The probability would be 1/15.
The first draw, taking a gold coin is 3/10.
Since we don't replace it, we draw again, but a value less- 2/9.
We multiply that together and get 6/90, then simplify it :)<span />
Answer:
I think the surface area is 382.
Answer:
The general limit exists at <em>x</em> = 9 and is equal to 300.
Step-by-step explanation:
We want to find the general limit of the function:
![\displaystyle \lim_{x \to 9}(x^2+2^7+(9.1\times 10))](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%209%7D%28x%5E2%2B2%5E7%2B%289.1%5Ctimes%2010%29%29)
By definition, a general limit exists at a point if the two one-sided limits exist and are equivalent to each other.
So, let's find each one-sided limit: the left-hand side and the right-hand side.
The left-hand limit is given by:
<h3>
![\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1 \times 10))](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%209%5E-%7D%28x%5E2%2B2%5E7%2B%289.1%20%5Ctimes%2010%29%29)
</h3>
Since the given function is a polynomial, we can use direct substitution. This yields:
![=(9)^2+2^7+(9.1\times 10)](https://tex.z-dn.net/?f=%3D%289%29%5E2%2B2%5E7%2B%289.1%5Ctimes%2010%29)
Evaluate:
![300](https://tex.z-dn.net/?f=300)
Therefore:
![\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1 \times 10))=300](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%209%5E-%7D%28x%5E2%2B2%5E7%2B%289.1%20%5Ctimes%2010%29%29%3D300)
The right-hand limit is given by:
![\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%209%5E%2B%7D%28x%5E2%2B2%5E7%2B%289.1%5Ctimes%2010%29%29)
Again, since the function is a polynomial, we can use direct substitution. This yields:
![=(9)^2+2^7+(9.1\times 10)](https://tex.z-dn.net/?f=%3D%289%29%5E2%2B2%5E7%2B%289.1%5Ctimes%2010%29)
Evaluate:
![=300](https://tex.z-dn.net/?f=%3D300)
Therefore:
![\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))=300](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%209%5E%2B%7D%28x%5E2%2B2%5E7%2B%289.1%5Ctimes%2010%29%29%3D300)
Thus, we can see that:
![\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1\times 10))=\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))=300](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%209%5E-%7D%28x%5E2%2B2%5E7%2B%289.1%5Ctimes%2010%29%29%3D%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%209%5E%2B%7D%28x%5E2%2B2%5E7%2B%289.1%5Ctimes%2010%29%29%3D300)
Since the two-sided limits exist and are equivalent, the general limit of the function does exist at <em>x</em> = 9 and is equal to 300.
D because its a whole number thats not a fraction