Answer:
![Probability = \frac{243}{1024}](https://tex.z-dn.net/?f=Probability%20%3D%20%5Cfrac%7B243%7D%7B1024%7D)
Step-by-step explanation:
Given
![Sum = \{7, 11, 12\}](https://tex.z-dn.net/?f=Sum%20%3D%20%5C%7B7%2C%2011%2C%2012%5C%7D)
![Rolls = 5](https://tex.z-dn.net/?f=Rolls%20%3D%205)
Required
Probability of not getting audited
If a pair of dice is rolled, the following are the observations of the sum
![Outcomes = 36](https://tex.z-dn.net/?f=Outcomes%20%3D%2036)
![Sum\ of\ 7 = 6](https://tex.z-dn.net/?f=Sum%5C%20of%5C%207%20%3D%206)
![Sum\ of\ 11 = 2](https://tex.z-dn.net/?f=Sum%5C%20of%5C%2011%20%3D%202)
![Sum\ of\ 12 = 1](https://tex.z-dn.net/?f=Sum%5C%20of%5C%2012%20%3D%201)
So, in a single roll; The probability of getting audited is:
![p= \frac{1 + 2 + 6}{36}](https://tex.z-dn.net/?f=p%3D%20%5Cfrac%7B1%20%2B%202%20%2B%206%7D%7B36%7D)
![p= \frac{9}{36}](https://tex.z-dn.net/?f=p%3D%20%5Cfrac%7B9%7D%7B36%7D)
![p= \frac{1}{4}](https://tex.z-dn.net/?f=p%3D%20%5Cfrac%7B1%7D%7B4%7D)
The probability of not getting audited in a single roll is:
--- Complement rule
![q = 1 - \frac{1}{4}](https://tex.z-dn.net/?f=q%20%3D%201%20-%20%5Cfrac%7B1%7D%7B4%7D)
Take LCM
![q = \frac{4 - 1}{4}](https://tex.z-dn.net/?f=q%20%3D%20%5Cfrac%7B4%20-%201%7D%7B4%7D)
![q = \frac{3}{4}](https://tex.z-dn.net/?f=q%20%3D%20%5Cfrac%7B3%7D%7B4%7D)
The probability of not getting audited in 5 rolls is:
![Probability = q^5](https://tex.z-dn.net/?f=Probability%20%3D%20q%5E5)
![Probability = (\frac{3}{4})^5](https://tex.z-dn.net/?f=Probability%20%3D%20%28%5Cfrac%7B3%7D%7B4%7D%29%5E5)
![Probability = \frac{3^5}{4^5}](https://tex.z-dn.net/?f=Probability%20%3D%20%5Cfrac%7B3%5E5%7D%7B4%5E5%7D)
![Probability = \frac{243}{1024}](https://tex.z-dn.net/?f=Probability%20%3D%20%5Cfrac%7B243%7D%7B1024%7D)
The area of the park will be 375 ft squared (rectangular shaped park that is)
Answer:
627
Step-by-step explanation:
![5 {}^{4} + 2 = 627](https://tex.z-dn.net/?f=5%20%7B%7D%5E%7B4%7D%20%20%2B%202%20%3D%20627)
Answer:
Number of
of pieces are 45 .
Step-by-step explanation:
Let us assume that the number of pieces be x .
As given
The length of the rope is 10m and
pieces are cut from it .
Than the equation becomes
![\frac{2\times x}{9} = 10](https://tex.z-dn.net/?f=%5Cfrac%7B2%5Ctimes%20x%7D%7B9%7D%20%3D%2010)
![\frac{9\times 10}{2} = x](https://tex.z-dn.net/?f=%5Cfrac%7B9%5Ctimes%2010%7D%7B2%7D%20%3D%20x)
9 × 5 = x
45 = x
Therefore the number of
of pieces are 45 .
Go crazy auahejekdis go stupid