She will need to cut 26.6 haircuts a month a location A to break even (1200/45 = 26.6) so roughly 27 haircuts to make a profit
She will need to cut 30 haircuts at location B to break even (1800/60 = 30) and 31 hair cuts to see a profit.
She will need to cut 30.67 haircuts at location A and 33 haircuts at location B to make the same profit at either location (Roughly $180).
30.67 x 45 = 1380.15 - 1200 = 180
33 x 60 = 1980 - 1800 = 180
?????? Is there a picture? I can’t see it if there is :)
Answer:
![\mathbf{\{ x \in Z: X_E(x) = 1\} = E}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5C%7B%20x%20%5Cin%20Z%3A%20X_E%28x%29%20%3D%201%5C%7D%20%20%3D%20E%7D)
Step-by-step explanation:
Let E be the set of all even positive integers in the universe Z of integers,
i.e
E = {2,4,6,8,10 ....∞}
be the characteristic function of E.
∴
![X_E(x) = \left \{ {{1 \ if \ x \ \ is \ an \ element \ of \ E} \atop {0 \ if \ x \ \ is \ not \ an \ element \ of \ E}} \right.](https://tex.z-dn.net/?f=X_E%28x%29%20%3D%20%5Cleft%20%5C%7B%20%7B%7B1%20%5C%20if%20%20%5C%20x%20%5C%20%5C%20%20is%20%5C%20an%20%5C%20element%20%5C%20of%20%5C%20E%7D%20%5Catop%20%7B0%20%5C%20if%20%20%5C%20x%20%5C%20%5C%20%20is%20%5C%20not%20%5C%20an%20%20%5C%20element%20%5C%20of%20%5C%20E%7D%7D%20%5Cright.)
For XE(2)
since x is an element of E (i.e the set of all even numbers)
For XE(-2)
since - 2 is less than 0 , and -2 is not an element of E
For { x ∈ Z: XE(x) = 1}
This can be read as:
x which is and element of Z such that X is also an element of x which is equal to 1.
∴
![\{ x \in Z: X_E(x) = 1\} = \{ x \in Z | x \in E\} \\ \\ \mathbf{\{ x \in Z: X_E(x) = 1\} = E}](https://tex.z-dn.net/?f=%5C%7B%20x%20%5Cin%20Z%3A%20X_E%28x%29%20%3D%201%5C%7D%20%3D%20%5C%7B%20x%20%5Cin%20Z%20%7C%20x%20%5Cin%20E%5C%7D%20%5C%5C%20%5C%5C%20%20%5Cmathbf%7B%5C%7B%20x%20%5Cin%20Z%3A%20X_E%28x%29%20%3D%201%5C%7D%20%20%3D%20E%7D)
E = {2,4,6,8,10 ....∞}