Full Question
<em>Of the cartons produced by a company, 10% have a puncture, 6% have a smashed corner, and 0.4% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner nothing ____%. (Type an integer or a decimal. Do not round.)</em>
<em />
Answer:
![P(Punctured\ or\ Smashed\ Corner) = 0.156](https://tex.z-dn.net/?f=P%28Punctured%5C%20or%5C%20Smashed%5C%20Corner%29%20%3D%200.156)
Step-by-step explanation:
Given
![Puncture\ Corner = 10\%](https://tex.z-dn.net/?f=Puncture%5C%20Corner%20%3D%2010%5C%25)
![Smashed\ Corner = 6\%](https://tex.z-dn.net/?f=Smashed%5C%20Corner%20%3D%206%5C%25)
![Punctured\ and\ Smashed\ Corner = 0.4\%](https://tex.z-dn.net/?f=Punctured%5C%20and%5C%20Smashed%5C%20Corner%20%3D%200.4%5C%25)
Required
![P(Punctured\ or\ Smashed\ Corner)](https://tex.z-dn.net/?f=P%28Punctured%5C%20or%5C%20Smashed%5C%20Corner%29)
For non-mutually exclusive event described above, P(Punctured or Smashed Corner) can be calculated as thus;
![P(Punctured\ or\ Smashed\ Corner) = P(Punctured\ Corner) + P(Smashed\ Corner) - P(Punctured\ and\ Smashed\ Corner)](https://tex.z-dn.net/?f=P%28Punctured%5C%20or%5C%20Smashed%5C%20Corner%29%20%3D%20P%28Punctured%5C%20Corner%29%20%2B%20P%28Smashed%5C%20Corner%29%20-%20P%28Punctured%5C%20and%5C%20Smashed%5C%20Corner%29)
Substitute:
10% for P(Puncture Corner),
6% for P(Smashed Corner) and
0.4% for P(Punctured and Smashed Corner)
![P(Punctured\ or\ Smashed\ Corner) = 10\% + 6\% - 0.4\%](https://tex.z-dn.net/?f=P%28Punctured%5C%20or%5C%20Smashed%5C%20Corner%29%20%3D%2010%5C%25%20%2B%206%5C%25%20-%200.4%5C%25)
![P(Punctured\ or\ Smashed\ Corner) = 15.6\%](https://tex.z-dn.net/?f=P%28Punctured%5C%20or%5C%20Smashed%5C%20Corner%29%20%3D%2015.6%5C%25)
Convert % to fraction
![P(Punctured\ or\ Smashed\ Corner) = \frac{15.6}{100}](https://tex.z-dn.net/?f=P%28Punctured%5C%20or%5C%20Smashed%5C%20Corner%29%20%3D%20%5Cfrac%7B15.6%7D%7B100%7D)
Convert to decimal
![P(Punctured\ or\ Smashed\ Corner) = 0.156](https://tex.z-dn.net/?f=P%28Punctured%5C%20or%5C%20Smashed%5C%20Corner%29%20%3D%200.156)
Answer:
Square Pyramid
Step-by-step explanation:
Thats what a Square Pyramid is
y = 0 is pretty much a hortizontal straight line
lines are parrallel when the gradient is the same in this case gradient is 0 so
y = 6
11.
Given:
![y=x^2](https://tex.z-dn.net/?f=y%3Dx%5E2)
Differentiate with respect to x, we get
![\frac{dy}{dx}=2x](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D2x)
The given point is (3,9)
Substitute x=3 in the derivative, we get
![\frac{dy}{dx}=2\times\times3=6](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D2%5Ctimes%5Ctimes3%3D6)
Hence the slope is 3.
12.
Given:
![y=x^2+4](https://tex.z-dn.net/?f=y%3Dx%5E2%2B4)
Differentiate with respect to x, we get
![\frac{dy}{dx}=2x+0](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D2x%2B0)
The given point is (0,4)
Substitute x=0 in the derivative, we get
![\frac{dy}{dx}=2(0)+0=0](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D2%280%29%2B0%3D0)
Hence the slope is 0.