X + 14 + x + 14 = 17 + x + 7
2x + 28 = 24 + x
2x - x = 24 - 28
x = -4
DF = x + 14
= (-4) + 14
= 10
The answer will be 15/14, or 1 1/14 for the simplest form.
12563 is the correct answer
Answer:
The first choice, students tend to have less siblings than teachers
Step-by-step explanation:
If you look at the dot plots you notice that the teachers have more numbers than the students do and that the students have less sibling. It is not answer 2 because the students have less sibling, it is not answer 3 b/c they do not have the same range, and it is not number 4 because they do not look the same or have the same shape.
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.
