Questions in mathematics

Questions in mathematics

📝 Answered - a. A tray of eggs contains 16 large sized eggs and 14 small sized egg. An egg is selected at random. Find the probability of selecting either a small sized or large-sized egg. b. If [tex]$T^2=4 \pi^2 \frac{\left(h^2+k^2\right)}{h g}$[/tex] make 'k' the subject of the formula.

📝 Answered - Complete the table. \begin{tabular}{|c|c|c|} \hline \begin{tabular}{c} Time \\ $( s )$ \end{tabular} & \begin{tabular}{c} Distance \\ $( m )$ \end{tabular} & \begin{tabular}{c} Height \\ $( m )$ \end{tabular} \\ \hline 0 & 0 & 0 \\ \hline$\frac{\pi}{2}$ & $a$ & $d$ \\ \hline$\pi$ & $b$ & $e$ \\ \hline$\frac{3 \pi}{2}$ & $c$ & $f$ \\ \hline $2 \pi$ & $2 \pi$ & 0 \\ \hline \end{tabular} Heights: $d=\square e=\square f=\square$ Distances: $a=\square \pi, b=\square \pi, c=\square \pi$

📝 Answered - If [tex]$p=2, q=-\frac{3}{2}$[/tex], and [tex]$r=-2$[/tex], evaluate [tex]$p q-r+1$[/tex].

📝 Answered - Which functions are even? Check all of the boxes that apply. [tex]f(x)=x^4-x^2[/tex] [tex]f(x)=x^2-3 x+2[/tex] [tex]f(x)=\sqrt{(x-2)}[/tex] [tex]f(x)=|x|[/tex]

📝 Answered - Jarred sells DVDs. His inventory shows that he has a total of 3,500 DVDs. He has 2,342 more contemporary titles than classic titles. Let [tex]$x$[/tex] represent the number of contemporary titles and [tex]$y$[/tex] represent the number of classic titles. The system of equations models the given information: [tex] \begin{array}{l} x+y=3,500 \\ x-y=2,342 \end{array} [/tex] Solve the system of equations. How many contemporary titles does Jarred have?

📝 Answered - What is the solution to this system of linear equations? [tex] \begin{array}{l} x-2 y=14 \ 5 x+y=32 \end{array} [/tex] A. (3,5) B. (6,2) C. (8,-1) D. (14,-18)

📝 Answered - \left(\frac{16}{81}\right)^{-\frac{3}{4}}

📝 Answered - Evaluate the step function for the given input values. [tex]\begin{array}{l} g(x)=\left\{\begin{array}{ll} -4, & -3 \leq x\ \textless \ -1 \\ -1, & -1 \leq x\ \textless \ 2 \\ 3, & 2 \leq x\ \textless \ 4 \\ 5, & x \geq 4 \end{array}\right. \\ g(2)=\square \\ g(-2)=\square \\ g(5)=\square \end{array}[/tex]

📝 Answered - The perimeter of a rectangle is $72 \sqrt{5} mm$ and the width of the rectangle is $3 \sqrt{20} mm$. Rhonda thinks the length is $36 \sqrt{5}-3 \sqrt{20} mm$ and Konrad thinks the length is $30 \sqrt{5} mm$. Who is correct? Explain fully.

📝 Answered - 1. In a survey of 120 people, 45 like to play football, 40 like to play volleyball, 60 like to play cricket, 10 like football as well as volleyball, 25 like football as well as cricket, 20 like volleyball as well as cricket, and 5 like to play all three games. a) If F, V, and C denote the set of people who like to play football, volleyball, and cricket respectively, write set notation to represent who do not like all three games. b) Represent the above information in a Venn diagram. c) Find the number of people who like at least one game. d) What percentage of people did not like all three games?