Answer:
Step-by-step explanation:
We are required to solve for c in the equation:
Step 1: Collect like terms
Step 2: Find the Lowest Common Multiple of the denominators
LCM of 8 and 5 is 40
Step 3: Multiply all through by 40
Step 4: Simplify
40c=32-5
40c=27
Step 5: Divide both sides by 40 and simplify if possible.
Using the normal distribution, it is found that the replacement time that separates the top 18% from the bottom 82% is of 11.23 years.
<h3>Normal Probability Distribution</h3>The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
In this problem, the mean and the standard deviation are, respectively, given by .
The desired value is the 82nd percentile, which is X when Z = 0.915, hence:
X - 9.4 = 0.915(2)
X = 11.23
The replacement time that separates the top 18% from the bottom 82% is of 11.23 years.
More can be learned about the normal distribution at brainly.com/question/24663213
Answer:
x = 70°
Step-by-step explanation:
Clockwise from top, call the three tangent points A, B, and C. Central angle AXC is the supplement of the marked external angle, so is 140°. Arc AB is bisected by the upper ray of angle x; and arc BC is bisected by the lower ray of angle x. That is to say x is half the measure of arc AC, so is 70°.
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Attached is the output of a geometry program. The angle at lower left is 40° as in the given figure. The central angle α (70°) remains the same as tangent point C is moved around, which is to say that the measure of the angle α does not depend on the dimensions of the triangle containing α. It just depends on the fact that the triangle is tangent to the circle.
