Express the confidence interval in the form of .
1 answer:
Answer:
0.075 - 0.022 < p < 0.075 + 0.022
Do <u>not</u> evaluate each of the math expressions above.
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Explanation:
The given confidence interval is in the form (L, U)
- L = lower bound = 0.053
- U = upper bound = 0.097
Find the midpoint of L and U to get
(L+U)/2 = (0.053+0.097)/2 = 0.075
This is the value of which is the symbol p-hat or phat (both pronounced the same). It's the sample proportion.
To get the margin of error E, we could do either of the following
- E = (U-L)/2 = (0.097-0.053)/2 = 0.022
- E = U - phat = 0.097 - 0.075 = 0.022
- E = phat - L = 0.075 - 0.053 = 0.022
This value of E represents half the width of the confidence interval. The full width being U-L.
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ANSWER
EXPLANATION
Since the directrix is
the axis of symmetry of the parabola is parallel to the y-axis.
Again, the focus being,
also means that the parabola will open upwards.
The equation of parabola with such properties is given by,
where
is the vertex of the parabola.
The directrix and the axis of symmetry of the parabola will intersect at
The vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix.
This implies that,
and
The equation of the parabola now becomes,
Thus, the distance between the vertex and the directrix.
This means that,
Since the parabola opens up, we choose
Our equation now becomes,
This simplifies to
or
This is the same as,
The correct answer is D .
EXPLANATION
Since the directrix is
the axis of symmetry of the parabola is parallel to the y-axis.
Again, the focus being,
also means that the parabola will open upwards.
The equation of parabola with such properties is given by,
where
is the vertex of the parabola.
The directrix and the axis of symmetry of the parabola will intersect at
The vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix.
This implies that,
and
The equation of the parabola now becomes,
Thus, the distance between the vertex and the directrix.
This means that,
Since the parabola opens up, we choose
Our equation now becomes,
This simplifies to
or
This is the same as,
The correct answer is D .