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: 3 f(8)=g(8)
Step-by-step explanation:
2(8)-3=3/2(8)+1
16-3=12+1
13=13
Step-by-step explanation:
20 x 399 x 5
= (20×5) × 399
= 100×399
= 39,900
The correct answer is D.
The LCD, least common denominator, is the smallest denominator that both denominators will go into. The LCD of 5 and 7 will be 35; the variable portion will be b³c, since that is the smallest thing the second fraction can go into.
This gives us a denominator of 35b³c.
The answer is c because of the fact that if the 2 angles at 55 and 20 that means that you have to add them together and get to 180 for the triangle to be true
