Solve the problem.A measure of diversity of species in an ecological community is given by the formula 
where P1, P2, ... ,Pn are the proportions of a sample belonging to each of n species found in the sample. A bog in northeastern Illinois has 5 species of birds with these proportions: cardinal, 0.204; robin, 0.28, sparrow, 0.217; oriole, 0.248; woodpecker, 0.051. Find the index of diversity, H.
A. 2.1782193
B. -2.1782193
C. -2.3299917
D. 2.3299917
Answer: A
Mathematics
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Use the Montonicity Theorem to find where the function is increasing and where it is decreasing.h(z) = 108z - z3
A. Increasing on [-36, 36], decreasing on (-?, -36] ? [36, ?) B. Increasing on (-?, 6], decreasing on [6, ?) C. Increasing on (-?, -6] ? [6, ?), decreasing on [-6, 6] D. Increasing on [-6, 6], decreasing on (-?, -6] ? [6, ?)
Mathematics
Solve the initial value problem.
= e10x cos e10x, y(0) = 0
A. y = 
sin e10x - 
sin 1
B. y = - 
sin e10x + 
sin 1
C. y = 
sin e10x - 
D. y = 
sin x
Mathematics
Use implicit differentiation to find dy/dx.y cos 
= 9x + 9y
A. 
B. 
C. 
D. 
Mathematics
Solve for real roots.2x1/2 - 19x1/4 - 10 = 0
A. x = 10, - 
B. x = 10,000, 
C. x = -10, -1
D. x = 10,000
Mathematics