Transforming between two encodings for boolean vectors. a boolean n-vector is one for which all entries are either 0 or 1. such vectors are used to encode whether each of n conditions holds, with ai = 1 meaning that condition i holds. another common encoding of the same information uses the two values −1 and +1 for the entries. for example the boolean vector (0,1,1,0) would be written using this alternative encoding as (−1, +1, +1, −1). suppose that x is a boolean vector with entries that are 0 or 1, and y is a vector encoding the same information using the values −1 and +1. express y in terms of x using vector notation. also, express x in terms of y using vector notation.

Ican interpret and represent the remainder in division calculations sensibly for the context (eg if we wont to know how many 40 seat buses will be needed to transport 170 students for on excursion, we divide 170 by 40 and realise buses and another smaller vehicle to that we need 4 transport 10 more students) solve the following questions. show your work! 11) the zoo had 420 butterflies that needed to be transported to a new enclosure. the boxes that the butterflies would be moved in only hold 80 butterflies in each. how many boxes would they need? 2 12) each classroom in the school can have exactly 25 students, if there are 345 students in the school how many full classrooms are there?

Jamie has 7/10 of a pound of chicken to cook for dinner if she's going to put the chicken in between three people how much chicken will each person get

Marcus needs to bike at least 80 miles this week for his training. if he has already biked 25 miles this week, then how many miles should he bike on each of the 5 remaining days this week ?