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
Mekhanik [1.2K]
3 years ago
6

Under which operation is the set {0, 1} closed?

Mathematics
1 answer:
Hoochie [10]3 years ago
7 0
Multiplication.

0\times0=0
0\times1=0
1\times0=0
1\times1=1

All the possible products are contained in the set, so the set is closed under multiplication.

This isn't true for any of the other three standard arithmetic operations (addition, subtraction, division), and it's easy to see why.

One caveat about addition, though. The set *is* closed under addition modulo 2. Any even number x is equivalent to 0 modulo 2, i.e. x\equiv 0\mod2, while any odd number y is equivalent to 1 modulo 2, i.e. y\equiv1\mod2.

When you add two even numbers together, you get another even number.
When you add two odd numbers together, you get an even number.
When you add an even number to an odd number, you get an odd number.

So if you represent every even number by 0 and every odd number by 1, you get the following results:

0+0=0 (even + even = even)
0+1=1 (even + odd = odd)
1+0=1 (odd + even = odd)
1+1=0 (odd + odd = even)

The same also goes for multiplication modulo 2.
You might be interested in
Find the 8th term of the geometric sequence 10,-40, 160, ...
Mars2501 [29]

Answer:

-163,840

Step-by-step explanation:

Because the pattern is -4 you just multiply it through until you get to the 8th term. ;)

5 0
3 years ago
Can someone please help me and explain? please
mariarad [96]
Composite figure is made up of 4 triangles and a square.

Area of Square = Length x Length 
Area of Square = 12 x 12
Area of Square= 144 cm²

Area of triangle = 1/2 x base x height
Area of triangle  = 1/2 x 12 x 8 
Area of triangle  = 48 cm²

Area of 4 Triangles = 48 x 4
Area of 4 Triangles = 192 cm²

Total Area = 144 + 192 = 336 cm² 

\Longrightarrow \boxed { \boxed { Answer : 336 cm^{2} }}


4 0
3 years ago
Find the area of the triangle described.
Artemon [7]

Answer:

28

Step-by-step explanation:

You multiply 7 and 8, and then divide it by two.

8 0
3 years ago
Read 2 more answers
34​% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and a
finlep [7]

Answer:

a) There is a 18.73% probability that exactly two students use credit cards because of the rewards program.

b) There is a 71.62% probability that more than two students use credit cards because of the rewards program.

c) There is a 82% probability that between two and five students, inclusive, use credit cards because of the rewards program.

Step-by-step explanation:

There are only two possible outcomes. Either the student use credit cards because of the rewards program, or they use for other reason. So, we can solve this problem by the binomial distribution.

Binomial probability

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And \pi is the probability of X happening.

In this problem, we have that:

10 student are sampled, so n = 10

34% of college students say they use credit cards because of the rewards program, so \pi = 0.34

(a) exactly​ two

This is P(X = 2).

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

P(X = 2) = C_{10,2}.(0.34)^{2}.(0.66)^{8} = 0.1873

There is a 18.73% probability that exactly two students use credit cards because of the rewards program.

(b) more than​ two

This is P(X > 2).

Either a value is larger than two, or it is smaller of equal. The sum of the decimal probabilities must be 1. So:

P(X \leq 2) + P(X > 2) = 1

P(X > 2) = 1 - P(X \leq 2)

In which

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)

So

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

P(X = 0) = C_{10,0}.(0.34)^{0}.(0.66)^{10} = 0.0157

P(X = 1) = C_{10,1}.(0.34)^{1}.(0.66)^{9} = 0.0808

P(X = 2) = C_{10,2}.(0.34)^{2}.(0.66)^{8} = 0.1873

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0157 + 0.0808 + 0.1873 = 0.2838

P(X > 2) = 1 - P(X \leq 2) = 1 - 0.2838 = 0.7162

There is a 71.62% probability that more than two students use credit cards because of the rewards program.

(c) between two and five inclusive

This is:

P = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

P(X = 2) = C_{10,2}.(0.34)^{2}.(0.66)^{8} = 0.1873

P(X = 3) = C_{10,3}.(0.34)^{3}.(0.66)^{7} = 0.2573

P(X = 4) = C_{10,4}.(0.34)^{4}.(0.66)^{6} = 0.2320

P(X = 5) = C_{10,5}.(0.34)^{5}.(0.66)^{5} = 0.1434

P = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.1873 + 0.2573 + 0.2320 + 0.1434 = 0.82

There is a 82% probability that between two and five students, inclusive, use credit cards because of the rewards program.

6 0
3 years ago
Simplify -3x^3(2x^2+3)+9x^4
SIZIF [17.4K]

Answer:

ANSWER = −6x^5 +9x^4 − 9x^3

Step-by-step explanation:

Let's simplify step-by-step.

(−3x^3) (2x^2 + 3) + 9x^4

Distribute:

=(−3x^3) (2x^2) + (−3x^3) (3) + 9x^4

=−6x^5 + − 9x^3 + 9x^4


Answer:

= −6x^5 +9x^4 − 9x^3


3 0
3 years ago
Other questions:
  • T he area of a square postage stamp is 81/100 in 2. What is the side length of the stamp?
    8·1 answer
  • an internet service provider charges a one time $25 connection fee and then charges $16 per month. write an expression to model
    6·1 answer
  • A paper clip is 7/8 inches. Each paper clip is $0.03. Lined up together they add up to 56inches. How much will it cost
    15·1 answer
  • 12=x+3. SOLVE FOR X<br>NEED HELP ASAP
    13·2 answers
  • Help with the answer
    14·1 answer
  • X² + 2x-3
    15·1 answer
  • I invested in a savings bond for two years and paid simple interest at an annual rate of 6%. The total interest I earned was $48
    7·1 answer
  • Use the perfect square trinomial identity to write this expression in factored form:
    15·2 answers
  • Whats the answer thanks!!!!!
    10·1 answer
  • Using the slope​ formula, find the slope of the line through the given points.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!