Answer:
You are expected to lose $0.05 (or win -$0.05)
Step-by-step explanation:
Since the roulette wheel has the numbers 1 through 36, 0, and 00, there are 38 possible outcomes.
In this bet, you are allowed to pick 3 out of the 38 numbers. Thus, your chances of winning (P(W)) and losing (P(L)) are:
![P(W)=\frac{3}{38}\\P(L) = 1 - P(W)\\P(L) = \frac{35}{38}\\](https://tex.z-dn.net/?f=P%28W%29%3D%5Cfrac%7B3%7D%7B38%7D%5C%5CP%28L%29%20%3D%201%20-%20P%28W%29%5C%5CP%28L%29%20%3D%20%5Cfrac%7B35%7D%7B38%7D%5C%5C)
The expected value of the bet is given by the sum of the product of each outcome pay by its probability. Winning the bet means winning $11 while losing the bet means losing $1. The expected value is:
![EV = (11*\frac{3}{38}) -(1*\frac{35}{38})\\EV = -\$0.0525](https://tex.z-dn.net/?f=EV%20%3D%20%2811%2A%5Cfrac%7B3%7D%7B38%7D%29%20-%281%2A%5Cfrac%7B35%7D%7B38%7D%29%5C%5CEV%20%3D%20-%5C%240.0525)
Therefore, with a $1 bet, you are expected to lose roughly $0.05
You FOIL
9x^2-15x+21x-35
Combine like terms
9x^2 + 6x - 35
Answer: ![\frac{17}{2}m^2+m-5](https://tex.z-dn.net/?f=%5Cfrac%7B17%7D%7B2%7Dm%5E2%2Bm-5)
Step-by-step explanation:
By definition, the perimeter of a rectangle is:
![P=2l+2w](https://tex.z-dn.net/?f=P%3D2l%2B2w)
Where "l" is the lenght and "w" is the width.
If you solve for "l":
![P-2w=2l\\\\l=\frac{P-2w}{2}](https://tex.z-dn.net/?f=P-2w%3D2l%5C%5C%5C%5Cl%3D%5Cfrac%7BP-2w%7D%7B2%7D)
In this case, you know that the following expression represents the perimeter of the rectangle:
![19m^2+2m-10](https://tex.z-dn.net/?f=19m%5E2%2B2m-10)
And the width of that rectanle is represented wih this expression:
![m^2](https://tex.z-dn.net/?f=m%5E2)
Therefore, based on the explained above, you can conclude that the lenght of that rectangle is given by:
![\frac{19m^2+2m-10-2(m^2)}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B19m%5E2%2B2m-10-2%28m%5E2%29%7D%7B2%7D)
Finally, simplifying the expression, you get:
![=\frac{17m^2+2m-10}{2}=\frac{17}{2}m^2+m-5](https://tex.z-dn.net/?f=%3D%5Cfrac%7B17m%5E2%2B2m-10%7D%7B2%7D%3D%5Cfrac%7B17%7D%7B2%7Dm%5E2%2Bm-5)
Answer:
2/8, 5/8
Step-by-step explanation:
![\frac{1}{4}*\frac{2}{2} =\frac{2}{8} \\\\\frac{3}{8} +\frac{2}{8} =\frac{5}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%2A%5Cfrac%7B2%7D%7B2%7D%20%3D%5Cfrac%7B2%7D%7B8%7D%20%5C%5C%5C%5C%5Cfrac%7B3%7D%7B8%7D%20%2B%5Cfrac%7B2%7D%7B8%7D%20%3D%5Cfrac%7B5%7D%7B8%7D)
Multiplying by 2/2 is like multiplying by 1, so it doesn't affect the value.
To add fractions with the same denominator just add the numerator, the denominator stays the same.