Answer:
![g(f(3))=-2](https://tex.z-dn.net/?f=g%28f%283%29%29%3D-2)
Step-by-step explanation:
So we have the two functions:
![g(x)=4x+2\text{ and } f(x)=3x-10](https://tex.z-dn.net/?f=g%28x%29%3D4x%2B2%5Ctext%7B%20and%20%7D%20f%28x%29%3D3x-10)
And we want to find g(f(3)).
So, let's find f(3) first:
![f(3)=3(3)-10](https://tex.z-dn.net/?f=f%283%29%3D3%283%29-10)
Multiply:
![f(3)=9-10](https://tex.z-dn.net/?f=f%283%29%3D9-10)
Subtract:
![f(3)=-1](https://tex.z-dn.net/?f=f%283%29%3D-1)
Therefore, we can substitute -1 for f(3):
![g(f(3))=g(-1)](https://tex.z-dn.net/?f=g%28f%283%29%29%3Dg%28-1%29)
Now, find g(-1):
![g(-1)=4(-1)+2](https://tex.z-dn.net/?f=g%28-1%29%3D4%28-1%29%2B2)
Multiply:
![g(-1)=-4+2](https://tex.z-dn.net/?f=g%28-1%29%3D-4%2B2)
Add:
![g(-1)=-2](https://tex.z-dn.net/?f=g%28-1%29%3D-2)
And we're done!
So:
![g(f(3))=-2](https://tex.z-dn.net/?f=g%28f%283%29%29%3D-2)
Answer:
The derivative is
![\frac{dy}{dx} = 2 - \frac{2\sqrt3}{\sqrt x}\\](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%202%20-%20%20%5Cfrac%7B2%5Csqrt3%7D%7B%5Csqrt%20x%7D%5C%5C)
Step-by-step explanation:
The function is given by
![y = 2x - 1 - \sqrt {3x}](https://tex.z-dn.net/?f=y%20%3D%202x%20-%201%20-%20%5Csqrt%20%7B3x%7D)
Differentiate with respect to x, we get
![\frac{dy}{dx} = 2 - 0 - \frac{2\sqrt3}{\sqrt x}\\\\\frac{dy}{dx} = 2 - \frac{2\sqrt3}{\sqrt x}\\](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%202%20-%200%20-%20%5Cfrac%7B2%5Csqrt3%7D%7B%5Csqrt%20x%7D%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%202%20-%20%20%5Cfrac%7B2%5Csqrt3%7D%7B%5Csqrt%20x%7D%5C%5C)
Answer:
We are given the correlation between height and weight for adults is 0.40.
We need to find the proportion of the variability in weight that can be explained by the relationship with height.
We know that coefficient of determination or R-square measures the proportion or percent of variability in dependent variable that can be explained by the relationship with independent variable. There the coefficient of determination is given below:
![R^{2}=r^{2}=0.40^{2}=0.16](https://tex.z-dn.net/?f=R%5E%7B2%7D%3Dr%5E%7B2%7D%3D0.40%5E%7B2%7D%3D0.16)
Therefore, the 0.16 or 16% of the variability in weight can be explained by the relationship with height
Answer:
The answer is 1 and 1/2 or 1.5.
Step-by-step explanation:
I did 3/5 ÷ 2/5. Then I got 3/2. Then I turned the improper fraction into a mixed number.