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.
Answer:
3x >/= 24 or 3x </= -24
Step-by-step explanation:
Plug in (-8) for (x) and solve.
Answer:
Function
Step-by-step explanation:
Since there is once variable of y for ever6y value of x in (-1,2), (-2,1), (-3,0), (-4,-1), this relation is a function.
Answer:
JKL = PQR and JKL = PQR
Step-by-step explanation:
Answer:
If the quetion is how much money I earned on both days it would be 56.25
Step-by-step explanation:
4hours times 6.25 an hour = 25 now we do 5hours times 6.25 an hour = 31.25 so add them to get 56.25
