Needed more details, but probably it was b^x, so yes. b<1 produces decay. Less and less.
The answer is
56x-(23y)^9/3 = 42
Answer:
Step-by-step explanation:
As stated in the question, the probability to toss a coin and turn up heads in the first try is
, in the second is
, in the third is
and so on. Then, P(C) is given by the next sum:
![P(C)=\sum^{\infty}_{n=1}(\frac{1}{2} )^{n}=1](https://tex.z-dn.net/?f=P%28C%29%3D%5Csum%5E%7B%5Cinfty%7D_%7Bn%3D1%7D%28%5Cfrac%7B1%7D%7B2%7D%20%29%5E%7Bn%7D%3D1)
This is a geometric series with factor
. Then is convergent to
. With this we have proved that P(C)=1.
Now, observe that
![P(H)=\frac{1}{2}, P(TH)=\frac{1}{4},P(TTH)=\frac{1}{8},P(TTTH)=\frac{1}{16},P(TTTTH)=\frac{1}{32},P(TTTTTH)=\frac{1}{64}.](https://tex.z-dn.net/?f=P%28H%29%3D%5Cfrac%7B1%7D%7B2%7D%2C%20P%28TH%29%3D%5Cfrac%7B1%7D%7B4%7D%2CP%28TTH%29%3D%5Cfrac%7B1%7D%7B8%7D%2CP%28TTTH%29%3D%5Cfrac%7B1%7D%7B16%7D%2CP%28TTTTH%29%3D%5Cfrac%7B1%7D%7B32%7D%2CP%28TTTTTH%29%3D%5Cfrac%7B1%7D%7B64%7D.)
Then
![P(C1)=P(H)+P(TH)+P(TTH)+P(TTTH)+P(TTTTH)=\frac{1}{2} +\frac{1}{4} +\frac{1}{8} +\frac{1}{16} +\frac{1}{32} =\frac{31}{32}](https://tex.z-dn.net/?f=P%28C1%29%3DP%28H%29%2BP%28TH%29%2BP%28TTH%29%2BP%28TTTH%29%2BP%28TTTTH%29%3D%5Cfrac%7B1%7D%7B2%7D%20%2B%5Cfrac%7B1%7D%7B4%7D%20%2B%5Cfrac%7B1%7D%7B8%7D%20%2B%5Cfrac%7B1%7D%7B16%7D%20%2B%5Cfrac%7B1%7D%7B32%7D%20%3D%5Cfrac%7B31%7D%7B32%7D)
![P(C2)=P(TTTTH)+P(TTTTTH)=\frac{1}{32}+\frac{1}{64} =\frac{3}{64}](https://tex.z-dn.net/?f=P%28C2%29%3DP%28TTTTH%29%2BP%28TTTTTH%29%3D%5Cfrac%7B1%7D%7B32%7D%2B%5Cfrac%7B1%7D%7B64%7D%20%3D%5Cfrac%7B3%7D%7B64%7D)
![P(C1\cap C2)=P(TTTTH)=\frac{1}{32}](https://tex.z-dn.net/?f=P%28C1%5Ccap%20C2%29%3DP%28TTTTH%29%3D%5Cfrac%7B1%7D%7B32%7D)
and
![P(C1\cup C2)=P(H)+P(TH)+P(TTH)+P(TTTH)+P(TTTTH)+P(TTTTTH)=\frac{1}{2} +\frac{1}{4} +\frac{1}{8} +\frac{1}{16} +\frac{1}{32} +\frac{1}{64}=\frac{63}{64}](https://tex.z-dn.net/?f=P%28C1%5Ccup%20C2%29%3DP%28H%29%2BP%28TH%29%2BP%28TTH%29%2BP%28TTTH%29%2BP%28TTTTH%29%2BP%28TTTTTH%29%3D%5Cfrac%7B1%7D%7B2%7D%20%2B%5Cfrac%7B1%7D%7B4%7D%20%2B%5Cfrac%7B1%7D%7B8%7D%20%2B%5Cfrac%7B1%7D%7B16%7D%20%2B%5Cfrac%7B1%7D%7B32%7D%20%2B%5Cfrac%7B1%7D%7B64%7D%3D%5Cfrac%7B63%7D%7B64%7D)
First step is Add 3 to both sides
hope it helps
Part A: David wrote 0.003 + 0.0001 instead of <span>0.03 + 0.001
Part B: T</span>he 1 should be in the thousandths place
Hope this helps, make sure to count each place from right after the decimal which is the tenths place, then hundredths, etc.