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Masteriza [31]
3 years ago
13

Twin Primes Conjecture A natural number is called a prime number if it has exactly two factors, 1 and itself. 1 is not a prime n

umber because it has exactly one factor. If a number is not prime it is called composi -List the numbers 1 through 31 and circle the primes. What do you see? -You might notice that some pairs of prime numbers have exactly one composite number between them. Such pairs of prime numbers include 3&5, 11&13, 17&19, 29&31. These pair numbers are called twin primes. -Write your first impression regarding this question: Are there an infinite number of twin primes? Provide a justification for your thinking. -Do a little research on the twin prime conjecture and describe at least one interesting fact ti you find.
Mathematics
1 answer:
strojnjashka [21]3 years ago
5 0

Answer:

See explanation below.

Step-by-step explanation:

The prime numbers are bold:

1  2  3 4  5 6  7  8  9  10  11 12  13  14  15  16  17

18  19  20  21  22  23  24  25  26  27  28  29  30  31

a) We can see that as we go higher, twin primes seem less frequent but even considering that, there is an infinite number of twin primes. If you go high enough you will still eventually find a prime that is separated from the next prime number by just one composite number.

b) I think it's interesting the amount of time that has been devoted to prove this conjecture and the amount of mathematicians who have been involved in this. One of the most interesting facts was that in 2004 a purported proof (by R. F. Arenstorf) of the conjecture was published but a serious error was found on it so the conjecture remains open.

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Tina spends $50.86 at the craft store. She buys 5 yards of fabric at $8.98 per yard and 2 spools of thread. What is the price of
irina1246 [14]
She spends $50.86.
Cost for 1 yard of fabric is $8.98.
So to find the the cost of 5 yards of fabric, multiply $8.98 x 5 = $44.9. Therefore for the 5 yards of fabric she paid $44.9.

To find how much she paid for 2 spools of thread subtract the amount she spent at the craft store and the cost for the 5 yards of fabric.
&50.86 - $44.9 = $5.96.
Therefore the cost of 2 spool of thread is $5.96 / 2 = $2.98

Therefore the cost of 1 spool of thread is $2.98.



To check if it’s correct just add the cost of the 5 yards of fabric and the 2 spools of thread.
$44.9 + $5.96 = $50.86
4 0
2 years ago
Which of these has the same answer as the problem in the box? [3 + 4 +5]
Dvinal [7]

Answer:

C

Step-by-step explanation:

7+5 makes 12 which is the same as 3+4+5 which is 12

5 0
3 years ago
Read 2 more answers
Solve the equation:<br> [3 2<br> 5 5]<br><br> [x1<br> x2]+<br> [1<br> 2]=<br> [2<br> -3]
dsp73

9514 1404 393

Answer:

  (x1, x2) = (3, -4)

Step-by-step explanation:

As with any 2-step linear equation, subtract the constant, then multiply by the inverse of the coefficient of the variable.

  \left[\begin{array}{cc}3&2\\5&5\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right]+\left[\begin{array}{c}1\\2\end{array}\right]=\left[\begin{array}{c}2\\-3\end{array}\right]\\\\\left[\begin{array}{cc}3&2\\5&5\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}1\\-5\end{array}\right]\\\\\left[\begin{array}{c}x\\y\end{array}\right]=\dfrac{1}{5}\left[\begin{array}{cc}5&-2\\-5&3\end{array}\right]\left[\begin{array}{c}1\\-5\end{array}\right]

Performing the multiplication of the matrix by the vector gives the solution.

  x = ((5)(1) +(-2)(-5))/5 = 15/5 = 3

  y = ((-5)(1) +(3)(-5))/5 = -20/5 = -4

Using your variables, x1, x2, the solution is ...

  (x1, x2) = (3, -4)

7 0
2 years ago
I know how to do it just then one’s a bit confusing
lubasha [3.4K]

Answer:

208 ft^3

Step-by-step explanation:

Let the plane through the 4 ft X 4ft square at the top of the figure break the figure into 2 boxes, one has dimensions (8-7) by 3 by 4 = 1ft X 3ft X 4ft, and the other has dimensions 7 by 7 by 4 = 7ft X 7ft X 4ft.

They have volumes of (1)(3)(4) = 12 ft^3, and (7)(7)(4) = 196 ft^3, respectively, so the total volume = 12 + 196 = 208 ft^3, the answer.

7 0
2 years ago
Which relationship describes angles 1 and 2?
vaieri [72.5K]

Answer:

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Step-by-step explanation:

5 0
2 years ago
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