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
What is the value of 3.2n when n=5
Lady bird [3.3K]
3.2n=3.2*5

3.2*5=16 the answer is 16

Hope this helps, have a great day!! 

:)
7 0
3 years ago
If 5 miles is 8km . Convert 33.7 km into miles
LenKa [72]

Answer:

20.94021

Step-by-step explanation:

mark me brainlist

7 0
3 years ago
Read 2 more answers
Lucy had 3 2/3 gal of paint. After painting a room she had 1 1/4 gal left how many gallons of paint did Lucy use to paint a room
garik1379 [7]

Answer:

2 \frac{5}{12}

gallons of paint was used by Lucy.

Step-by-step explanation:

3\frac{2}{3}  - 1\frac{1}{4}  =  \frac{44}{12}  -  \frac{15}{12} =  \frac{29}{12}

29/12 = 2 5/12

7 0
3 years ago
Which of these is the absolute value parent function?
bija089 [108]

Answer:

  D.  f(x) = |x|

Step-by-step explanation:

The absolute value parent function has nothing added or subtracted or multiplied. It is simply ...

  f(x) = |x|

8 0
3 years ago
Help me with this question please.
Tems11 [23]

Answer:

38.6 m

Step-by-step explanation:

cos 75° = 10/x

x= 10/cos75°= 38.637 ≈ 38.6m

8 0
3 years ago
Other questions:
  • What the Answer please?
    11·1 answer
  • Who knows this work?
    12·2 answers
  • Which statement best demonstrates why the following is a non-example of a polynomial?
    6·1 answer
  • Doreen schmidt is a chemist. She needs to prepare 36 ounces of a 10% shydrochloric acid solution. Find the amount of 18% solutio
    11·1 answer
  • caleb throws a ball three times for his dog leo. for each throw. leo either catches the ball of misses it. identify the sample s
    11·1 answer
  • Convert 40 miles per hour to feet per second.
    7·2 answers
  • What is 9 006 in word​
    6·2 answers
  • 20 POINTSS Select all the values that are equivalent to the given expression. Express your answer in scientific notation.
    11·1 answer
  • Solve for x and y if: <br> {6x - 11y=-58 8x+y=1
    10·1 answer
  • What percent of 513 is 248
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!