Help please Draw an obtuse angle (labeled BIG) Place a point P inside the angle. Now construct perpendiculars form the point to
both sides of the angle. Which side is closer to point P? please explain and draw this
1 answer:
Answer:
The side closest to P is the side that is on the same side of the angle bisector as P.
Step-by-step explanation:
The angle bisector is the line containing all the points equidistant from the sides of the angle. Points on one side of the angle bisector are closer to the angle side that is on that side of the angle bisector.
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The attached diagram shows the angle bisector as a dashed line. A couple of different locations for P are shown (P1 and P2). Apparently, we're concerned here with the distance from P along the perpendicular to each side of the angle. For P2 (on the left side of the angle bisector), it may be clear that the left perpendicular is shorter than the right one. Likewise, for P1, the right perpendicular will be shorter.
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The rocks are chosen without replacement, which means that the hypergeometric distribution is used to solve this question. First we get the parameters, and then we answer the questions. From this, we get that:
- P(X < 6) = 0.9545
- P(all specimens of one of the two types of rock are selected for analysis) = 0.2046.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
The mean and the variance are:
We have that:
5 + 7 = 12 rocks, which means that
9 are chosen, which means that
7 are granite, which means that
Question a:
Thus:
Question b:
Since there are only 5 specimens of basaltic rock, at least 9 - 5 = 4 specimens of granite are needed, which means that:
In which
Thus
So P(X < 6) = 0.9545.
Question c:
5 of basaltic and 4 of granite: 0.1591 probability.
7 of granite is P(X = 7), in which
0.1591 + 0.0455 = 0.2046, thus:
P(all specimens of one of the two types of rock are selected for analysis) = 0.2046.
A similar question is found at brainly.com/question/24008577