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.
P(more than 1 hour of TV | 6th period class) is 0.352.
<h3>What is the probability?</h3>
Probability determines the odds that a random event would happen. The odds of the random event happening lie between 0 and 1.
P(more than 1 hour of TV | 6th period class) = number of 6th period class students who watch tv for more than an hour / total number of students surveyed
12 / (12 + 9 + 5 + 8)
12 / 34 = 0.352
To learn more about probability, please check: brainly.com/question/13234031
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Answer:
w = 6
RS = 13
Step-by-step explanation:
RS + ST = RT
(2w + 1) + (w - 1) = 18
3w = 18
; w = 6
Hence the value of RS = 2(6) + 1
; RS = 13
AC = AB + BC
56 = (x + 16) + (5x + 10)
56 = 6x + 26....then rearrange the equation to form...;
56 - 26 = 6x
30 = 6x...
where...; x = 5
AB = 5 + 16 and BC = 5(5) + 10
;AB = 21 ;BC = 35
18- j
19- c
20- h
Hope this is right lol
