Six less than "b"
i think this would be the answer
good luck!!
Answer:
3/2 pages per hour
Step-by-step explanation:
1 : 2/3
= 3/2 : 1
11 liters of 25% orange juice, 4 liters of 10% orange juice:
1' let x to be 25% orange juice and y be 10% orange juice
2' .25x+.10y=(15).21
3' x+y=15
4' 2.5x+y=31.5 divide all sides by 10
5' -x-y=-15 multiply all sides by -1
6' 1.5x=16.5
7' x=11
8' y=15-11=4
so 11 and 4 are the answers.
Answer:
35
Step-by-step explanation:
Alright this is like a linear pair. All three angles add up to 180; so this is the set up:
40 + 2x + 30 + 40 = 180
2x + 110 = 180
2x = 70
x=35
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.
