A high school athletic department bought 40 soccer uniforms at a cost of $4,000. After soccer season, they returned some of the
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Answer:
There are 2,520 unique permutations.
Step-by-step explanation:
When we have a set of N different elements, the total number of permutations is given by:
P = N! = N*(N - 1)*(N - 2)*...*(2)*(1)
Particularly, if out of these N elements, there are a given element that is repeated K times, then the permutations of these K elements actually do not add new unique permutations, then in that case the total number of unique permutations is:
P = N!/K!
And if we have another element that is repeated L times, then with the same reasoning than above, the total number of unique permutations is:
P = N!/(K!*L!)
Now, we have the set:
{C, E, A, S, E, L, E, S, S}
So we have a set of 9 letters, then:
N = 9
And, the letter S is repeated 3 times
The letter E is repeated 3 times
Then, using the above notation, we can define:
K = 3
L = 3
The total number of permutations is then:
So there are 2,520 unique permutations.
Step-by-step explanation:
Complete the proof of the Pythagorean theorem is given below.
Statement Reason
1. ΔABC is a right triangle, with a 1. Given
right angle at ∠C
2. Draw an altitude from point C 2. From a point not on a line, exactly
to AB one perpendicular can be drawn through the point to the line
3. ∠CDB and ∠CDA are right 3. Definition of altitude
angles
4. ∠BCA ≅ ∠BDC 4. All right angles are congruent
5. ∠B ≅ ∠B 5.
6. ΔCBA ~ ΔDBC 6. AA Similarity Postulate
7. 7.
8. 8.
9. ∠CDA ≅ ∠BCA 9.
10. ∠A ≅ ∠A 10.
11. ΔCBA ~ ΔDBA 11. AA Similarity Postulate
12. 12.
13. 13.
14. 14.
15. 15. Distributive Property
16. 16.
17. 18.