Answer:
1/4
Step-by-step explanation:
Casserole received by Jackie and Alicie = 1/2 x 3/4 = 3/8 of the whole
Portion eaten by Jackie = 2/3 x 3/8 = 1/4 of the whole
Answer:
Domain: [-4, ∞]
Range: [-6, ∞]
Step-by-step explanation:
The domain is the set of the possible x values
The range is the set of the possible y values.
In the graph, we can see that the function cuts in a given part. We can see that for the x-values, the smallest one is x = -4, and then the function extends to the right (we see no limit at the right, then there is none)
This means that the domain is:
D: [-4, ∞]
For the y-values, the smallest value is when x = -4, and the y-value is -6
Then we can see that, as x increases, the same happens for y.
Then the range is:
R: [-6, ∞]
If you mean
![\dfrac{\mathrm d}{\mathrm dx}\left[4^x\ln(x)\right]](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B4%5Ex%5Cln%28x%29%5Cright%5D)
then first write
. Then by the product rule,
![\dfrac{\mathrm d}{\mathrm dx}\left[4^x\ln(x)\right] = \ln(4)e^{\ln(4)x}\ln(x) + \dfrac{e^{\ln(4)x}}x = \ln(4)4^x\ln(x)+\dfrac{4^x}x=\dfrac{4^x}x\left(\ln(4)x\ln(x)+1\right)](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B4%5Ex%5Cln%28x%29%5Cright%5D%20%3D%20%5Cln%284%29e%5E%7B%5Cln%284%29x%7D%5Cln%28x%29%20%2B%20%5Cdfrac%7Be%5E%7B%5Cln%284%29x%7D%7Dx%20%3D%20%5Cln%284%294%5Ex%5Cln%28x%29%2B%5Cdfrac%7B4%5Ex%7Dx%3D%5Cdfrac%7B4%5Ex%7Dx%5Cleft%28%5Cln%284%29x%5Cln%28x%29%2B1%5Cright%29)
If you instead mean
![\dfrac{\mathrm d}{\mathrm dx}\left[4^{x\ln(x)}\right]](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B4%5E%7Bx%5Cln%28x%29%7D%5Cright%5D)
you can again rewrite
. Then by the chain and product rules,
![\dfrac{\mathrm d}{\mathrm dx}\left[4^{x\ln(x)}\right] = e^{x\ln(x)\ln(4)}\ln(4)\left(\ln(x)+1\right) = 4^{x\ln(x)}\ln(4)(\ln(x)+1)](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B4%5E%7Bx%5Cln%28x%29%7D%5Cright%5D%20%3D%20e%5E%7Bx%5Cln%28x%29%5Cln%284%29%7D%5Cln%284%29%5Cleft%28%5Cln%28x%29%2B1%5Cright%29%20%3D%204%5E%7Bx%5Cln%28x%29%7D%5Cln%284%29%28%5Cln%28x%29%2B1%29)
Add the temps up
-24 + (-15) + (-21) + (-32) + (-18) + (-9) + (-14) = -133
now divide by how many numbers there are
-133/7 = -19 <== the mean (average)