Answer: 212,520
Step-by-step explanation:
Given : A pianist plans to play 4 pieces at a recital from her repertoire of 23 pieces, and is carefully considering which song to play first, second, etc.
It means the repetition of pieces is not allowed.
When repetition is not allowed , then the number of ways to arrange n things where r things taken together is given by :-
![^nP_r=\dfrac{n!}{(n-r)!}](https://tex.z-dn.net/?f=%5EnP_r%3D%5Cdfrac%7Bn%21%7D%7B%28n-r%29%21%7D)
Now, the number of different recital programs are :-
![^{23}P_4=\dfrac{23!}{(23-4)!}=\dfrac{23\times22\times21\times20\times19!}{19!}=212,520](https://tex.z-dn.net/?f=%5E%7B23%7DP_4%3D%5Cdfrac%7B23%21%7D%7B%2823-4%29%21%7D%3D%5Cdfrac%7B23%5Ctimes22%5Ctimes21%5Ctimes20%5Ctimes19%21%7D%7B19%21%7D%3D212%2C520)
Hence, there are 212,520 different recital programs possible.
The answer is 50.24. First, take the diameter and divide it by two (4). Then, multiply it by itself (16). Lastly, multiply it by pi,(3.14).
X=25 because they are congruent so 4x25=100 and 100-25=75
Multiply both sides by 19 to get w=171