Let x = Tom’s allowance
Let x/2 = the amount he spent going to the movies.
So x – x/2 = the amount he has left after she went to the movies
he washed the car and earned nine dollars, so you’d add that amount in
x – x/2 + 9
the amount he has left over is 13 dollars
x – x/2 + 9 = 13
Now you solve for x
x – x/2 + 9 = 13
x/2 + 9 = 13
x/2 = 4
x = 8
His allowance is $8
To check your work, plug 8 into the equation:
8 – 8/2 + 9 = 13
8 – 4 + 9 = 13
<span>13 = 13</span>
Answer:
It should be 1/18
Step-by-step explanation:
Answer:
0.4375
Step-by-step explanation:
Lets say that X is the random varaible that determine the arrival time of Bob and Y the random variable that determine the arrival time of Alice. Bot X and Y are Independent random variables with uniform [0,1] distribution. 15 minutes is the quarter of an hour, so we want to calculate P(|X-Y|) < 0.25.
Note that P(|X-Y| < 0.25) = P(|X-Y| < 0.25 | X ≥ Y) * P(X≥ Y) + P(|X-Y| < 0.25 | Y ≥ X) * P(Y ≥ X) = P(X-Y < 0.25 | X ≥Y) * P(X≥Y) + P(Y-X < 0.25 | Y≥X)*P(Y ≥ X).
For a simmetry argument, that expression is equivalent to 2*P(Y-X < 0.25 | Y≥X)*P(Y ≥ X) = 2*P(0 < Y-X < 0.25). The region 0 < Y-X < 0.25 is, for X between 0 and 0.75, a parallelogram, of base 0.75 and height 0.25, and for X between 0.75 and 1, it is a Triangle of base and height equal to 0.25. Therefore P(0 < Y-X < 0.25) = 0.25*0.75 + 0.25² * 0.5 = 7/32. Hence 2*P(0 < Y-X < 0.25) = 14/32 = 0.4375.
They will meet for lunch with probability 0.4375