Step-by-step explanation:
since Poisson distribution parameter is not given so we have to estimate it from the sample data. The average number of of arrivals per minute at an ATM is
![\hat{\lambda}=\bar{x}=\frac{\sum x}{n}=\frac{30}{30}=1](https://tex.z-dn.net/?f=%5Chat%7B%5Clambda%7D%3D%5Cbar%7Bx%7D%3D%5Cfrac%7B%5Csum%20x%7D%7Bn%7D%3D%5Cfrac%7B30%7D%7B30%7D%3D1)
So probabaility for
is
![P(X=1)=\frac{e^{-\lambda} \lambda^{x}}{x !}=\frac{e^{-1} \cdot 1^{1}}{1 !}=0.3679](https://tex.z-dn.net/?f=P%28X%3D1%29%3D%5Cfrac%7Be%5E%7B-%5Clambda%7D%20%5Clambda%5E%7Bx%7D%7D%7Bx%20%21%7D%3D%5Cfrac%7Be%5E%7B-1%7D%20%5Ccdot%201%5E%7B1%7D%7D%7B1%20%21%7D%3D0.3679)
So expected frequency for
is
(or
.
9105-4031= 5074
Step-by-step explanation:
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Keeping in mind that x = rcos(θ) and y = rsin(θ).
we know the magnitude "r" of U and V, as well as their angle θ, so let's get them in standard position form.
![\bf u= \begin{cases} x=7cos(330^o)\\ \qquad 7\cdot \frac{\sqrt{3}}{2}\\ \qquad \frac{7\sqrt{3}}{2}\\ y=7sin(330^o)\\ \qquad 7\cdot -\frac{1}{2}\\ \qquad -\frac{7}{2} \end{cases}\qquad \qquad v= \begin{cases} x=8cos(30^o)\\ \qquad 8\cdot \frac{\sqrt{3}}{2}\\ \qquad \frac{8\sqrt{3}}{2}\\ y=8sin(30^o)\\ \qquad 8\cdot \frac{1}{2}\\ \qquad 4 \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20u%3D%0A%5Cbegin%7Bcases%7D%0Ax%3D7cos%28330%5Eo%29%5C%5C%0A%5Cqquad%207%5Ccdot%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%5C%5C%0A%5Cqquad%20%5Cfrac%7B7%5Csqrt%7B3%7D%7D%7B2%7D%5C%5C%0Ay%3D7sin%28330%5Eo%29%5C%5C%0A%5Cqquad%207%5Ccdot%20-%5Cfrac%7B1%7D%7B2%7D%5C%5C%0A%5Cqquad%20-%5Cfrac%7B7%7D%7B2%7D%0A%5Cend%7Bcases%7D%5Cqquad%20%5Cqquad%20v%3D%0A%5Cbegin%7Bcases%7D%0Ax%3D8cos%2830%5Eo%29%5C%5C%0A%5Cqquad%208%5Ccdot%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%5C%5C%0A%5Cqquad%20%5Cfrac%7B8%5Csqrt%7B3%7D%7D%7B2%7D%5C%5C%0Ay%3D8sin%2830%5Eo%29%5C%5C%0A%5Cqquad%208%5Ccdot%20%5Cfrac%7B1%7D%7B2%7D%5C%5C%0A%5Cqquad%204%0A%5Cend%7Bcases%7D)
![\bf u+v\implies \left( \frac{7\sqrt{3}}{2},-\frac{7}{2} \right)+\left( \frac{8\sqrt{3}}{2},4 \right)\implies \left( \frac{7\sqrt{3}}{2}+\frac{8\sqrt{3}}{2}~~,~~ -\frac{7}{2}+4\right) \\\\\\ \left(\stackrel{a}{\frac{15\sqrt{3}}{2}}~~,~~ \stackrel{b}{\frac{1}{2}}\right)\\\\ -------------------------------](https://tex.z-dn.net/?f=%5Cbf%20u%2Bv%5Cimplies%20%5Cleft%28%20%5Cfrac%7B7%5Csqrt%7B3%7D%7D%7B2%7D%2C-%5Cfrac%7B7%7D%7B2%7D%20%5Cright%29%2B%5Cleft%28%20%5Cfrac%7B8%5Csqrt%7B3%7D%7D%7B2%7D%2C4%20%5Cright%29%5Cimplies%20%5Cleft%28%20%5Cfrac%7B7%5Csqrt%7B3%7D%7D%7B2%7D%2B%5Cfrac%7B8%5Csqrt%7B3%7D%7D%7B2%7D~~%2C~~%20-%5Cfrac%7B7%7D%7B2%7D%2B4%5Cright%29%0A%5C%5C%5C%5C%5C%5C%0A%5Cleft%28%5Cstackrel%7Ba%7D%7B%5Cfrac%7B15%5Csqrt%7B3%7D%7D%7B2%7D%7D~~%2C~~%20%20%5Cstackrel%7Bb%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D%5Cright%29%5C%5C%5C%5C%0A-------------------------------)
1.4 decameter because a decameter equals to meter divided by 10