Let's rewrite the binomial as:
![(1 - 2x)^{19}](https://tex.z-dn.net/?f=%281%20-%202x%29%5E%7B19%7D)
![\text{Binomial expansion:} (1 + x)^{n} = \sum_{r = 0}^n\left(\begin{array}{ccc}n\\r\end{array}\right) (x)^{r}](https://tex.z-dn.net/?f=%5Ctext%7BBinomial%20expansion%3A%7D%20%281%20%2B%20x%29%5E%7Bn%7D%20%3D%20%5Csum_%7Br%20%3D%200%7D%5En%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7Dn%5C%5Cr%5Cend%7Barray%7D%5Cright%29%20%28x%29%5E%7Br%7D)
Using the binomial expansion, we get:
![\text{Binomial expansion: } (1 - 2x)^{19} = \sum_{r = 0}^{19}\left(\begin{array}{ccc}19\\r\end{array}\right) (-2x)^{r}](https://tex.z-dn.net/?f=%5Ctext%7BBinomial%20expansion%3A%20%7D%20%281%20-%202x%29%5E%7B19%7D%20%3D%20%5Csum_%7Br%20%3D%200%7D%5E%7B19%7D%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7D19%5C%5Cr%5Cend%7Barray%7D%5Cright%29%20%28-2x%29%5E%7Br%7D)
For the 15th term, we want the term where r is equal to 14, because of the fact that the first term starts when r = 0. Thus, for the 15th term, we need to include the 0th or the first term of the binomial expansion.
Thus, the fifteenth term is:
Step-by-step explanation:
100-15=85%
85% × 29.99
=$25.49
Answer: 3 cm
Work Shown:
(1 cm)/(5 m) = (x cm)/(15 m)
1/5 = x/15
1*15 = 5*x ... cross multiply
15 = 5x
5x = 15
x = 15/5
x = 3
The model is 3 cm tall.