Advanced Quizzes — Quiz 20

Questions in this quiz (10)

1. Of the $$200$$ jellybeans in a jar, $$70\%$$ are green and the rest are red. How many green jellybeans must be removed so that $$60\%$$ of the remaining jellybeans are green?

   • 50

2. If the line $$ax+3y=15$$, where $$a$$ is a constant, has an $$x$$-intercept that is twice the value of the $$y$$-intercept, what is the value of $$a$$?

   • $$\frac{1}{2}$$
   • $$\frac{1}{5}$$
   • $$\frac{3}{2}$$
   • $$\frac{5}{3}$$

3. If $$f(x)$$ is a linear function such that $$f(2)\le f(3)$$, $$f(4)\ge f(5)$$, and $$f(6)=10$$, which of the following must be true?

   • $$f(3)$$ < $$f(0)$$ < $$f(4)$$
   • $$f(0)=0$$
   • $$f(0)$$ > $$10$$
   • $$f(0)=10$$

4. The relationship between the daily profit $$y$$, in dollars, of a bakery and the number of cakes sold $$x$$ by the bakery is graphed in the $$xy$$-plane. What does it mean that $$(5,0)$$ is a solution to the equation of the line?

   • The bakery needs to sell $$5$$ cakes per day to cover its daily expenses.
   • Each cake must be sold for at least $$5$$ dollars to cover the cost of making it.
   • It costs $$5$$ dollars to make each cake.
   • Each day, the bakery gives the first $$5$$ cakes away for free.

5. Functions $$f$$ and $$g$$ are defined by $$f(x)=x+1$$ and $$g(x)=\frac{x}{2}$$. If $$f(g(f(k)))=10$$, what is the value of $$k$$?

   • 17

6. The graph of the function $$y=9-x^2$$ is shown in the $$xy$$-plane. What is the length of $$\overline{AB}$$?

   • $$3\sqrt{2}$$
   • $$3\sqrt{10}$$
   • $$9$$
   • $$9\sqrt{10}$$

7. In the $$xy$$-plane, the parabola with equation $$y=x^2-5x+6$$ intersects the line $$y=3x-10$$ at point $$(a,b)$$. What is the value of $$b$$?

   • 2

8. A biologist uses the function $$p(n)=-100n^2+1,000n$$ to model the population of seagulls on a beach in year number $$n$$, where $$1\le n\le10$$. Which of the following equivalent forms of $$p(n)$$ displays the maximum population and the number of the year in which the population reaches that maximum as constants or coefficients?

   • $$p(n)=-4n(25n-250)$$
   • $$p(n)=-10(10n^2-100n)$$
   • $$p(n)=-100(n-5)^2+2500$$
   • $$p(n)=-100(n-7)^2+4900$$

9. For the polynomial $$f(x)=3x^3+kx^2+5x+2$$, $$k$$ is a constant. If $$f(x)$$ is divisible by $$x-2$$, what is the value of $$k$$?

   • $$-12$$
   • $$-9$$
   • $$-6$$
   • $$-3$$

10. $$2z^3-kxz^2+5xz+2x-2$$In the polynomial above, $$k$$ is a constant. If $$z-1$$ is a factor of the polynomial above, what is the value of $$k$$?

    • $$-2$$
    • $$2$$
    • $$5$$
    • $$7$$