For c to be positive, and for b to be negative, m must be negative and n must be negative.
X^2 - bx + c = (x - m)(x - n).
c is the product of m and n. If both m and n are positive, c would be positive. However b is the sum of m and n, therefore to make b negative, both m and n must be negative to ensure that the product of m and n is positive
The correct answer would be choice A: 1.
When 3 coins are flipped, there are 8 possible outcomes.
0 Tails = 1 ways
1 Tails = 3 ways
2 Tails = 3 ways
3 Tails = 1 ways
If you add up all the different tails, you could get 12 tails. Divide 12 by 8 and you have 1.5 which is the average number of tails you could expect to get by flipping 3 coins.
<span>Logarithm form is another way to express a number in exponential (exp.) form. log 8 (2) is the same as 8 (x) = 2 or in words, eight with exp. x equals two. If we take that equation and cube both sides, or raise each side to the power of 3, [8 (x)] with exp. 3 = 2 with exp. 3. This simplifies to 8 (3x) = 8. By definition, 8 is the same as 8 with exp. 1. So the equation is now 8 (3x) = 8 (1). This means 3x = 1. We can simplify to x = 1/3.</span>
<span>2/15 if drawn without replacement.
1/9 if drawn with replacement.
Assuming that the chips are drawn without replacement, there are 6 * 5 different possibilities. And that's a low enough number to exhaustively enumerate them. So they are:
1,2 : 1,3 : 1,4 : 1,5 : 1,6
2,1 : 2,3 : 2,4 : 2,5 : 2,6
3,1 : 3,2 : 3.4 : 3,5 : 3,6
4,1 : 4,2 : 4.3 : 4,5 : 4,6
5,1 : 5,2 : 5.3 : 5,4 : 5,6
6,1 : 6,2 : 6.3 : 6,4 : 6,5
Of the above 30 possible draws, there are 4 that add up to 5. So the probability is 4/30 = 2/15
If the draw is done with replacement, then there are 36 possible draws. Once again, small enough to exhaustively list, they are:
1,1 : 1,2 : 1,3 : 1,4 : 1,5 : 1,6
2,1 : 2,2 : 2,3 : 2,4 : 2,5 : 2,6
3,1 : 3,2 : 3,3 : 3.4 : 3,5 : 3,6
4,1 : 4,2 : 4.3 : 4,4 : 4,5 : 4,6
5,1 : 5,2 : 5.3 : 5,4 : 5,5 : 5,6
6,1 : 6,2 : 6.3 : 6,4 : 6,5 : 6,6
And of the above 36 possibilities, exactly 4 add up to 5. So you have 4/36 = 1/9</span>
