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.
How do write whole numbers without scientific notation? can you elaborate on your question.
Answer:
-9,-21
Step-by-step explanation:
let the numbers be x and y and x>y
x-y=12
y=2x-3
x-(2x-3)=12
x-2x+3=12
-x=12-3
-x=9
x=-9
y=2(-9)-3=-18-3=-21
A random guess could be 495866 because if you round is to the nearest thousandths it will be 500000
I am making one________________
Katy has 5 cakes with each cake having 1/4 of a whole left. How many pieces does Katy have in all?
