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)
Answer:
y = -x/3 + 6
General Formulas and Concepts:
<u>Pre-Algebra</u>
<u>Algebra I</u>
Standard Form: Ax + By = C
Slope-Intercept Form: y = mx + b
- m - slope
- b - y-intercept
Step-by-step explanation:
<u>Step 1: Define</u>
Standard Form: x + 3y = 18
<u>Step 2: Rewrite</u>
<em>Find slope-intercept form</em>
- Subtract <em>x</em> on both sides: 3y = -x + 18
- Divide 3 on both sides: y = -x/3 + 6
Answer:
Each angle is 67 degrees
Step-by-step explanation:
Bisected angles are divided in half
134/2 =67
Each angle is 67 degrees
Both solutions:
x = -1, -7/3
Answer:
Debit Cost of Goods Sold $710
Credit Material Price Variance $40
Credit Material Usage Variance $225
Credit Labor Rate Variance $110
Credit Labor Efficiency Variance $335
Step-by-step explanation:
Preparation of the journal entry to be passed by Theta Company at the end of the month of February to close the variances
Debit Cost of Goods Sold $710
($40+$225+$110+$335)
Credit Material Price Variance $40
Credit Material Usage Variance $225
Credit Labor Rate Variance $110
Credit Labor Efficiency Variance $335
(To close the variances)