Describe in English a PDA accepting the language L as follows: L = { w1#w2# . . . #wk#w : w, wi ∈ {0, 1} ∗ and wj = w R for some j }. That is, for a string to be in L, it must have alphabet a subset of {0, 1, #}, and when cut up into pieces by omitting the #, the final piece is the reverse of one of the other pieces.

Afurniture manufacturer produces chairs and sofas. each chair requires 10 yards of fabric, and each sofa requires 20 yards of fabric. the manufacturer has 300 yards of fabric available. to fulfill orders, the number of sofas must be at least twice the number of chairs. let x be the number of chairs and y the number of sofas. which inequalities are described in the problem? check all of the boxes that apply

According to the data set, where should the upper quartile line of the box plot be placed?

The table shows the age and finish time of ten runners in a half marathon. identify the outlier in this data set. drag into the table the ordered pair of the outlier and a reason why that point is an outlier.