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Questions in mathematics

[Answered] A piecewise function is defined as shown. [tex]f(x)=\left\{\begin{array}{cc}-x, & x \leq-1 \\ 1, & x=0 \\ x+1 & x \geq 1\end{array}\right.[/tex] What is the value of [tex]f(x)[/tex] when [tex]x=3[/tex]? A. -3 B. -2 C. 1 D. 4

[Answered] Which equation represents a line that passes through $\left(4, \frac{1}{3}\right)$ and has a slope of $\frac{3}{4}$? A. $y-\frac{3}{4}=\frac{1}{3}(x-4)$ B. $y-\frac{1}{3}=\frac{3}{4}(x-4)$ C. $y-\frac{1}{3}=4\left(x-\frac{3}{4}\right)$ D. $y-4=\frac{3}{4}\left(x-\frac{2}{3}\right)$

[Answered] The following two-way table represents data from a survey asking students whether they have visited Alaska, Hawaii, or both. \begin{tabular}{|l|l|l|l|} \hline & Alaska & Not Alaska & Total \\ \hline Hawaii & 6 & 15 & 21 \\ \hline Not Hawaii & 8 & 21 & 29 \\ \hline Total & 14 & 36 & 50 \\ \hline \end{tabular} What is the relative frequency for students who have been to Alaska? $\square$ What is the relative frequency for students who have been to Hawaii but not Alaska? $\square$ What is the relative frequency for students who have not been to Alaska or Hawaii? $\square$

[Answered] The pair of parametric equations represent a line, parabola, circle, ellipse, or hyperbola. Name the type of basic curve that the pair of equations represents. [tex] \begin{array}{l} x+4=-6 t \\ y-8=4 t \end{array} [/tex]

[Answered] Approximate the number using a calculator. [tex]e^{2.1}[/tex] [tex]e^{2.1} \approx[/tex] $\square$ (Round to three decimal places.)

[Answered] Analyze the following budget, with an income of $600, to determine how much can be spent on food for the month. | Month | Budgeted Amount | | :-------- | :------- | | Cell Phone | $65 | | Food | $ | | Entertainment | $95 | | College Savings | $200 | | Car Expenses - Gas, Insurance | $160 | a. $210 can be spent on food. b. $145 can be spent on food. c. $80 can be spent on food. d. $260 can be spent on food. Please select the best answer from the choices provided

[Answered] [Clean the question above and then proceed with classification] $11 / 2 \div 33 / 5=$

[Answered] Which polynomial is prime? [tex]7 x^2-35 x+2 x-10[/tex] [tex]9 x^3+11 x^2+3 x-33[/tex] [tex]10 x^3-15 x^2+8 x-12[/tex] [tex]12 x^4+42 x^2+4 x^2+14[/tex]

[Answered] Find the exact value of the following expression. [tex]$\tan ^{-1}\left(\frac{\sqrt{3}}{3}\right)$[/tex] Select the correct choice below and, if necessary, fill in the answer box to A. [tex]$\tan ^{-1}\left(\frac{\sqrt{3}}{3}\right)=[/tex] $\square$ (Simplify your answer. Type an exact answer, using [tex]$\pi$[/tex] as needed.

[Answered] $[(5,577)-2] \div 2 \cdot(8+18 \div 9)$