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
vampirchik [111]
3 years ago
5

Consider the following statement: The square of a prime number is not prime. (a) Write this as an if-then statement, using caref

ul mathematical language and notation. (b) Prove or disprove the statement.
Mathematics
1 answer:
Hitman42 [59]3 years ago
7 0

The square of a prime number is not prime.

a) let x ∈ R, If x  ∈ {prime numbers}, then x^{2}∉{prime numbers}

there says that if x is a real and x is in the set of the prime numbers, then the square of x isn't in the set of prime numbers.

b) Prove or disprove the statement.

ok, if x is a prime number, then x only can be divided by himself. Now is easy to see that x^{2} = x*x can be divided by himself and x, then x*x is not a prime number, because can be divided by another number different than himself

You might be interested in
Choose 5 cards from a full deck of 52 cards with 13values (2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A) and 4 kinds(spade, diamond, h
Delvig [45]

Answer:

a) 182 possible ways.

b) 5148 possible ways.

c) 1378 possible ways.

d) 2899 possible ways.

Step-by-step explanation:

The order in which the cards are chosen is not important, which means that we use the combinations formula to solve this question.

Combinations formula:

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

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

In this question, we have that:

There are 52 total cards, of which:

13 are spades.

13 are diamonds.

13 are hearts.

13 are clubs.

(a)Two-pairs: Two pairs plus another card of a different value, for example:

2 pairs of 2 from sets os 13.

1 other card, from a set of 26(whichever two cards were not chosen above). So

T = 2C_{13,2} + C_{26,1} = 2*\frac{13!}{2!11!} + \frac{26!}{1!25!} = 182

So 182 possible ways.

(b)Flush: five cards of the same suit but different values, for example:

4 combinations of 5 from a set of 13(can be all spades, all diamonds, and hearts or all clubs). So

T = 4*C_{13,5} = 4*\frac{13!}{5!8!} = 5148

So 5148 possible ways.

(c)Full house: A three of a kind and a pair, for example:

4 combinations of 3 from a set of 13(three of a kind ,c an be all possible kinds).

3 combinations of 2 from a set of 13(the pair, cant be the kind chosen for the trio, so 3 combinations). So

T = 4*C_{13,3} + 3*C_{13.2} = 4*\frac{13!}{3!10!} + 3*\frac{13!}{2!11!} = 1378

So 1378 possible ways.

(d)Four of a kind: Four cards of the same value, for example:

4 combinations of 4 from a set of 13(four of a kind, can be all spades, all diamonds, and hearts or all clubs).

1 from the remaining 39(do not involve the kind chosen above). So

T = 4*C_{13,4} + C_{39,1} = 4*\frac{13!}{4!9!} + \frac{39!}{1!38!} = 2899

So 2899 possible ways.

4 0
3 years ago
Natalie made blueberry muffins for a bake sale. Each muffin cost her about $0.25 to make. She spent $8.75 to make all of the muf
Scilla [17]

aaaaaaaaaaaaaaaaaaaaaaaaadsfgfdgdfgdfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff

5 0
3 years ago
The zeros of the function f(x)=3x^2-3x-6 are
Mrac [35]
3x^2-3x-6=0\\
3(x^2-x-2)=0\\
x^2-x-2=0
x^2+x-2x-2=0\\
x(x+1)-2(x+1)=0\\
(x-2)(x+1)=0\\
x=2 \vee x=-1

7 0
3 years ago
Someone help me plz:/)
mario62 [17]
Your answer would be the letter B
6 0
3 years ago
Read 2 more answers
The diagram shows a square ABCD with sides of length 20cm. it also shows a semi circle and an arc circle AB is the diameter of t
Brut [27]

Answer:

Area of Shaded Region =50\pi$ cm^2

Area of Semicircle =50\pi$ cm^2

\dfrac{\text{Area of Shaded region}}{\text{Area of Square}}=\dfrac{ \pi}{8}

Step-by-step explanation:

Area of Shaded Region = Area of Sector - Area of Semicircle

<u>Area of Sector</u>

Radius of the sector =20cm

=\frac{90}{360}X\pi *20^2\\ =100\pi cm^2

<u>Area of Semicircle</u>

Since AB is the diameter of the semicircle

Radius of the Semicircle=20/2=10cm

Area of semicircle

=\frac{\pi r^2}{2}\\ =\frac{\pi *10^2}{2}\\=50\pi cm^2

Therefore, area of Shaded Region

=100\pi -50 \pi\\=50\pi$ cm^2

Area of Square =20 X 20 =400 cm^2

\dfrac{\text{Area of Shaded region}}{\text{Area of Square}} \\=\dfrac{50 \pi}{400} \\=\dfrac{ \pi}{8}

4 0
3 years ago
Other questions:
  • The circumference of a circle is 5 π cm. What is the area of the circle?
    6·1 answer
  • Which algebraic expression represents this phase the product of 50 and the number of employees
    7·1 answer
  • Solve the equation 6t-1/6=9
    14·2 answers
  • Need help with 8,9, and 10
    12·1 answer
  • Simplify -4/7 + (-4/3)
    11·1 answer
  • Which statements correctly compare the two​ numbers?
    12·2 answers
  • Write the equation for a line in standard form (Ax+By+C) that is perpendicular to y = 3x -
    8·1 answer
  • 208+8x−718+2x SIMPLIFY PLEASE
    11·2 answers
  • Help please and ty ! (no its not 388)
    8·2 answers
  • Name_<br> Simplify. Your answer should contain only positive exponents.<br> 1) 4².4²
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!