Answer:
![d_{n+1}=d_n\,+\,2^n](https://tex.z-dn.net/?f=d_%7Bn%2B1%7D%3Dd_n%5C%2C%2B%5C%2C2%5En)
with ![d_1=81](https://tex.z-dn.net/?f=d_1%3D81)
Step-by-step explanation:
We can study what happens day by day starting with day one (1) to understand how the recursive relation can be constructed:
Day # Number of stamps What is added relative to previous day
1 d1 = 80 + 1 = 81
2 d2 = 81 + 2 = 83 d2 = d1 + 2
3 d3 = 83 + 4 = 87 d3 = d2 + ![2^2](https://tex.z-dn.net/?f=2%5E2)
4 d4 = 87 + 8 = 95 d4 = d3 + ![2^3](https://tex.z-dn.net/?f=2%5E3)
5 d5 = 95 + 16 = 111 d5 = d4 + ![2^4](https://tex.z-dn.net/?f=2%5E4)
6 d6 = 111 + 32 = 143 d6 = d5 + ![2^2](https://tex.z-dn.net/?f=2%5E2)
(n+1) d(n+1) = dn + ![2^n](https://tex.z-dn.net/?f=2%5En)
Answer:
what class are you in? if you have a book you can use this site called slader it gives you every answer for free and there is steps. HOPE THIS HELPS.
Step-by-step explanation:
When you have 3 choices for each of 6 spins, the number of possible "words" is
3^6 = 729
The number of permutations of 6 things that are 3 groups of 2 is
6!/(2!×2!×2!) = 720/8 = 90
A) The probability of a word containing two of each of the letters is 90/729 = 10/81
The number of permutations of 6 things from two groups of different sizes is
(2 and 4) : 6!/(2!×4!) = 15
(3 and 3) : 6!/(3!×3!) = 20
(4 and 2) : 15
(5 and 1) : 6
(6 and 0) : 1
B) The number of ways there can be at least 2 "a"s and no "b"s is
15 + 20 + 15 + 6 + 1 = 57
The probability of a word containing at least 2 "a"s and no "b"s is 57/729 = 19/243.
_____
These numbers were verified by listing all possibilities and actually counting the ones that met your requirements.
- Midpoint Formula:
![(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})](https://tex.z-dn.net/?f=%20%28%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%20%5Cfrac%7By_1%2By_2%7D%7B2%7D%29%20)
Given our two points, (-3,9) and (-1,4), we can apply them to the midpoint formula and solve for it as such:
![(\frac{(-3)+(-1)}{2}, \frac{9+4}{2})\\\\(\frac{(-4)}{2}, \frac{13}{2}) \\\\(-2,6.5)](https://tex.z-dn.net/?f=%20%28%5Cfrac%7B%28-3%29%2B%28-1%29%7D%7B2%7D%2C%20%5Cfrac%7B9%2B4%7D%7B2%7D%29%5C%5C%5C%5C%28%5Cfrac%7B%28-4%29%7D%7B2%7D%2C%20%5Cfrac%7B13%7D%7B2%7D%29%20%5C%5C%5C%5C%28-2%2C6.5%29%20)
<u>Your midpoint is (-2,6.5)</u>
Given that,
An expression : 4(n- 3²) + n
To find,
The equivalent expression.
Solution,
We have,
4(n- 3²) + n
As 3²= 9
= 4(n- 9) + n
Opening the brackets,
= 4n-4(9) + n
= 4n-36 +n
= 5n-36
Hence, the equivalent expression is 5n-36.