Answer:
that's the lowest term actually
Answer:
![a_1=2](https://tex.z-dn.net/?f=a_1%3D2)
![a_{20}=1048576](https://tex.z-dn.net/?f=a_%7B20%7D%3D1048576)
Step-by-step explanation:
<u>Geometric Series</u>
The sum of the first n terms of a geometric series whose first term is a1 and a common ratio r is
![\displaystyle S_n=a_1\cdot \frac{r^n-1}{r-1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20S_n%3Da_1%5Ccdot%20%5Cfrac%7Br%5En-1%7D%7Br-1%7D)
The problem provides the following data
![S_{12}=8190](https://tex.z-dn.net/?f=S_%7B12%7D%3D8190)
![r=2](https://tex.z-dn.net/?f=r%3D2)
![n=12](https://tex.z-dn.net/?f=n%3D12)
Replacing the values in the formula:
![\displaystyle 8190=a_1\cdot \frac{2^{12}-1}{2-1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%208190%3Da_1%5Ccdot%20%5Cfrac%7B2%5E%7B12%7D-1%7D%7B2-1%7D)
Operating
![\displaystyle 8190=a_1\cdot 4095](https://tex.z-dn.net/?f=%5Cdisplaystyle%208190%3Da_1%5Ccdot%204095)
Solving for a1
![a_1=8190/4095=2](https://tex.z-dn.net/?f=a_1%3D8190%2F4095%3D2)
![\boxed{a_1=2}](https://tex.z-dn.net/?f=%5Cboxed%7Ba_1%3D2%7D)
The first term is 2
The general term of the series is
![a_n=a_1.r^{n-1}](https://tex.z-dn.net/?f=a_n%3Da_1.r%5E%7Bn-1%7D)
Compute the 20th term
![a_{20}=2\cdot 2^{20-1}](https://tex.z-dn.net/?f=a_%7B20%7D%3D2%5Ccdot%202%5E%7B20-1%7D)
![\boxed{a_{20}=1048576}](https://tex.z-dn.net/?f=%5Cboxed%7Ba_%7B20%7D%3D1048576%7D)
Answer:
40%
Step-by-step explanation:
The first step is to add 18 girls + 12 boys, which gives you the total number of people on the swim team, 30.
Next, you divide the 12 boys by the total swim team members, so:
= 0.4
Then, you multiply 0.4 by 100 to get the percentage:
0.4 × 100 = 40
Therefore, the swim team is made up of 40% boys, and 60% girls.
What is the probability, that a leap year selected at random will contain 53 Sundays?
Sol.: A leap year has 366 days, therefore 52 weeks i.e. 52 Sunday and 2 days.
The remaining 2 days may be any of the following :
(i) Sunday and Monday
(ii) Monday and Tuesday
(iii) Tuesday and Wednesday
(iv) Wednesday and Thursday
(v) Thursday and Friday
(vi) Friday and Saturday
(vii) Saturday and Sunday
For having 53 Sundays in a year, one of the remaining 2 days must be a Sunday.
n(S) = 7
n(E) = 2
<span>P(E) = n(E) / n(S) = 2 / 7
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
</span>
Answer:
125
Step-by-step explanation: