • $$\{3\}$$
   • $$\{-3,6\}$$

3. A data set of $$27$$ different numbers has a mean of $$33$$ and a median of $$33$$. A new data set is created by adding $$7$$ to each number in the original data set that is greater than the median and subtracting $$7$$ from each number in the original data set that is less than the median. Which of the following measures does NOT have the same value in both the original and new data sets?

   • Median
   • Mean
   • Sum of the numbers
   • Standard deviation

4. The concentration of a chemical compound is equal to the amount of the substance, in moles, divided by the volume of the solution, in cubic centimeters. A chemist has two containers of different sizes in the shape of a cube. The edge length of the larger container is $$4$$ times the edge length of the smaller container. Each cube contains $$144$$ moles of a substance. The concentration of the compound in the larger container is $$3$$ moles per cubic centimeter. What is the positive difference between the larger container's volume and the smaller container's volume, in cubic centimeters?

   • $$\frac{3}{4}$$
   • $$\frac{189}{4}$$
   • $$\frac{4}{3}$$
   • $$\frac{9}{4}$$

5. In the figure, a right triangle is inscribed in a circle, with the hypotenuse of the triangle passing through the center of the circle. If the legs of the right triangle are $$6$$ and $$8$$, what is the area of the shaded region?

   • $$100\pi$$
   • $$100\pi-48$$
   • $$25\pi-48$$
   • $$25\pi-24$$

6. A researcher conducted a survey of $$1000$$ randomly selected residents to determine their favorite park. The survey showed that $$48\%$$ of the residents preferred Park A, with a margin of error of $$3\%$$. Which of the following is the best conclusion?

   • Exactly $$48\%$$ of all residents in the city prefer Park A.
   • Between $$45\%$$ and $$51\%$$ of the people surveyed prefer Park A.
   • It is highly likely that between $$45\%$$ and $$51\%$$ of all residents in the city prefer Park A.
   • The survey is flawed because the margin of error is greater than $$0\%$$.

7. The function $$f$$ is defined by $$f(x)=5(0.92)^{3x}$$ The equation can be rewritten as $$f(x)=5\left(1-\frac{r}{100}\right)^x$$, where $$r$$ is a constant. Which of the following is closest to the value of $$r$$?

   • $$8$$
   • $$12$$
   • $$22$$
   • $$24$$

8. A particular integer $$N$$ is divisible by two different prime numbers $$p$$ and $$q$$. Which of the following must be true?I. $$N$$ is not a prime number.II. $$N$$ is divisible by $$pq$$.III. $$N$$ is an odd integer.

   • I only
   • II only
   • I and II only
   • I and III only

9. For an electric field passing through a flat surface perpendicular to it, the electric flux is the product of the electric field's strength and the area of the surface. A certain flat surface consists of two adjacent squares, where the side length of the larger square is $$3$$ times the side length of the smaller square. An electric field with strength $$29.00$$ volts per meter passes uniformly through this surface. If the total electric flux through this surface is $$4640$$ volt-meters, what is the electric flux, in volt-meters, of the electric field through the larger square?

   • 4176

10. Let $$p(x)=x^3-3x^2+kx-4$$, where $$k$$ is a constant. If the polynomial $$p(x)$$ is divisible by $$x-2$$, what is the value of $$k$$?

    • $$2$$
    • $$3$$
    • $$4$$
    • $$5$$