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.
Try 21 if its wrong sorry im not very smart
Answer:
Jared worked 11 days as full 8-hour days.
Step-by-step explanation:
We have:
First day = 2 h
Second day = 4 h
After that = 8 h each day
Since his paycheck shows 94 hours of work, we can find the number of days that he works 8-hour day:
Where x is the number of days that he works 8-hours.
Therefore, Jared worked 11 days as full 8-hour days.
I hope it helps you!
Answer:
x= 6/7 or x = −10/7
Step-by-step explanation:
Let's solve your equation step-by-step.
4(|7x+2|)=32
Step 1: Divide both sides by 4.
4(|7x+2|)/4 =32/4
|7x+2|=8
Step 2: Solve Absolute Value.
|7x+2|=8
We know either 7x+2=8 or 7x+2=−8
7x+2=8 (Possibility 1)
7x+2−2=8−2 (Subtract 2 from both sides)
7x/7 = 6/7
(Divide both sides by 7)
7x/7= 6/7
x= 6/7
7x+2=−8 (Possibility 2)
7x+2−2=−8−2 (Subtract 2 from both sides)
7x/7 = −10/7
(Divide both sides by 7)
x= −10/7
Answer:
x= 6/7 or x = −10/7
obtuse angles are having value greater than 90 degree.
so ans is option A
angle DBC is greater than 90
