Answer:
0.14% probability of a person guessing the right combination
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the numbers are selected is important. For example, 1,3,2 is a different combination than 3,1,2. So we use the permutations formula to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:

Desired outcomes:
One right combination, so 
Total outcomes:
10 numbers from a set of 3. So

What is the probability of a person guessing the right combination?

0.14% probability of a person guessing the right combination
-3/7 is obviously the least because it is a negative number.Then 2/5 because if you think about it if 2/5 is 2 of 5 equal pieces. 2/3 is 2 of 3 pieces.So if you think about a pizza if you cut the pizza into 3 pieces and ate 2 imagine how much you would have left and then think about cutting the pizza into 5 pieces and only eating 2 . Think about that. So the answer in the end is -3/7,2/5, and then 2/3. Hope I helped!
sorry been trying to find something to say but i don't have a answer for it wish i could help
1/4 (8 + 6z + 12)
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Combine like terms :
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1/4 (6z + 20)
------------------------------------------------------------
Apply distributive property :
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1/4(6z) + 1/4(20)
3/2z + 5
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Answer: 3/2z + 5
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Answer:
(See attached graph)
Step-by-step explanation:
To solve a second-order homogeneous differential equation, we need to substitute each term with the auxiliary equation
where the values of
are the roots:

Since the values of
are complex conjugate roots, then the general solution is
where
.
Thus, the general solution for our given differential equation is
.
To account for both initial conditions, take the derivative of
, thus, ![y'(x)=-2e^{-2x}[C_1cos(\sqrt{6}x+C_2sin(\sqrt{6}x)]+e^{-2x}[-C_1\sqrt{6}sin(\sqrt{6}x)+C_2\sqrt{6}cos(\sqrt{6}x)]](https://tex.z-dn.net/?f=y%27%28x%29%3D-2e%5E%7B-2x%7D%5BC_1cos%28%5Csqrt%7B6%7Dx%2BC_2sin%28%5Csqrt%7B6%7Dx%29%5D%2Be%5E%7B-2x%7D%5B-C_1%5Csqrt%7B6%7Dsin%28%5Csqrt%7B6%7Dx%29%2BC_2%5Csqrt%7B6%7Dcos%28%5Csqrt%7B6%7Dx%29%5D)
Now, we can create our system of equations given our initial conditions:
![y(x)=e^{-2x}[C_1cos(\sqrt{6}x)+C_2sin(\sqrt{6}x)]\\\\y(0)=e^{-2(0)}[C_1cos(\sqrt{6}(0))+C_2sin(\sqrt{6}(0))]=3\\\\C_1=3](https://tex.z-dn.net/?f=y%28x%29%3De%5E%7B-2x%7D%5BC_1cos%28%5Csqrt%7B6%7Dx%29%2BC_2sin%28%5Csqrt%7B6%7Dx%29%5D%5C%5C%5C%5Cy%280%29%3De%5E%7B-2%280%29%7D%5BC_1cos%28%5Csqrt%7B6%7D%280%29%29%2BC_2sin%28%5Csqrt%7B6%7D%280%29%29%5D%3D3%5C%5C%5C%5CC_1%3D3)
![y'(x)=-2e^{-2x}[C_1cos(\sqrt{6}x+C_2sin(\sqrt{6}x)]+e^{-2x}[-C_1\sqrt{6}sin(\sqrt{6}x)+C_2\sqrt{6}cos(\sqrt{6}x)]\\\\y'(0)=-2e^{-2(0)}[C_1cos(\sqrt{6}(0))+C_2sin(\sqrt{6}(0))]+e^{-2(0)}[-C_1\sqrt{6}sin(\sqrt{6}(0))+C_2\sqrt{6}cos(\sqrt{6}(0))]=-2\\\\-2C_1+\sqrt{6}C_2=-2](https://tex.z-dn.net/?f=y%27%28x%29%3D-2e%5E%7B-2x%7D%5BC_1cos%28%5Csqrt%7B6%7Dx%2BC_2sin%28%5Csqrt%7B6%7Dx%29%5D%2Be%5E%7B-2x%7D%5B-C_1%5Csqrt%7B6%7Dsin%28%5Csqrt%7B6%7Dx%29%2BC_2%5Csqrt%7B6%7Dcos%28%5Csqrt%7B6%7Dx%29%5D%5C%5C%5C%5Cy%27%280%29%3D-2e%5E%7B-2%280%29%7D%5BC_1cos%28%5Csqrt%7B6%7D%280%29%29%2BC_2sin%28%5Csqrt%7B6%7D%280%29%29%5D%2Be%5E%7B-2%280%29%7D%5B-C_1%5Csqrt%7B6%7Dsin%28%5Csqrt%7B6%7D%280%29%29%2BC_2%5Csqrt%7B6%7Dcos%28%5Csqrt%7B6%7D%280%29%29%5D%3D-2%5C%5C%5C%5C-2C_1%2B%5Csqrt%7B6%7DC_2%3D-2)
We then solve the system of equations, which becomes easy since we already know that
:

Thus, our final solution is:
![y(x)=e^{-2x}[C_1cos(\sqrt{6}x)+C_2sin(\sqrt{6}x)]\\\\y(x)=e^{-2x}[3cos(\sqrt{6}x)+\frac{2\sqrt{6}}{3}sin(\sqrt{6}x)]](https://tex.z-dn.net/?f=y%28x%29%3De%5E%7B-2x%7D%5BC_1cos%28%5Csqrt%7B6%7Dx%29%2BC_2sin%28%5Csqrt%7B6%7Dx%29%5D%5C%5C%5C%5Cy%28x%29%3De%5E%7B-2x%7D%5B3cos%28%5Csqrt%7B6%7Dx%29%2B%5Cfrac%7B2%5Csqrt%7B6%7D%7D%7B3%7Dsin%28%5Csqrt%7B6%7Dx%29%5D)