Given circle X with radius 10 units and chord AB with length 12 units, what is the length of segment CX, which bisects the chord
? A. 10 units B. 8 units C. 6 units D. 16 units
1 answer:
For the circle centered at X, as illustrated:
Draw a diameter that runs parallel to chord AB, as depicted in the figure.
Given that the diameter and AB are parallel, the line segment XC, which intersects AB at midpoint C, will be at a right angle to AB.
Thus, triangle XCB forms a right triangle. Consequently, using the Pythagorean theorem, the length of CX is
units.
The answer is: 8 units
Draw a diameter that runs parallel to chord AB, as depicted in the figure.
Given that the diameter and AB are parallel, the line segment XC, which intersects AB at midpoint C, will be at a right angle to AB.
Thus, triangle XCB forms a right triangle. Consequently, using the Pythagorean theorem, the length of CX is
The answer is: 8 units
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Answer:
a)
The probability can be determined using the complement rule, with the standard normal distribution, an excel sheet, or a calculator.
b)
This probability can also be calculated using the normal standard distribution, an excel sheet, or a calculator.
c)
For this one, the probability can likewise be derived from the standard normal distribution, excel, or a calculator, with specific adjustments:
Step-by-step explanation:
Previous concepts
Normal distribution refers to a symmetric probability distribution centered around the mean, indicating that occurrences near the mean are more common than those far from it.
The Z-score is a statistic that represents a value's relationship to the average of a set of values, expressed in terms of how many standard deviations it is away from the mean.
Part a
Let X denote the random variable representing the lengths within a population, and for our case, the distribution for X is as follows:
Where and
We seek the probability:
The most effective way to solve this is by leveraging the normal distribution and the corresponding Z-score:
By applying this formula, we can find the probability:
Again, this probability can be obtained either using the complement rule, the standard normal distribution, or a calculator.
Part b
This probability can also be computed using either the normal standard distribution, an excel sheet, or a calculator.
Part c
In this case, the probability can similarly be acquired with the help of the standard normal distribution, an excel sheet, or a calculator, with particular adjustments:
Response: The outcome is
Detailed explanation: Suppose that
we need to finalize the subsequent sentence:
We have the polynomial division algorithm as follows
In this equation, a(x) denotes the quotient, b(x) indicates the divisor, and c(x) stands for the dividend.
Using this principle in the current problem, it results in
Consequently, the full sentence would be