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Questions in mathematics

📝 Answered - A college cafeteria is looking for a new dessert to offer its 5,000 students. The table shows the preference of 225 students. | Ice Cream | Candy | Cake | Pie | Cookies | |---|---|---|---|---| | 81 | 9 | 72 | 36 | 27 | Which statement is the best prediction about the scoops of ice cream the college will need? A. The college will have about 1,800 students who prefer ice cream. B. The college will have about 800 students who prefer ice cream. C. The college will have about 600 students who prefer ice cream. D. The college will have about 144 students who prefer ice cream.

📝 Answered - If [tex]$a: b=3: 5$[/tex] and [tex]$a: c=5: 7$[/tex], what is the value of [tex]$b: c$[/tex]? A. [tex]$3: 7$[/tex] B. [tex]$5: 7$[/tex] C. [tex]$21: 25$[/tex] D. [tex]$25: 21$[/tex]

📝 Answered - The tables represent two linear functions in a system. | x | y | |---|---| | -6 | -22 | | -3 | -10 | | 0 | 2 | | 3 | 14 | | x | y | |---|---| | -6 | -30 | | -3 | -21 | | 0 | -12 | | 3 | -3 | What is the solution to this system? A. [tex]\left(-\frac{13}{3},-25\right)[/tex] B. [tex]\left(-\frac{14}{3},-54\right)[/tex] C. (-13, -50) D. (-14, -54)

📝 Answered - $\frac{\frac{2}{3}}{\frac{1}{3}+\frac{2}{3}}+1$

📝 Answered - (b) [tex]2 x^2+4 x+1=0[/tex] [tex]x=[/tex]

📝 Answered - At which root does the graph of [tex]f(x)=(x-5)^3(x+2)^2[/tex] touch the [tex]x[/tex]-axis? A. -5 B. -2 C. 2 D. 5

📝 Answered - $\begin{array}{c} 10 n+16=6(n+2) \\ 10(\square+16 \stackrel{?}{\neq 6}(\square+2) \end{array}$

📝 Answered - Work out $\frac{5}{6} \times \frac{7}{3}$. Give your answer as a fraction in its simplest form.

📝 Answered - Which graph is the graph of this function? [tex]f(x)=\left\{\begin{array}{cl}3 \sqrt{x+1} & \text { if } 0 \leq x\ \textless \ 3 \\5-x & \text { if } 3 \leq x \leq 5\end{array}\right.[/tex] A. graph A B. graph B C. graph C D. graph D

📝 Answered - Let $f(x)=x^2-7x$ and $g(x)=6+x$. Find the following: (a) $(f+g)(x)$ (b) $(f - g)(x)$ (c) $(f \cdot g)(x)$ (d) $\left(\frac{f}{g}\right)(x)$ (e) The domain of $\frac{f}{g}$ (a) $(f+g)(x)=x^2-6x+6$ (Simplify your answer. Do not factor.) (b) $( f - g )( x )=\square$ (Simplify your answer. Do not factor.)