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:
Step-by-step explanation:
#456sghSDFG
Answer:
2 x 40 is = 80
Step-by-step explanation:
i hope that helps
The answer is “A” as when the width is multiplied by the row foot, you get approximately 3 times the amount.
I hope that’s correct and I hope I could help :)
Answer:
The solution is x=4.75 and y = -22
Step-by-step explanation:
To find the solution to the system of equations, we will follow the steps below:
3.2x + 0.5y = 4.2 --------------------------------------------------------------------------(1)
-1.6x -0.5y = 3.4 ----------------------------------------------------------------------------(2)
add equation (1) and equation (2)
1.6x =7.6
Divide both-side of the equation by 1.6 to get the value of x
1.6x /1.6 =7.6/1.6
x =4.75
substitute x = 4.75 into equation (1) and solve for y
3.2(4.75) + 0.5y = 4.2
15.2 + 0.5y = 4.2
subtract 15.2 from both-side of the equation
15.2 - 15.2 + 0.5y = 4.2-15.2
0.5y = -11
Divide both-side of the equation by 0.5
0.5y/0.5 = -11/0.5
y = -22
The solution is x=4.75 and y = -22
