Answer and Explanation: The results of the survey would not be accurate to the whole of springfield, as the sample was not a random sample. A random sample is where each person in a given area (Springfield in this case) has an equal chance of being surveyed. In this case, only walmart shoppers were surveyed. Therefor, the results can only apply to shoppers at walmart, not the whole of Springfield.
Answer:
Definition:
The Jacobian of the transformation x = f(r, θ) and y = g(r ,θ) is:
=
......[1]
Given:
and ![y=e^{3r}\cos 2\theta](https://tex.z-dn.net/?f=y%3De%5E%7B3r%7D%5Ccos%202%5Ctheta)
then,
![\frac{\partial x}{\partial r} = -18e^{-3r}\sin 2\theta](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20x%7D%7B%5Cpartial%20r%7D%20%3D%20-18e%5E%7B-3r%7D%5Csin%202%5Ctheta)
![\frac{\partial y}{\partial r} = 3e^{3r}\cos 2\theta](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20y%7D%7B%5Cpartial%20r%7D%20%3D%203e%5E%7B3r%7D%5Ccos%202%5Ctheta)
and
Substitute these value in [1] ;
![\begin{vmatrix}\frac{\partial x }{\partial r} & \frac{\partial x }{\partial \theta} \\ \frac{\partial y }{\partial r} & \frac{\partial y }{\partial \theta}\end{vmatrix}=\begin{vmatrix}-18e^{-3r}\sin 2\theta & 12e^{-3r}\cos 2\theta\\ 3e^{3r}\cos 2\theta &- 2e^{3r}\sin 2\theta\end{vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bvmatrix%7D%5Cfrac%7B%5Cpartial%20x%20%7D%7B%5Cpartial%20r%7D%20%26%20%5Cfrac%7B%5Cpartial%20x%20%7D%7B%5Cpartial%20%5Ctheta%7D%20%5C%5C%20%5Cfrac%7B%5Cpartial%20y%20%7D%7B%5Cpartial%20r%7D%20%26%20%5Cfrac%7B%5Cpartial%20y%20%7D%7B%5Cpartial%20%5Ctheta%7D%5Cend%7Bvmatrix%7D%3D%5Cbegin%7Bvmatrix%7D-18e%5E%7B-3r%7D%5Csin%202%5Ctheta%20%26%2012e%5E%7B-3r%7D%5Ccos%202%5Ctheta%5C%5C%203e%5E%7B3r%7D%5Ccos%202%5Ctheta%20%26-%202e%5E%7B3r%7D%5Csin%202%5Ctheta%5Cend%7Bvmatrix%7D)
=![(-18e^{-3r}\sin 2\theta)\cdot(-2e^{3r}\sin 2\theta)-(12e^{-3r}\cos 2\theta)\cdot(3e^{3r}\cos 2\theta)](https://tex.z-dn.net/?f=%28-18e%5E%7B-3r%7D%5Csin%202%5Ctheta%29%5Ccdot%28-2e%5E%7B3r%7D%5Csin%202%5Ctheta%29-%2812e%5E%7B-3r%7D%5Ccos%202%5Ctheta%29%5Ccdot%283e%5E%7B3r%7D%5Ccos%202%5Ctheta%29)
=![(-18 \cdot -2)e^{-3r+3r} \sin^2 2\theta - (12 \cdot 3)e^{-3r+3r} \cos^2 2\theta](https://tex.z-dn.net/?f=%28-18%20%5Ccdot%20-2%29e%5E%7B-3r%2B3r%7D%20%5Csin%5E2%202%5Ctheta%20-%20%2812%20%5Ccdot%203%29e%5E%7B-3r%2B3r%7D%20%5Ccos%5E2%202%5Ctheta)
On simplify:
=
[ Use
]
therefore, the jacobian transformation of
and
is;
Answer:
3 months
Step-by-step explanation:
constant slope option a has a higher y value but in 3 months option b will be greater than a
Answer:d
Step-by-step explanation:
Answer:
x = 15
Step-by-step explanation:
x multiplied by 0.4 = 6
so you divide 0.4 by each side
x = 6/0.4
and plug that into the calculator.