Which geometric object is defined as the set of all points in a plane equidistant from a single point and a single line?
2 answers:
Answer:
The geometric object that matches the definition is the parabola.
Step-by-step explanation:
A parabola is the set of all points in a plane equidistant from a fixed point (the focus) and a fixed-line (the directrix) that lie in the plane.
A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle.
An angle bisector is a line or ray that divides an angle into two congruent angles.
A hyperbola is the set of all points in a plane such that the absolute value of the difference of the distances between two fixed points stays constant.
Therefore the geometric object that matches the definition is the parabola.
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Answer:
26.11% of the test scores during the past year exceeded 83.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by
After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
It is known that for all tests administered last year, the distribution of scores was approximately normal with mean 78 and standard deviation 7.8. This means that .
Approximately what percentatge of the test scores during the past year exceeded 83?
This is 1 subtracted by the pvalue of Z when . So:
has a pvalue of 0.7389.
This means that 1-0.7389 = 0.2611 = 26.11% of the test scores during the past year exceeded 83.