The regular hexagon shown below has a perimeter of 30 and center C. What is the perimeter of triangle ABC.
1 answer:
Answer:
Option (3)
Step-by-step explanation:
Perimeter of a regular hexagon = 30 units
Length of one side =
= 5 units
Interior angle of hexagon =
=
= 120°
BC is an bisector of the angle measuring 120°.
m∠ABC = 60°
Similarly, m∠BCA ≅ ∠CAB ≅ 60°
Therefore, ΔABC is an equilateral triangle.
By the property of equilateral triangle, all sides of the triangle will be equal in measure.
AB ≅ BC ≅ AC ≅ 5 units
Perimeter of triangle ABC = AB + BC + AC
= 5 + 5 + 5
= 15 units
Option (3) will be the answer.
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Answer:
91.92% probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
What is the probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches
This is the pvalue of Z when X = 106.8. So
By the Central Limit Theorem
has a pvalue of 0.9192
0.9192 = 91.92% probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches
Answer:
Step-by-step explanation:
This is horizontal parabola.
It has a directrix at x=-6.
The vertex is (0,0).
The focus is (6,0)
The equation of this parabola is of the form
Where (p,0) is the focus
By comparison, p=6
Therefore the equation of the parabola is
This implies that