1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
olganol [36]
3 years ago
15

How many subsets of {1, 2, 3, 4, 6, 8, 10, 15} are there for which the sum of the elements is 15?

Mathematics
1 answer:
stepladder [879]3 years ago
8 0

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.

You might be interested in
Will mark u BRAINLIEST! Please help this is due ASAP
serious [3.7K]

Answer + Explanation:

let x be the measure of angle x

let y be the measure of angle y

\left \{ {{x + y = 180} \atop {x=24+y}} \right.

Now, solve:

plug x = 24 + y into x + y = 180

24 + y + y = 180

24 + 2y = 180

2y = 156

y = 78

Now, plug this back into the equation x = 24 + 78

x = 102

8 0
3 years ago
Read 2 more answers
Exercise #1: The amount of money in Nicole's bank account can be represented by the function f(x) = 32.50x + 200,
kolezko [41]
The initial amount in the account was $200 (y intercept). She adds $32.50 each day to her bank account (slope).
7 0
3 years ago
I need help on this question
gtnhenbr [62]
8:20 pm because if Prisha read 60 pages for a half hour, and she read 40 until 8:40, it would be 8:20 pm
8 0
3 years ago
What does X equal. If the area is 12 units.
Ray Of Light [21]
Im not sure, you didn't put a question
3 0
3 years ago
Identify the constant of proportionality from the table.
ivann1987 [24]

Answer:

The constant of proportionality is 3.

Step-by-step explanation:

6/2 is 3 and so on.

Correct me if I'm wrong

3 0
2 years ago
Other questions:
  • HELP ASAP!!!!!
    10·2 answers
  • Can -2y = -6 be written in slope-intercept form? If so, what is it?
    8·2 answers
  • What are some fractions less than 1/2
    8·2 answers
  • A solar powered water pumping system in Desert Range, Utah, has six solar panels, each containing 6 rows modules. Each row has 6
    5·1 answer
  • Can somebody help me find the slope of this line?
    14·2 answers
  • Is 33,44,55 a right triangle?
    13·2 answers
  • What is the quotient?<br><br> -4/5 *2
    15·1 answer
  • Unit Trigonomteric Function Pre calc Please help
    13·1 answer
  • Please help me with this.
    9·1 answer
  • Find the perimeter or circumference and area of each figure if each unit on the graph measures
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!