just a quick clarification, tis usually -4.9 and that's a rounded number to reflect earth's gravity on an object in motion, but -5 is close enough :)
![\bf ~~~~~~\textit{initial velocity in meters} \\\\ h(t) = -4.9t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}\\ \qquad \textit{of the object}\\ h=\textit{object's height}\\ \qquad \textit{at "t" seconds} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~%5Ctextit%7Binitial%20velocity%20in%20meters%7D%20%5C%5C%5C%5C%20h%28t%29%20%3D%20-4.9t%5E2%2Bv_ot%2Bh_o%20%5Cquad%20%5Cbegin%7Bcases%7D%20v_o%3D%5Ctextit%7Binitial%20velocity%7D%5C%5C%20%5Cqquad%20%5Ctextit%7Bof%20the%20object%7D%5C%5C%20h_o%3D%5Ctextit%7Binitial%20height%7D%5C%5C%20%5Cqquad%20%5Ctextit%7Bof%20the%20object%7D%5C%5C%20h%3D%5Ctextit%7Bobject%27s%20height%7D%5C%5C%20%5Cqquad%20%5Ctextit%7Bat%20%22t%22%20seconds%7D%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
![\bf h(x)=-5(\stackrel{\mathbb{F~O~I~L}}{x^2-8x+16})+180\implies h(x)=-5x^2+40x-80+180 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill h(x)=-5x^2+\stackrel{\stackrel{v_o}{\downarrow }}{40} x+\stackrel{\stackrel{h_o}{\downarrow }}{\boxed{100}}~\hfill](https://tex.z-dn.net/?f=%5Cbf%20h%28x%29%3D-5%28%5Cstackrel%7B%5Cmathbb%7BF~O~I~L%7D%7D%7Bx%5E2-8x%2B16%7D%29%2B180%5Cimplies%20h%28x%29%3D-5x%5E2%2B40x-80%2B180%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20~%5Chfill%20h%28x%29%3D-5x%5E2%2B%5Cstackrel%7B%5Cstackrel%7Bv_o%7D%7B%5Cdownarrow%20%7D%7D%7B40%7D%20x%2B%5Cstackrel%7B%5Cstackrel%7Bh_o%7D%7B%5Cdownarrow%20%7D%7D%7B%5Cboxed%7B100%7D%7D~%5Chfill)
-2 = -2 because of the slope
The answer is 15/121.
Since we have red AND blue, that means that both of these events occur, so we will use the multiplication rule and multiply these two probabilities:
- A probability of choosing a red marble: 3/11. (because there are 3 marbles out of total 11 marbles)
- A probability of choosing a blue marble after the red one: 5/11. (because there are 3 marbles out of total 11 marbles; there are 11 in total again because the first marble has been returned)
So, P(red and blue) is 3/11 * 5/11 = (3*5)/(11*11) = 15/121
Answer:
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Step-by-step explanation:
when you multiply 3/2 by 6 you get 18/12
