Answer:
![d = \sqrt{205}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B205%7D%20)
Step-by-step explanation:
![d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2%20-%20y_1%29%5E2%7D%20)
![d = \sqrt{(-8 - (-2))^2 + (7 - (-6))^2}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B%28-8%20-%20%28-2%29%29%5E2%20%2B%20%287%20-%20%28-6%29%29%5E2%7D%20)
![d = \sqrt{(-6)^2 + 13^2}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B%28-6%29%5E2%20%2B%2013%5E2%7D%20)
![d = \sqrt{36 + 169}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B36%20%2B%20169%7D%20)
![d = \sqrt{205}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B205%7D%20)
Answer: 203,280
Step-by-step explanation:
Given: A catering service offers 11 appetizers, 12 main courses, and 8 desserts.
Number of combinations of choosing r things out of n = ![^nC_r=\dfrac{n!}{r!(n-r)!}](https://tex.z-dn.net/?f=%5EnC_r%3D%5Cdfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D)
A customer is to select 9 appetizers, 2 main courses, and 3 desserts for a banquet.
Total number of ways to do this:
![=\dfrac{11!}{9!2!}\times\dfrac{12!}{2!10!}\times\dfrac{8!}{3!5!}\\\\=\dfrac{11\times10}{2}\times\dfrac{12\times11}{2}\times\dfrac{8\times7\times6}{3\times2}\\\\= 203280](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B11%21%7D%7B9%212%21%7D%5Ctimes%5Cdfrac%7B12%21%7D%7B2%2110%21%7D%5Ctimes%5Cdfrac%7B8%21%7D%7B3%215%21%7D%5C%5C%5C%5C%3D%5Cdfrac%7B11%5Ctimes10%7D%7B2%7D%5Ctimes%5Cdfrac%7B12%5Ctimes11%7D%7B2%7D%5Ctimes%5Cdfrac%7B8%5Ctimes7%5Ctimes6%7D%7B3%5Ctimes2%7D%5C%5C%5C%5C%3D%09203280)
hence , this can be done in 203,280 ways.
Answer:
7
Step-by-step explanation:
Yes. The timing is compatible with that answer.
The property is distributive