Answer:
512
Step-by-step explanation:
Suppose we ask how many subsets of {1,2,3,4,5} add up to a number ≥8. The crucial idea is that we partition the set into two parts; these two parts are called complements of each other. Obviously, the sum of the two parts must add up to 15. Exactly one of those parts is therefore ≥8. There must be at least one such part, because of the pigeonhole principle (specifically, two 7's are sufficient only to add up to 14). And if one part has sum ≥8, the other part—its complement—must have sum ≤15−8=7
.
For instance, if I divide the set into parts {1,2,4}
and {3,5}, the first part adds up to 7, and its complement adds up to 8
.
Once one makes that observation, the rest of the proof is straightforward. There are 25=32
different subsets of this set (including itself and the empty set). For each one, either its sum, or its complement's sum (but not both), must be ≥8. Since exactly half of the subsets have sum ≥8, the number of such subsets is 32/2, or 16.
The correct answer is A. 3x8=24, 5x8=40, and 6x8=48
to solve this, you need to set up an equation to solve for <em>x, </em>the number of square meters waxed in an hour:
you can use cross multiplication to solve for x:
so jessica can wax 100/3 square meters per hour. you can convert this to decimal form (which would be 33.3 repeating) or you can leave it in fraction form.
Answer:
960
Step-by-step explanation:
We can find the number of unique combinations by
Multiplying 4*5*6*8
960
There are 960 possible choices by picking 1 from each group
The answer will be D, -15, -5, 0, 10, 25
