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P (top 3 students are chosen)  =  

1  - P ( none of the  top  three are chosen )  =

             C(27,4)

1 -        ________   =       

              C(30,4)

         130

1 -    ____  =        [ 203 - 130 ] / 203   =     73/203

         203

f(0)  =  we are just  replacing  x with  0  =     sqrt (0)  / (0 + 1)  =  0/1   =  0

f(2) =   sqrt (2) /(2 + 1)  =  sqrt (2) / 3

f( a + 2) =     sqrt (a+2) / [ (a + 2) + 1  ]  =    sqrt (a + 2)  / ( a + 3)

Domain

We have two things to consider  .....in the  numerator, x   cannot  be   <   0

In the denominator,  x  cannot  = -1   (we would be dividing  by  0 if it were )

So  we need to take the most restrictive  domain.....this is   [ 0 , infinity )

Avg  rate of  change be between 2  and 10

f(10)   =sqrt (10) /(10 + 1)  =  sqrt (10)/ 11

f(2)   =sqrt  ( 2) / (2 + 1)  = sqrt (2) / 3

Avg rate of change =   

f(10) - f(2)                sqrt (10) /11   +  sqrt (2)/3

_________  =        ______________________  ≈  .0949

   10    - 2                               8

To determine  a decimal value  of a fraction   a/b.....

a/b = 5/32  = 

          .15625

32 [  50

        32

      ____

        180

        160

       _____

           200

           192

          _____ 

                80

                64

               ___

                160

                160

               _____

Try the rest for yourself.....you can double-check your answers with the  onsite calculator

thank you so much i remember you because back when I was in 6th grade you use to help me in my math 

it is dollar+dollar(x=x)x?2*23)-dg=34)d*u)w-z><9*3+r6/3*6/3

Bill  =  850  + 10%  of 850   =

850  +  850 (.10)  =

850  + 85  =

$935

Just giving answers isn't really helping anyone to undertand how to solve problems !!!

Don't see how this is possible

The center would have to be  (0,0)  since the  foci    are (0, ±10)  = (0,  ±c)

The hyperbola   opens up/down  and has the form

y^2/a^2  - x^2/b^2   =  1

The equation  for the asymptotes  is    y  =   ±(a/b) x

So......c =  the distance  from the center to the foci   =   sqrt  [ a^2 + b^2 ] =  sqrt  [ 3^2 + 4^2] = sqrt [ 25] =  5

So....the foci should be   at  (0,  ±5)

And the vertices  are  (0,  ±3)

And the equation  is

y^2/ 3^2    - x^2/4^2    =1     →   y^2/9  - x^2/16   =  1

Here's a graph :  https://www.desmos.com/calculator/ciaausrfvm

Force norml to the floor    97 kg * 9.81 m/s^2      951.57  N 

friction force_s = 698

698 = u_s 951.57                     u_s = .733

526 = u_k 951.57                     u_k = .552

=

(a) - Common ratio, r ==3/15 == 1 / 5

(b) The formula for the nth term of the sequence is: a(n) =3 * 5^(2 - n)

(c) Find the 10th term of the sequence. Use the above formula in (b)

a(10) =3 * 5^(2 - 10) =3 x 5^(-8) =3 *  1/390,625 =3 /390,625 - this is the 10th term

Simplify the following:
abs((7 i)/6 - 4)

Put each term in (7 i)/6 - 4 over the common denominator 6: (7 i)/6 - 4 = (7 i)/6 - 24/6:
abs((7 i)/6 - 24/6)

(7 i)/6 - 24/6 = (7 i - 24)/6:
abs((7 i - 24)/6)

abs(1/6 (7 i - 24)) = abs(7 i - 24)/6:
abs(7 i - 24)/6

abs(7 i - 24) = sqrt(Re(7 i - 24)^2 + Im(7 i - 24)^2) = sqrt((-24)^2 + 7^2):
(sqrt((-24)^2 + 7^2))/6
(sqrt(576 + 7^2))/6

=25/6

1. \(\frac{5}{32}=0.15625\)

2. \(6 \frac{1}{16}=\frac{97}{16}=6.0625\)

3. \(8 \frac{21}{40}=\frac{341}{40}=8.525\)

4. \(8 \frac{43}{80}=\frac{1003}{80}=12.5375\)

5. \(9 \frac{9}{32}=\frac{297}{32}=9.28125\)

5/32   means    5 ÷ 32  

    use the calculator to find   this equals    . 15625

I think you can do the others now .....

Not sure if this helps.

0^1=0

0^2=0

0^3=0

1^2=1

1^3=1

2^3=8

0+0+0+1+1+8=10

whoah

If   2x - x^2 is negative , the result would be an imaginary number

so     2x-x^2 >= 0

         x(2-x) >= 0     for this to be true ....both must be >= 0

          x >= 0    and    2-x >=0

                                   2 >= x

0<= x <= 2

The recursion f(2n + 1) = f(n) + 1 tells us that f(1), f(2), f(3), ... satisfies an arithmetic progression with common difference 2.  The terms f(1) = 1 and f(15) are separated by 14 terms, so f(15) = 2*14 + 1 = 29.

55n mod 260 =165, solve for n

The largest 3-digit integer that satisfies the congruence is:

n =260 *3 + 211 ==991

rate * time = distance     (and the distance each way is equal)

50 m/hr * x  =  70 m/hr ( 24/5 -x)                      24/5 is 4 4/5       x is amount of time at 50m/hr

50x = 336-70x

120x = 336

x = 2.8 hrs at 50 m/r                   50 m/hr * 2.8 hr = 140 miles  

Good job but it is supposed to only be 8/7 because x is bigger than 0 so it can not be -5/3.

Solve for x:
-21 x^2 - 11 x + 40 = 0

The left hand side factors into a product with three terms:
-(3 x + 5) (7 x - 8) = 0

Multiply both sides by -1:
(3 x + 5) (7 x - 8) = 0

Split into two equations:
3 x + 5 = 0 or 7 x - 8 = 0

Subtract 5 from both sides:
3 x = -5 or 7 x - 8 = 0

Divide both sides by 3:
x = -5/3 or 7 x - 8 = 0

Add 8 to both sides:
x = -5/3 or 7 x = 8

Divide both sides by 7:
 
x = -5/3        or          x = 8/7

 41x + 53y = 18

x = 25,    y = - 19

25 mod 53 = 25

Note: There are an infinite number of solutions for x and y. They should have specified the pair, such as: the "smallest pair", which is what I used. There is also a solution where x =- 28 and y = 22, in which case:

-28 mod 53 = - 28

53 + (-28) ==25.  In either case , the answer appears to be 25.