He has $90 in total to spend
He spent (31/45) of this money on ticket
so money spent on ticket =(31/45) *90 =2790/45 =62
Now money left with him is 90-62 =28 $
Now it says that he spent (3/7) of this remaining money at concession stand
so money spent on concession stand =(3/7)*28 =84/7 =12
Now money left with him = 28-12 =16
So money left with him is $16 but hat costs for $18
So Mr. O'Connor didnt have enough moeny to buy the hat
binomial(16 + 7, 16) 2^(-(16 + 7)) = ((16 + 7)!)/(16! 7! 2^(16 + 7)) = 245157/8388608 ≈ 0.02922 ≈ 1/34.22
(assuming children are independent and male and female are equally likely)
| probability
less than 16 boys | 0.9534
16 or less boys | 0.9827
more than 16 boys | 0.01734
16 or more boys | 0.04657
fraction of boys | 16/(16 + 7) ≈ 0.695652
fraction of girls | 7/(16 + 7) ≈ 0.304348
expected value | 11.5
standard deviation | 2.398
variance | 5.75
11.5
A) The length of the longer leg is x-1
b) Based on the area, the other leg is 2*30/(x -1). Based on the Pythagorean theorem, the other leg is √(x^2 -(x -1)^2).
c) Equating the two expressions for the shorter leg, we have
.. 60/(x -1) = √(2x -1)
.. 3600/(x -1)^2 = (2x -1)
.. (2x -1)(x^2 -2x +1) = 3600
.. 2x^3 -5x^2 +4x -3601 = 0
d) There is one positive real root, at x=13. A graphical solution works well.
The three sides of the triangle are 5 in, 12 in, 13 in.
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5-12-13 is a well-known Pythagorean triple. It is the next smallest one after 3-4-5.