<span>Ending Amt = Bgng Amt * e ^-0.03t
In this equation, the "-0.03" is the decay factor or "k"
We can now solve for half-life by this equation:
</span>t = <span>(<span>ln [y(t) ÷ a]<span>)<span> ÷ -k (we can say beginning amount = 200 and ending amount = 100
</span></span></span></span>t = <span>(<span>ln [200 ÷ 100]<span>)<span> ÷ -k
</span></span></span></span>t = <span>(<span>ln [2]<span>)<span> ÷ -k
</span></span></span></span>t = 0.69314718056<span> ÷ --.03
t =</span><span><span><span> 23.1049060187
</span>
about 23 years
</span></span>
Answer:
a) 0.0016
b) 0.0224
Step-by-step explanation:
If every question has 5 possible answers, the probability of getting the correct answer by guessing would be 0.20. The probability of getting an incorrect answer would be 0.80.
a)Find the probability she lucks out and answers all four questions correctly.
To do this, Allison would have to guess right the first, second, third AND fourth answers. Therefore, we have to multiply the probabilities:
0.20 x 0.20 x 0.20 x 0.20 = 0.0016
The probability that she answers all 4 questions correctly is 0.0016.
b) Find the probability that she passes the quiz.
To pass the quiz, she has to have three OR 4 correct answers:
- The probability that she has 3 correct answers is: 0.20 x 0.20 x 0.20 x 0.80 (since she has to have 1 correct answer and 1 incorrect one) = .0064.
- We already calculated the probability that she guesses 4 answers correctly: 0.0016.
Now, we have to sum up these two scenarios:
0.0064 + 0.016 = 0.0224.
Thus, the probability that she passes the quiz is 0.0224
Answer:
4.
Step-by-step explanation:
We are asked to find the value of expression
at
.
First of all, we will find the derivative of the given expression using "Quotient Rule of Derivatives" as shown below:
![(\frac{f(x)}{g(x)})'=\frac{f'(x)\cdot g(x)-f(x)\cdot g'(x)}{(g(x))^2}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D%29%27%3D%5Cfrac%7Bf%27%28x%29%5Ccdot%20g%28x%29-f%28x%29%5Ccdot%20g%27%28x%29%7D%7B%28g%28x%29%29%5E2%7D)
![\frac{d}{dx}(\frac{2x+3}{3x^2-4})](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%28%5Cfrac%7B2x%2B3%7D%7B3x%5E2-4%7D%29)
![\frac{\frac{d}{dx}(2x+3)*(3x^2-4)-(2x+3)*\frac{d}{dx}(3x^2-4)}{(3x^2-4)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7Bd%7D%7Bdx%7D%282x%2B3%29%2A%283x%5E2-4%29-%282x%2B3%29%2A%5Cfrac%7Bd%7D%7Bdx%7D%283x%5E2-4%29%7D%7B%283x%5E2-4%29%5E2%7D)
![\frac{2*(3x^2-4)-(2x+3)*(6x)}{(3x^2-4)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B2%2A%283x%5E2-4%29-%282x%2B3%29%2A%286x%29%7D%7B%283x%5E2-4%29%5E2%7D)
![\frac{6x^2-8-12x^2-18x}{(3x^2-4)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B6x%5E2-8-12x%5E2-18x%7D%7B%283x%5E2-4%29%5E2%7D)
![\frac{-6x^2-18x-8}{(3x^2-4)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B-6x%5E2-18x-8%7D%7B%283x%5E2-4%29%5E2%7D)
Therefore, our required derivative is
.
Now, we will substitute
in our derivative to find the required value as:
![\frac{-6(-1)^2-18(-1)-8}{(3(-1)^2-4)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B-6%28-1%29%5E2-18%28-1%29-8%7D%7B%283%28-1%29%5E2-4%29%5E2%7D)
![\frac{-6(1)+18-8}{(3(1)-4)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B-6%281%29%2B18-8%7D%7B%283%281%29-4%29%5E2%7D)
![\frac{-6+18-8}{(3-4)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B-6%2B18-8%7D%7B%283-4%29%5E2%7D)
![\frac{4}{(-1)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B%28-1%29%5E2%7D)
![\frac{4}{1}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B1%7D)
![4](https://tex.z-dn.net/?f=4)
Therefore, the value of expression
at
is 4.
Look at the picture below. Sorry if its hard to understand.
Answer:
10y+4
Step-by-step explanation:
perimeter=2(l+b)
2(4y+(y+2))
2(4y+y+2)
2(5y+2)
10y+4