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.
I believe it's B. If you graph, then you put a vertical line. If there are 2 points on the line, it's not a function. Every x-value has 1 y-value for a function. Hope this helps! ;)
Answer:
The slope of the line for Restaurant B is 2 times greater than the slope of the line for Restaurant A.
Step-by-step explanation:
Answer:
I'm pretty sure the answer is B
Step-by-step explanation:
sorry if I'm wrong
The profit to be made when she sells the house is $103,800.
The first step is to determine the value of Tammy's house in 13 years. The formula to be used is:
- FV = P (1 + r)^n
- FV = Future value
- P = Present value
- R = interest rate
- N = number of years
$184,000 x (1.035)^13 = $287,767.92
Profit = value of the house in 13 years - cost of the house
$287,767.92 - $184,000 = 103,767 = $103,800
To learn more about future value, please check: brainly.com/question/18760477
