To check all the events (6), we label the chips. Suppose one chip with 1 is labeled R1 and the other B1 (as if they were red and blue). Now, lets take all combinations; for the first chip, we have 4 choices and for the 2nd chip we have 3 remaining choices. Thus there are 12 combinations. Since we dont care about the order, there are only 6 combinations since for example R1, 3 is the same as 3, R1 for us.
The combinations are: (R1, B1), (R1, 3), (R1, 5), (B1, 3), (B1, 5), (3,5)
We have that in 1 out of the 6 events, Miguel wins 2$ and in five out of the 6 events, he loses one. The expected value of this bet is: 1/6*2+5/6*(-1)=-3/6=-0.5$. In general, the expected value of the bet is the sum of taking the probabilities of the outcome multiplied by the outcome; here, there is a 1/6 probability of getting the same 2 chips and so on. On average, Miguel loses half a dollar every time he plays.
Answer:
-3x+30
Step-by-step explanation:
Expand 
Simplify
Let the total number of sweatshirts sold be S and the total number of baseball caps sold be B
Total sales is the total number of sweatshirts sold times $20 plus the total number of baseball caps sold times 10.
Equation 1: 20S + 10B = 2860
people bought 6 times as many sweatshirts as caps. Which means the number of sweatshirts sold (S) is 6 times caps sold(B)
Equation 2: S = 6B --- substitute S in equation 1 with 6B
=> 20(6B) + 10B = 2860
=> 120B + 10B = 2860
=> 130B = 2860 --- divide both side by 130
=> B = 2860/130
=> B = 22 --- is the number of caps sold.
To find the number of sweatshirts sold we use equation 2
S = 6B --- but we know now B = 22
=> S = 6(22)
=> S = 132
therefore 132 sweatshirts sold and 22 baseball caps sold.
Basically, you just divide each term in the equation by b^2.
So 35b^5 / b^2 = 35b^3, 30ab^3 / b^2 = 30ab, and 20a^2b^2 / b^2 = 20a^2.
So your final answer is 35b^3 + 30ab + 20a^2.
First, you have to set up two equations.
X + y = 45
18x + 24y = 1,050
To do this, you have to solve for an exponent by cancelling out the other one. To solve for y, you multiply everything in the first equation by -18.
-18x -18y = -810
This cancels out the x and leaves you with 6y = 240. Divide both sides by 6 and you have the number of Yankee hats that were bought.
Then, you have to substitute 40 for y in the first equation and solve for x.
