If xj ∈ {0, 1}, write a constraint to enforce the logical condition that x1 can be 1 only if both x2 = 1 and x3 = 1 (in other words, if either x2 = 0 or x3 = 0 then x1 = 0 but if both x2 = 1 and x3 = 1 then x1 can be either 0 or 1). is your constraint linear in the xj?

Which of these numbers of simulations of an event would be most likely to produce results that are closest to those predicted by probability theory? 15, 20, 5, 10

Which sum or difference identity would you use to verify that cos (180° - q) = -cos q? a.) sin (a -b) = sin a cos b – cos a sin b b.) cos (a -b) = cos a cos b – sin a sin b c.) cos (a -b) = cos a cosb + sin a sin b d.) sin (a + b) = sin a cos b + cos a sin b

As voters exit the polls, you ask a representative random sample of voters if they voted for a proposition. if the true percentage of voters who vote for the proposition is 63%, what is the probability that, in your sample, exactly 5 do not voted for the proposition before 2 voted for the proposition? the probability is