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How come CPhill answers every question!!!

15?   59 ?  92?

Added together equals 166

1. Let f(x) = x^4-3x^2 + 2 and g(x) = 2x^4 - 6x^2 + 2x -1. Let a be a constant. What is the largest possible
degree of f(x) + a * g(x)?

As long as "a" isn't  -1/2,  the largest possible degree for f(x) + a* g(x)  is the fourth degree

2. Let f(x) = x^4-3x^2 + 2 and g(x) = 2x^4 - 6x^2 + 2x -1. Let b be a constant. What is the smallest possible degree of the polynomial f(x) + b * g(x)?

If "b" = -1/2, then the smallest possible degree for f(x) + b* g(x)  is one

3. Suppose f is a polynomial such that f(0) = 47, f(1) = 32, f(2) = -13, and f(3)=16. What is the sum of the coefficients of f?

If f(0) = 47 .....then the constant term of the polynomial must be 47

And if  f(1)  = 32....this will equal the sum of all the coeficients.....and the sum of the  coefficients on the non-constant terms  of the polynomial  must be - 15 because   -15 + 47  = 32

HAHAHAHA!!!!!....I'd forgotten that one........the forum used to be a bit more " lively, "  didn't it???

If you divide by 5, the remainder is 1

If you divide by 4, the remainder is 3

If you divide by 3, the remainder is 1

The second condition means that our integers are odd

And,by the first condition, the possibilites are

11, 21, 31, 41, 51, 61, 71, 81, 91

And by the third condition, 31 and 91 are the two integers

And the sum of these =  122

The two integers are: 31 and 91.

31 + 91 =122

1. Solve the congruence   \(3n \equiv 2 \pmod{11}\)        , 

as a residue modulo 11. (Give an answer between 0 and 10.)

3*1=3 = 3mod11

3*2=6 = 6mod11

3*3=9 = 9mod11

3*4=12 = 1mod11

3*5=15 = 4mod11

3*6=18= 7mod11

3*7=21 = 10mod11

3*8=24 = 2mod11         The answer is 8

3*9=27 = 5mod11

3*10=30 = 8mod11

3*11=33 = 0mod11

3*12=36 = 3mod11       Patteren starts repeating here     8+11t   is the more general answer

3*13=39 = 6mod11

3*14=42 = 9mod11

It might have been quicker just to say     3*-3=-9=2(mod 11)     so the general solutions is -3+11t 

-3+11=  8

I'm just getting confused on what will I use a formula on that probability. 

I get a little different result from Max, but since I'm not great at probability, maybe mine is more of an "educated" guess.....

If  we have picked a blue or yellow card on the first draw, then the chances of selecting a blue or yellow card on the second draw = 34/44

Then....the chances of NOT selecting a blue or yellow card on the second draw = the probability of selecting a red card on the second draw =  1 - 34/44 =  10/44  = 5/22

Can someone else check this ?????

Order of operations is 

parenthesis

exponents

multiplication and division 

addition and subtraction

You would do the exponent before the multiplication, so -3^2 = 9, and then 2*9 = 18.

Using order of operations:

14-3(2x+3)=2 --->  expand -3(2x+3) to get

14-6x-9 = 2    --->  combine 14-9 to get

5-6x = 2         --->  subtract 5 from both sides to get

-6x = -3          --->  divide both sides by -6 to get

x  = 1/2          

Hi Max,

It was Xin Hu that was being asked - by a different anon   :)

Nauseated was our pet troll for a long time.  He lived under out toll bridge but I think the great flood of  May '16  sent him hurling down the river never to be seen again - not yet anyway.... :(

GingerAle was Nauseated's apprentice - she still shows her colours occasionally.   :)

A group of N students, where N < 50, is on a field trip. If their teacher puts them in groups of 8, the last group has 5 students. If their teacher instead puts them in groups of 6, the last group has 3 students. What is the sum of all possible values of N?

We have this system

N = 8m + 5

N = 6n + 3      subtracting the second equation from the first gives

8m - 6n  + 2  = 0  → 8m = 6n - 2

The possible solutions for m. n  are

{ 2, 3} and {5, 7}

So.....N = 21   or N = 45

And the sum of all possible values of N  =  21 + 45  = 66

14-3(2x+3)=3

1. 5(x + 5) = 5x+25

2. 4(b - 4) = 4b-16

3. -2(x - 1) = -2x+2

4. -3(a - b) = -3a+3b

5.(1 + y)(-1) = -1-y

6. -(-a - 1) = a+1

Copy and paste this into Wolfram/Alpha and see if their answer makes sense to you.

3^(1/3)^(3^(1/3)^(3^(1/3)^3^(1/3)))

Yes I thought that might be the case.  :)

I did look at breaking up 348989 into its prime factors but it is a prime number already so that didn't help.

I am relatively new at modular arithemtic too.  I don't think I had ever done any of it before they started appearing on this site.  So no I don't have any great ideas either.

P(picking a red card after picking a yellow card or blue card)

= 7/9 x 5/22

= \(\dfrac{35}{198}\)

Ooh this is not quite possible actually...... I thought this probability would be large! :D

I have just seen this! :D

I guess I couldn't have done this but I am going to try to explain next time :D

6 divided by 1/3

Thanks Chris,    (I had wanted Max to answer but never mind )

Here is the answer I had in mind.

6 divided by 2 =3

this is because there are  3 groups of 2 in 6       2+2+2=6

1 divided by 1/3    is   3   because there are  3 thirds in 1 whole      1/3   +   1/3    +   1/3   = 1

so

2 divided by 1/3    is   6   because there are  3 thirds in 1 whole      1/3   +   1/3    +   1/3 + 1/3   +   1/3    +   1/3 = 2

so

2 divided by 1/3    is the same answer as   2 * 3/1 = 6

so

6 divided by  1/3    has the same answer as   6   * 3/1  =  6*3 = 18    

2)Using CPhill's method......

N = 3x + 1 ----(1)

N = 4y + 1 ----(2)

N = 5z + 4 ----(3)

(1) x 2 - (2) - (3)

6x + 2 - (4y + 1) - (5z + 4) = 0

6x + 2 - 4y - 1 - 5z - 4 = 0

6x - 4y - 5z = 3

Smallest integer solutions are: x = 16, y = 12, z = 9

N = 3(16) + 1 = 49

Final answer:49!!