Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron in an atom. The four quantum numbers, the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (ml), and the spin quantum number (ms) have strict rules which govern the possible values. Identify allowable combinations of quantum numbers for an electron. Select all that apply.

a) n= 3 l= -2 ml=-1 ms= +1/2

b) n=3 l= 2 ml= -1 ms= -1/2

c) n= 4 l=4 ml=-1 ms= +1/2

d) n=2 l=1 ml=-1 ms=1

e) n=4 l=1 ml=2 ms=-1/2

f) n=5 l=4 ml=4 ms=+1/2

For g(x) = 5x - 3 and h(x) = [tex]\sqrt{x}[/tex], find (g · h)(4)

Questions 9-10. use the table of educational expenditures to answer the questions. k-12 education expenditures population indiana $9.97 billion 6.6 million illinois $28.54 billion 12.9 million kentucky $6.58 billion 4.4 million michigan $16.85 billion 9.9 million ohio $20.23 billion 11.6million 9. if the amount of k-12 education expenses in indiana were proportional to those in ohio, what would have been the expected value of k-12 expenditures in indiana? (give the answer in billions rounded to the nearest hundredth) 10. use the value of k-12 education expenditures in michigan as a proportion of the population in michigan to estimate what the value of k-12 education expenses would be in illinois. a) find the expected value of k-12 expenditures in illinois if illinois were proportional to michigan. (give the answer in billions rounded to the nearest hundredth) b) how does this compare to the actual value for k-12 expenditures in illinois? (lower, higher, same? )

Find the center of the circle that can be circumscribed about efg with e(4,4) f(4,2) g(8,2)