Automated electron backscattered diffraction is now being used in the study of fracture phenomena. The following information is on mis-orientation angle (degrees) was extracted from the article "Observations on the Faceted Initiation Site in the Dwell-Fatigue Tested Ti-6242 Alloy: Crystallographic Orientation and Size Effects" Class: 0-<5 5-<10 10-<15 15-<20
Rel freq: 0.172 0.166 0.180 0.130
Class: 20-<30 30-<40 40-<60 60-<90
Rel freq: 0.199 0.074 0.046 0.033
A) Is it true that more that 50% of the sampled angles are smaller than 15 degrees, as asserted in the paper?
B) What proportion of the sampled angles are at least 30 degrees?
C) Roughly what proportion of angles are between 10 degrees and 25 degrees?
D) Construct a histogram and comment on any interesting feature.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12