Draw an imaginary line from the vertex of angle x to the center of the circle.
This divides the 4-sided polygon into two right triangles. For example, the upper right triangle has an acute angle whose measure is 135 degrees / 2, or 67.5 degrees, and the another acute angle whose measure is x/2.
x/2 and 67.5 degrees are complementary angles, so x/2 + 67.5 deg = 90 deg. Thus, x/2 = 22.5 deg, and so x = 45 deg. (answer)
Answer:
Step-by-step explanation:
<u>The factored form, use variables/numbers outside the square:</u>
<u>The standard form, use variables/numbers inside the square:</u>
- x² + 6x - 4x - 24 = x² + 2x - 24
A 52-gon has an interior angle sum 9000<span>°</span>
Answer:
The middle 92% of all heights fall between 64.4 inches and 74.2 inches.
Step-by-step explanation:
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.
In this problem, we have that:

Between what two values does that middle 92% of all heights fall?
The middle 92% falls from X when Z has a pvalue of 0.5 - 0.92/2 = 0.04 to X when Z has a pvalue of 0.5 + 0.92/2 = 0.96. So from the 4th percentile to the 96th percentile.
4th percentile
X when 




96th percentile
X when 




The middle 92% of all heights fall between 64.4 inches and 74.2 inches.