The factorial ! just means we multiply by every natural number less that the value so
6! =6×5×4×3×2×1= 720
for permutations we use the formula n!/(n-r)!
so we have 8!/(8-5)!=8!/3!=8×7×6×5×4
for combinations s we have n!/(n-r)!r!
so we have 12!/(12-4)!4!=12!/8!4!=12×11×10×9/4×3×2=11×10×9/2=99×5
Answer:
![x=5](https://tex.z-dn.net/?f=x%3D5)
Step-by-step explanation:
<u>Similar Triangles</u>
By looking at the construction of the figure, we can safely assume both triangles are similar, i.e. their internal angles are equal and their sides are proportional. Following the proportion of the heights and bases of both triangles we can set this relationship:
![\displaystyle \frac{45}{36}=\frac{5x}{20}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B45%7D%7B36%7D%3D%5Cfrac%7B5x%7D%7B20%7D)
Simplifying both fractions
![\displaystyle \frac{5}{4}=\frac{x}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B5%7D%7B4%7D%3D%5Cfrac%7Bx%7D%7B4%7D)
Solving for x
![x=5](https://tex.z-dn.net/?f=x%3D5)
Answer:
13.5 meters
Step-by-step explanation:
25 / 2 = 13.5
because if a human is 3 meters tall and cast 2 times the length of himself then if a building casts 25 meters then it should be 2 times less than its shadow.