Let:
Vbu= Volume of the buret
Vbk= Volume of the beaker
A buret initially contains 70.00 millimeters of a solution and a beaker initially contains 20.00 ml of the solution the buret drips solution into the Beaker. each drip contains 0.05 mL of solution, therefore:
x = Number of drips
a = volume of each drip
![\begin{gathered} Vbu=70-ax \\ Vbk=20+ax \\ \text{where:} \\ a=0.05 \\ Vbu=70-0.05x \\ Vbk=20+0.05x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20Vbu%3D70-ax%20%5C%5C%20Vbk%3D20%2Bax%20%5C%5C%20%5Ctext%7Bwhere%3A%7D%20%5C%5C%20a%3D0.05%20%5C%5C%20Vbu%3D70-0.05x%20%5C%5C%20Vbk%3D20%2B0.05x%20%5Cend%7Bgathered%7D)
after how many drips will the volume of the solution in the buret and beaker be equal ? Vbu = Vbk:
Answer:
24 feet
Step-by-step explanation:
Set up a ratio which is 15/x=40/64 and cross multiply to get 960=40x and divide to get 24
![\textbf{ \underline{Using middle term splitting:}} \\ \\ {x}^{2} - 10x + 25 \\ = {x}^{2} - 5x - 5x + 25 \\ = x(x - 5) - 5(x - 5) \\ = (x - 5)(x - 5) \\ = {(x - 5)}^{2}](https://tex.z-dn.net/?f=%20%5Ctextbf%7B%20%5Cunderline%7BUsing%20middle%20term%20splitting%3A%7D%7D%20%5C%5C%20%20%5C%5C%20%20%7Bx%7D%5E%7B2%7D%20%20-%2010x%20%2B%2025%20%5C%5C%20%20%3D%20%7Bx%7D%5E%7B2%7D%20%20-%205x%20-%205x%20%2B%2025%20%5C%5C%20%20%3D%20x%28x%20-%205%29%20-%205%28x%20-%205%29%20%5C%5C%20%3D%20%20%28x%20-%205%29%28x%20-%205%29%20%5C%5C%20%20%3D%20%20%7B%28x%20-%205%29%7D%5E%7B2%7D%20)
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Answer:
The probability that more than 30 minutes will elapse before the next fraudulent corporate tax return is discovered=0.1353
Step-by-step explanation:
We are given that
![\beta=15](https://tex.z-dn.net/?f=%5Cbeta%3D15)
We have to find the probability that more that 30 minutes will elapse before the next fraudulent corporate tax return is discovered.
Using exponential distribution
![P(X> x)=e^{-\frac{x}{\beta}}](https://tex.z-dn.net/?f=P%28X%3E%20x%29%3De%5E%7B-%5Cfrac%7Bx%7D%7B%5Cbeta%7D%7D)
The probability that more than 30 minutes will elapse before the next fraudulent corporate tax return is discovered
![=P(x>30)=e^{-\frac{30}{15}}](https://tex.z-dn.net/?f=%3DP%28x%3E30%29%3De%5E%7B-%5Cfrac%7B30%7D%7B15%7D%7D)
The probability that more than 30 minutes will elapse before the next fraudulent corporate tax return is discovered
![P(x>30)=0.1353](https://tex.z-dn.net/?f=P%28x%3E30%29%3D0.1353)
Hence, the probability that more than 30 minutes will elapse before the next fraudulent corporate tax return is discovered=0.1353
Answer:
its D
Step-by-step explanation: