All Answers 352567 Answers

First we try to find the number of 3 digit numbers.

100-999 that is 900 three digit numbers.

You do not need the divisibility rule.

In these problems justs divide 900 by 11, and you will get 81.81818181818181...

round

82

then

So your answer is 82/900 -> 41/450

The area =  L x W   =  9

(x + 2) * ( 2x + 3)  = 9  simplify

2x^2 + 4x + 3x + 6 = 9

2x^2 + 7x - 3  = 0     

Using the quadratic formula to  find both solutions

[ - 7  ± √ [ 7^2 - 4(2)(-3) ] ]               -7  ± √[ 73]

_____________________  =    ______________     take the positive solution  ⇒ x ≈ .386 ft

             2 (2)                                          2(2)

So   the dimensions are =   (.386 + 2)  = 2.386 ft    x  (2(.386) + 3) = 3.772 ft

The perimeter =   2 [ 2.386 + 3.772 ]  ≈  12.316 ft

\(A x = 2x\\ A^7x = A^6(Ax) =\\ A^6 (2x) = \\ 2 A^5(Ax) = 4 A^5 x\\ \text{etc. See if you can finish}\)

It says its wrong i dont know why

That was much simpler than what I was thinking

1.  7^(-1) (mod 13). Multiply both sides by two, such that when the result is divisible by thirteen the remainder is one. Thus, the answer is 2.3

2. We have 8^(-1) (mod 35), or 8*k is congruent to 1 (mod 35), and 8*22 is 176, which s 1 (mod 35), so 22 is the answer,

3. 3^(-1) (mod 100)m or 3*k is congruent to 1 (mod 100). Can you find the answer? Give it a try. 

Yes thank you, Melody, I never thought that my answer could be negative. I am lucky that the problem only had one answer.

Next time in these problems, I will make sure there are no negative answers

%%time a = 7 m =13 def modInverse(a, m) : a = a % m for x in range(1, m) : if ((a * x) % m == 1) : return x print("The MMI = ", modInverse(a, m)):

1 - 7^(-1) mod 13 = 2
2 - 8^(-1) mod 35 = 22
3 - 3^(-1) mod 100= 67
4 - 15^(-1) mod 18= None [15 is not invertible modulo 18]
5 - 42^(-1) mod 43= 42

I know that is right Alan and I think CalculatorUser does too, he wanted to do it without the calc I think.

BUT I just wanted him/her to think about wether there could be a negative answer.

I know the answer to this, I just want to be sure that CalculatorUser has thought about it too.  

n⁷² < 5⁹⁶ < (n+1)⁷²  

n < 5^96/72 < n+1

n < 5^4/3 < n+1

n < 8.55 < n+1

n = 8

In these problems, I always try to match it to the form y=kx.

You can do this by isolating k

n choose k is NOT divisible by some prime number p if and only if:

\(\{\frac{k}{p^i}\} \leq \{\frac{n}{p^i}\} \) ({x} is the fractional part of x) for all \(i\in\mathbb{N}\) 

In other words, if the representation of n in base p is a_ma_m-1....a₀ and the representation of k in base p is b_mb_m-1....b₀ then n choose k is NOT divisible by p if and only if \(\forall 0\leq i \leq m\enspace b_i \leq a_i\)

conclusion: if the representation in base p of n is a_ma_m-1....a₀ then there are exactly \(\prod_{i=0}^{m} (a_i+1)\) values of k between 0 and n such that n choose k is NOT divisible by p

This is not a statistics calculator.

There are some really good specialised calculators available for statistics.

Here is one.

I just googles, pvalue calculator.

Thanks Chris   

I am not saying that your answer is wrong CalculatorUser  BUT did you consider the possibility that n could be negative?

18y  = 2x       divide both sides by 18

y  = (2/18) x

y = (1/9) x 

So   k = 1/9

First....there is no "set" way of doing this.....using EP's  idea we have 

-2x + 2y - 6z  = -12

2x -  2y + 5z  = 9          add these  and we get

-z  = -3

z = 3

Now using the first equation we have that 

x - y +  3(3) = 6

x - y + 9  = 6        subtract 9 from both sides

x - y  = -3    

So now we have two equations to work with

x - y  = - 3     multiply through by - 1   ⇒   -x + y  = 3      (4)

x - 2y  = 5       (5)

Add  (4)  and (5)  and we have that

-y = 8   ⇒    y  = - 8

And using (4) to find x   -x + (-8) = 3       add 8 to both sides

-x = 11

x = -11

So

{x, y, z}  = { -11, -8, 3 }

These take some real practice, GM.......also......easy to make mistakes.....be careful !!!

27 out of 60 ....    27/60 x 100% =

532 oout of 580     is   .....

START this way:

Multiply FIRST equation by  -2

   then add to equation 3 

      this will allow you to solve for z...........continue on your own and see if you can find x and y

I'm not well-versed on this, either, GM.....but I believe the Sample Proportion  for 1(a)  is  just

837 / 1150  ≈  . 7278  =   72.8%

You should be able to do the other two, based on this....

I agree with Melody

Let  m and n be the other two roots

This would   imply that    r^2 * m * n  =  18  ⇒   m * n  = 18 / r^2

Using the Rational Zeroes Theorem, the divisors of 18  are

± [ 1,2, 3, 6, 9 , 18 ]

If we have integer coefficients, then m and n must be integers themselves....and their product must also be an integer

But  this can only be true if   r = ±1  or  r = ±3

I couldn't find any way to do randint on this site.

Well.....   there's one sure way to know......

5^96 > 8^72  ????  True

5^96 < (9)^72 ???? True

Looks like your solution is just fine, CU!!!

Very ingenious !!!!