There are
ways of selecting two of the six blocks at random. The probability that one of them contains an error is
So
has probability mass function
These are the only two cases since there is only one error known to exist in the code; any two blocks of code chosen at random must either contain the error or not.
The expected value of finding an error is then
Divide 4 by 12, which equals approximately 0.33333, then multiply that to 180, which gives us 60. So she sold 180 ears of corn for $60.
The coefficient of y is 14 and the constant is 13.
You can find this by combining like terms first.
6x + 12y + 5 + 2y + 8
6x + 14y + 5 + 8
6x + 14y + 13
Now the coefficient is the number next to y. The constant is the number on its own.
Let s represent the length of any one side of the original square. The longer side of the resulting rectangle is s + 9 and the shorter side s - 2.
The area of this rectangle is (s+9)(s-2) = 60 in^2.
This is a quadratic equation and can be solved using various methods. Let's rewrite this equation in standard form: s^2 + 7s - 18 = 60, or:
s^2 + 7s - 78 = 0. This factors as follows: (s+13)(s-6)=0, so that s = -13 and s= 6. Discard s = -13, since the side length cannot be negative. Then s = 6, and the area of the original square was 36 in^2.
1/3
because a foot is a third of a yard and a yard is 3 feet.
