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:
50.6
Step-by-step explanation:
it says 7 students traveled by car so you need to take 7 from 311, then divide your answer (304) by 6, which is 50.6
The way i did that in middle school was plot the points then find the slpoe and work it out from there
<h3>
Answer: 112 square cm</h3>
=====================================
Work Shown:
area = base*height
area = 16*7
area = 112 square cm
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Extra info (optional section):
The area formula for a parallelogram is the same as the formula for a rectangle. Imagine tilting a rectangle so that it's slanted. The area has not changed.
Or another thing to imagine is that let's say we had a stack of 2 by 4s. If the stack is perfectly vertical, aka forming a rectangle, then we can nudge the beams so that we can form a slanted parallelogram instead. Both configurations involve the same amount of wood, and therefore would lead to the same frontal surface area.
Cookie sales: 12 weeks divided by 2 weeks = 6 weeks x $360 = $2,160
Car wash: 12 weeks divided by 3 weeks = 4 weeks x $450 = $1,800
Recycling: 12 weeks divided by 4 weeks = 3 weeks x $600 = $1,800
Yard work: 12 weeks divided by 2/5 weeks = 30 x $80 = $2,400
