Solve this following algebraic expression
2 answers:
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Answer:
Around 5.5 square meters
Step-by-step explanation:
You can start by finding the area of the segment. Since the rest of the circle that is not in the segment is 240 degrees, the segment is 120 degrees or a third of the circle. You can therefore find the area of that segment with the formula square meters. Now, you need to find the area of the triangle inside the sector. This is more difficult than last time, because it is not a 90 degree angle. However, you can solve this by dividing this triangle into two 30-60-90 triangles, which you know how to find the ratio of sides for. In a 30-60-90 triangle, the hypotenuse is twice the length of the smallest leg, and the larger leg is
times larger than the smaller leg. In this case, these dimensions are a base of
for the smaller leg and
for the larger leg, or the base. Using the triangle area formula and multiplying by 2 (because remember, we divided the big triangle in half), you get
square meters. Subtracting this from the area of the segment, you get about 5.5 square meters. Hope this helps!
Answer:
D. a = 60 and b = 58.8
Step-by-step explanation:
Z-score:
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. 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 p-value, we get the probability that the value of the measure is greater than X.
Z-score for data point a is 0.
This means that a is the mean, that is, a = 60.
The z-score for data point b is -0.4.
This means that b must be a value below the mean, that is, a value below 60.
The option that satisfies a = 60 and b < 60 is option D, which is the answer.