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Questions in mathematics

[Done] What is the solution of the equation [tex]2^x=7[/tex]? Round your answer to the nearest ten-thousandth.

[Done] What is the discriminant of [tex]3 x^2-10 x=-2[/tex]?

[Done] ABCD is a trapezium with BC = a, AD = b, the perpendicular distance between AD and BC is h. (a) Using the small letters given, write down the area of triangle ABC. (b) What is the height of triangle ADC with AD as the base? (c) Using the small letters given, write down the area of triangle ADC. (d) Write down the area of trapezium ABCD using the letters, a, b and h. (e) Write a formula for the area of the trapezium with parallel sides of length a and b units and height h units.

[Done] Type the correct answer in each box. Use numerals instead of words. The zeros of the function [tex]$f(x)=-(x+1)(x-3)(x+2)$[/tex] are -1, 3, and $\boxed{}$ and the [tex]$y$[/tex]-intercept of the function is located at (0, $\boxed{}$ ).

[Done] An ice cube is freezing in such a way that the side length [tex]$s$[/tex], in inches, is [tex]$s(t)=\frac{1}{2} t+4$[/tex], where [tex]$t$[/tex] is in hours. The surface area of the Part A: Write an equation that gives the volume at [tex]$t$[/tex] hours after freezing begins. (2 points) Part B: Find the surface area as a function of time, using composition, and determine its range. (4 points) Part C: After how many hours will the surface area equal 294 square inches? Show all necessary calculations, and check for extra [tex]$\varsigma \rightarrow q_{\sim}$[/tex] Paragraph [tex]$\sim I_x B I \subseteq \underline{u} \quad x^2 \Omega \vee-$[/tex] [tex]$\begin{array}{l} v(s)=\left(\frac{1}{2} t+4\right)^3 \\ \left(\frac{1}{n}+4\right)\left(\frac{1}{n}+4\right)\left(\frac{1}{-}+4\right) \end{array}$[/tex]

[Done] $\frac{1}{1+\frac{1}{1+\frac{1}{9}}}$

[Done] An electronics company polled 300 random people to find out whether they own cell phones and laptops. The results are shown in the table. \begin{tabular}{|c|c|c|c|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & \begin{tabular}{c} Cell \\ Phone \end{tabular} & \begin{tabular}{c} No Cell \\ Phone \end{tabular} & Total \\ \hline Laptop & 82 & 11 & $b$ \\ \hline \begin{tabular}{c} No \\ Laptop \end{tabular} & 159 & $a$ & 207 \\ \hline Total & 241 & 59 & 300 \\ \hline \end{tabular} Use the table to complete the statements. The cell labeled $a$ is a $\square$ The cell labeled $b$ is $a$ $\square$

[Done] A party has 14 girls and 15 boys. Four more boys arrived and 2 girls left. How many people are at the party now?

[Done] Use the union rule to answer the question. If [tex]$n(A)=9, n(B)=12$[/tex], and [tex]$n(A \cap B)=3$[/tex], what is [tex]$n(A \cup B)$[/tex]? [tex]$n(A \cup B)= \square$[/tex] (Type a whole number.)

[Done] John's father will be arriving from Dubai. If his plane leaves Dubai airport at 10:00 A.M. with a travel time of 8 hours and 45 minutes, what time will John's father arrive in Manila? Express in 12-hour clock time and 24-hour clock time.