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I'm not.....there are many here better than me...!!!

Some questions...I just take a guess at......sometimes I'm correct....sometimes I'm not.....

I think this might be correct

The number of  pairings  (nights) will  be  C(10, 2)  = 45

Each meerkat  will  pair with the other 9 one time

So.....each meerkat will stand guard  9 nights and sleep 36 nights

The sum of the elements in the nth row of Pascal's triangle  is just  2^n

So....

log 2^n  =  n*log(2)

So   f(n) =  n*log (2)

And    f(n) / log 2    =   n*log (2)  / log(2)     =    n

 f(x)=3x^2+5 and g(x)=x−2

(f * g) (x)  =

3x^2 ( x - 2) + 5(x - 2)

3x^3 - 6x^2 + 5x - 10

f(x)=2x^2−5x−3 and g(x)=2x^2+x

(f * g) (x)  =

2x^2(2x^2 + x)  - 5x(2x^2 + x)  -3(2x^2 + x)

4x^2 + 2x^3  - 5x^3 - 5x^2 - 6x^2 - 3x

-3x^3  - 7x^2 - 3x

your the man, phill! thank you!

(p * c)  =

(120 -2x) (50 + 5x)

So

(p * c) (2)  =

(120 - 2*2) (50 + 5*2)  =

(116) (60)  = 

$6960

The last option is correct

 f(x)=3x^2+4x and g(x)=2x^2−x+1

(f + g)x  =

[  3x^2+4x ] +   [ 2x^2−x+1 ]     =

5x^2 + 3x + 1

If  f (2)  = 5

Then   this implies that :

f^-1 (5)  = 2   ...so....

2f^-1 (5) + 1   =   f^-1 (5 + 4)

2*2 + 1 =  f^-1 ( 5 + 4)

5 = f^-1 (9)  

2f^-1(9) + 1 =  f^-1(9 + 4)

2*5 + 1  = f^-1(13)

11 =  f^-1 (13)

2 f^-1 (13) + 1    =  f^-1(13 + 4)

2  * 11 + 1  =  f^-1 (17)

23 = f^-1(17)

8t^2 ≤ 3 - 10t     rearrange as

8t^2 + 10t - 3 ≤ 0    factor

This graph may help :

https://www.desmos.com/calculator/tmxfctalnk

The values that make this true  are   t  =   [ -1.5, 0.25 ]

helpppppppppppp

Thank you

It must be  1

That's pretty short ....!!!

Volume of a cone  =

3.14 * (diameter/2)^2 * height

________________________  =

            3

3.14 * ( 3/2)^2 * (6)

________________    =

             3

3.14 * 2 * (9/4)  ≈      14.13   in^3

B

A

B

A

XZ / YZ  = DF / EF

15 / 10  =  DF  / 8

3 / 2  =  DF / 8       multiply both sides by 8

8 * 3 / 2   =  DF

24 /2   =  DF

12  = DF

3 + 8  + 13 + 18

The 19th term is given by

3 + 5(19-1)  =  3 + 5(18)  =  93

And the sum is given by

[ 93 + 3]  (19/2) =

96/2  * 19 =

48 * 19  = 

912

The second isn't showing up for me

For the third, we have

(n) (n + 1)        where n  =  75

75 * 76   =

5700

Note that the sum of the first n positive integers is

n (n + 1)  / 2

For the first one we have this :

Total Profit  =

1300  + 150 ( 1 + 2 + 3 +....+ 10 + 11) =

1300 + 150 [ 11 (12)] /2 =

1300 + 75 * (132)  =

$11200

The second is easier  

The number of seats  is  given by

(33 + 10) * (n/2)    where n is the number of rows  = 24  and the last row has 33 seats

(43) (24/2)  = 

43 * 12  =

516 seats

Thank you

It is a parabola opening upward.......Manuel

"U -shaped" is probably good enough....

Ha! Great solution!

so what exactly is the answer?

I meant playing away.

Thanks, guest....!!!

You are correct....the width is determined by "a"....so  "U-shaped" might not be  exact

are the events losing and playing at home independed as well, or no?