Advanced Quizzes — Quiz 15

Questions in this quiz (10)

1. A circle in the $$xy$$-plane has its center at $$(2,-3)$$ and has a radius of $$7$$. An equation of this circle is $$x^2+y^2+ax+by+c=0$$, where $$a$$, $$b$$, and $$c$$ are constants. What is the value of $$a-b+c$$?

   • -46

2. If $$n^{5/3}=k^{3/2}$$ and $$n^{4a+1}=k$$, then what is $$a$$?

   • $$\frac{5}{36}$$
   • $$\frac{10}{9}$$
   • $$\frac{1}{36}$$
   • $$\frac{3}{5}$$

3. In the expression $$26z^{18}+bz^9+70$$, $$b$$ is a positive integer. If $$qz^9+r$$ is a factor of the expression, where $$q$$ and $$r$$ are positive integers, what is the greatest possible value of $$b$$?

   • 1821

4. $$\frac{49}{p}=\frac{49}{q}-\frac{49}{r}-\frac{49}{s}$$The given equation relates the positive variables $$p$$, $$q$$, $$r$$, and $$s$$. Which of the following is equivalent to $$q$$?

   • $$p+r+s$$
   • $$49(p+r+s)$$
   • $$\frac{prs}{pr+ps+rs}$$
   • $$\frac{prs}{49p+49r+49s}$$

5. One of the factors of $$2x^3+44x^2+234x$$ is $$x+b$$, where $$b$$ is a positive constant. What is the smallest possible value of $$b$$?

   • 9

6. If the polynomial $$P(x)=27x^3-9kx^2-Nk^3$$ is divisible by $$(3x-2k)$$, where $$k$$ and $$N$$ are constants and $$k\ne0$$, what is the value of $$N$$?

   • 4

7. $$y\ge3x-8$$$$2x+y\le18$$$$x\ge2$$If $$x$$ and $$y$$ are integers, what is the maximum possible value of $$y$$?

   • 4
   • 8
   • 10
   • 14

8. A researcher uses the least-squares regression line $$\hat{y}=1.8x+22$$ to predict a patient's recovery score, where $$x$$ is the dosage in milligrams. One patient received $$35$$ mg and had an actual recovery score of $$92$$. What is the residual, and what does it suggest?

   • 7; the model underpredicted by 7 units.
   • -7; the model overpredicted by 7 units.
   • 7; the model overpredicted by 7 units.
   • -7; the model underpredicted by 7 units.

9. A factory produces three types of parts: Type A, Type B, and Type C. Of all parts produced, $$25\%$$ are Type A, $$50\%$$ are Type B, and $$25\%$$ are Type C. The defective rates are $$4\%$$ for Type A, $$3\%$$ for Type B, and $$6\%$$ for Type C. If a randomly selected part is defective, what is the probability that it is Type B?

   • $$\frac{3}{8}$$
   • $$\frac{5}{12}$$
   • $$\frac{1}{2}$$
   • $$\frac{3}{20}$$

10. A company sells two products, Product A and Product B. In Quarter 1, Product A made up $$55\%$$ of total sales, and Product B made up the rest. From Quarter 1 to Quarter 2, total sales increased by $$30\%$$. During the same period, Product A sales increased by $$40\%$$. What was the percentage increase in sales for Product B from Quarter 1 to Quarter 2?

    • 15.2%
    • 17.8%
    • 20%
    • 25.9%