A possible reaction of ethane with chlorine is shown below. \( \mathrm{CH}_{3} \mathrm{CH}_{3}+\mathrm{Cl}_{2} \) This reaction could conceivably occur by the following chain mechanisms [1], [2], and [3]. The chain initiating step(s) is (are) [1] \( \mathrm{Cl}_{2} \) [2] \( \mathrm{Cl}_{3} \mathrm{CH}_{2} \mathrm{Cl}+\mathrm{CH}_{3} \mathrm{CH}_{3} \xrightarrow{\text { slow }} \mathrm{HCl} \) [3] \( \mathrm{CH}_{3} \mathrm{CH}_{2}^{*}+\mathrm{Cl}_{2} \xrightarrow{\text { fast }} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Cl}+\mathrm{CH}_{3} \mathrm{CH}_{2}^{*} \) Only [1] Only [2] Only [3] Only [1] and [2]

How much money will you make if you invest \( \$ 3,200 \) with a simple interest rate of \( 4.25 \% \) over the course of 18 years? Round your answer to the nearest cent. (Just enter a value, do not include units in your answer)

Use Simpson's Rule with \( n=10 \) to estimate the arc length of the curve. (Round your answer to four decimal places.) \[ y=x \sin (x), \quad 0 \leq x \leq 2 \pi \] Find the answer produced by a calculator or computer to compare with the previous result. (Round your answer to four decimal places.) Enter a number. Need Help? Read lt

Plot the intercepts to graph the equation. \[ x+y=-4 \]

194. \( 12 \sqrt[4]{27} \div 4 \sqrt[4]{3} \)

Let \( f(x)=7 x+4 \) and \( g(x)=4 x-7 \). Find \( (f+g)(x),(f-g)(x),(f g)(x) \), and \( \left(\frac{f}{g}\right)(x) \). Give the domain of each. \( (f+g)(x)=\square( \) Simplify your answer.)