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Questions in mathematics

[Done] 3. Solve the equation. $-\frac{m}{4} = 5$ 5. Solve the equation. $2v + 7 = 3$

[Done] Simplify $22-5(2 x+4)$.

[Done] \begin{tabular}{|c|c|c|c|} \hline & \begin{tabular}{c} Rate \ (Sheds per Day) \end{tabular} & \begin{tabular}{c} Time \ (Days) \end{tabular} & Fraction Completed \ \hline Kaitlyn & $\frac{1}{6}$ & $d$ & $\frac{1}{8} d$ \ \hline Mark & $\frac{1}{8}$ & $d$ & $\frac{1}{8} d$ \ \hline \end{tabular} $\frac{1}{6} d-\frac{1}{8} d=48$ $\frac{1}{6} d+\frac{1}{8} d=48$ $\frac{1}{6} d-\frac{1}{8} d=1$ $\frac{1}{d} d+\frac{1}{8} d-$

[Done] Find the derivative of [tex]f(x)=7 \sin x+x^3 \cos x[/tex]. a.) [tex]f^{\prime}(x)=7 \cos x-3 x^2 \sin x[/tex] b.) [tex]f^{\prime}(x)=-7 \cos x-3 x^2 \cos x+x^3 \sin x[/tex] c.) [tex]f^{\prime}(x)=7 \cos x+3 x^2 \cos x-x^3 \sin x[/tex] d.) [tex]f^{\prime}(x)=-7 \cos x+3 x^2 \sin x[/tex]

[Done] Use integration by parts to evaluate the integral: \[\int_1^3 \frac{\ln (x)}{x^8} d x=\]

[Done] Fiona recorded the number of miles she biked each day last week as shown below: [tex]$4, 7, 4, 10, 5$[/tex] The mean is given by [tex]$m = 6$[/tex]. Which equation shows the variance for the number of miles Fiona biked last week? A. [tex]$s^2=\frac{(4-6)^2+(7-6)^2+(4-6)^2+(10-6)^2+(5-6)^2}{6}$[/tex] B. [tex]$\sigma=\sqrt{\frac{(4-6)^2+(7-6)^2+(4-6)^2+(10-6)^2+(5-6)^2}{5}}$[/tex] C. [tex]$S=\sqrt{\frac{(4-6)^2+(7-6)^2+(4-6)^2+(10-6)^2+(5-6)^2}{4}}$[/tex] D. [tex]$2(4-6)^2+(7-6)^2+(4-6)^2+(10-6)^2+(5-6)^2$[/tex]

[Done] The equation $y=\frac{1}{5} x$ represents a proportional relationship. Explain how you can tell the relationship is proportional from the graph of the equation, and how you can find the constant of proportionality.

[Done] A firm's marginal demand function is [tex]D^{\prime}(x)=-\frac{2000}{\sqrt{25-x^2}}[/tex]. Estimate the demand function [tex]D(x)[/tex] given that [tex]D(3)=13,000[/tex]. (Assume [tex]-5\ \textless \ x\ \textless \ 5[/tex].)

[Done] Solve: [tex]\frac{x^2-x-6}{x^2}=\frac{x-6}{2 x}+\frac{2 x+12}{x}[/tex] After multiplying each side of the equation by the LCD and simplifying, the resulting equation is [tex]\square[/tex]

[Done] Add or subtract. Write in simplest form. 7 - 6 7/8