Automated electron backscattered diffraction is now being used in the study of fracture phenomena. the following information on misorientation 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 fraq: .177 .166 .175 .136

class: 20-< 30 30-< 40 40-< 60 60-< 90
rel fraq: .194 .078 .044 .030

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 features.

step-by-step explanation:

im not sure what the answer is

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

the answer would be 0.54