Here's a problem that occurs in automatic program analysis. for a set of variables x1; : : : ; xn, you are given some equality constraints, of the form xi = xj and some disequality constraints,
of the form xi 6= xj . is it possible to satisfy all of them?
for instance, the constraints
x1 = x2; x2 = x3; x3 = x4; x1 6= x4
cannot be satis ed. give an ef cient algorithm that takes as input mconstraints over n variables
and decides whether the constraints can be satisfied.

Given: circle o, cd is diameter, chord ab || cd. arc ab = 74°, find arc ca.

Hurry if the population of of an ant hill doubles every 10 days and there are currently 100 ants living in the ant hill what will the ant population be in 20 days

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? )