Which is the best estimate for 10 drops of liquid?
1 answer:
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Answer:
Step-by-step explanation:
We have the function:
And we want to find x=d for which the minimum/maximum value will occur.
Notice that our function is a quadratic in factored form.
Remember that the minimum/maximum value always occurs at the vertex point.
And remember that the x-coordinate of the vertex is the axis of symmetry.
Since a quadratic is always symmetrical on both sides of its axis of symmetry, a quadratic’s axis of symmetry is the average of the two roots/zeros of the quadratic.
Therefore, the value x=d such that it produces the minimum/maximum value is the average of the two roots.
Our factors are <em>(x-2) </em>and <em>(x-1)</em>.
Therefore, our roots/zeros are <em>x=1, 2</em>.
So, the average of them are:
Therefore, regardless of the value of <em>a</em>, the minimum/maximum value will occur at <em>x=d=1.5</em>.
Alternative Method:
Of course, we can also expand to confirm our answer. So:
The x-coordinate of the vertex is still going to be the place where the minimum/maximum is going to occur.
And the formula for the vertex is:
So, we will substitute <em>-3a</em> for <em>b</em> and <em>a</em> for <em>a</em>. This yields:
Confirming our answer.
Step-by-step explanation:
We are dealing with theoretical probability. This means that our probability of said outcome is
where x is the outcome we want, and y is the total number of outcomes possible.
28. There is 3 triangles out of 6 polygons so the probability is 1/2.
29.There is 1 Pentagon so the probability is 1/6.
30. This is a complement to question 28. A complement is the inverse of the problem. A complement and its original add to 1 so the probability of both getting a triangle is 1/2.
31. There is 4 non quadraletrial so the probability is 2/3.
32. There is 3 figures that has more sides than three so 1/2 is the probability.
33.There is only multi right angles figures so 1/2 is the probability.
34. There is 30 days in April so the probability it's the 29th is
35. There is 31 days in July and 15 days after the 16th. So the probability
is