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3/4*(-8)*2/-9

\(\frac{3}{4}\times (-8) \times \frac{2}{-9}\) = \(\frac{-2\times 2}{-3}=1\frac{1}{3}\)

  !

[( 1,000,000 * 0.0254 ) /102] * 6 sec  =

1494.1176470588235294 sec  / 3600 sec ≈ 0.4150 hr  * 60 min  = 

24.9 min  ≈   25 min

12/3+12/4+12/5..... 12/52  =

     52

12 ∑   (1 / n)   ≈  36.4565

      3

sin(3a)cos(a)-cos(3a)sin(a) = 2sin(a)cos(a)

Use the identity that    (sinAcosB - sinBcosA) = sin (A - B)

sin (3a - a )  =

sin(2a)  =  2sin(a)cos(a)

Let's see how long it would take to fill it completely  ....this is easy....subtract the fractions....take the reciprocal

1/2  - 1/3  = 1/6 ......  take the reciprocal of this =  6 hrs to fill it completely

.....so....

60%  of this = .60 * 6 =   3.6 hrs

Yes....hit the  ' 2nd ' button first....the tan button will become  atan  which is tan^-1

 c pounds / m people   = c/m  pounds per person   if you add n   you must add this amount per n

c/m x n =  n c/m   d would be the answer

acceleration is change in velocity over time   (m/s^2)

4 m/s  /  2.5 s   = 1.6 m/s^2 = her acceleration 

 n(2a + n - 1) / 2  =  100

a=18, n=5

a=9, n=8

never mid got it :P

Since the sum of  a + (a + 1) + (a + 2) + ,,, + (a + n - 1)  =  n(a + (a + n - 1) ) / 2  =  n(2a + n - 1) / 2,

we need  n(2a + n - 1) / 2  =  100

or                   n(2a + n - 1)  =  200      with both  n  and  a  to be whole numbers.

Since  n  must divide  200,  the possible values for  n  are:  4, 5, 8, 10, 20, 25, 40, 50, 100, 200.

If  n = 4:  4(2a + 4 - 1)  =  200     --->   4(2a + 3)  =  200   --->   2a + 3  =  50   --->   impossible

If  n = 5:  5(2a + 5 - 1)  =  200     --->   5(2a + 4)  =  200   --->   2a + 4  =  40   --->   a  =  18

If  n = 8:  8(2a + 8 - 1)  =  200     --->   8(2a + 7)  =  200   --->   2a + 7  =  25   --->   a  =  9

If  n = 10:  10(2a + 10 - 1)  =  200     --->   10(2a + 9)  =  200   --->   2a + 9  =  20   --->   impossible

and, you can check the rest ...

I realize that this isn't an elegant solution, but ...

"Brute force"  method......LOL!!!

No 2 ,3 or 4 consecutive integer combos are possible     

 Five consecutive integers 18 - 22       a = 18, n = 5

Six consecutive integers  = not possible

Seven consecutive integers  = not possible

Eight consecutive integers = 9 - 16     a = 9, n = 8

I think that's all..........

You can multiply each of the preceding terms by either  3  or  -3.

If you use  -3,  you will get:  1/27 , -1/9 , 1/3 , -1 , 3, -9, 27.

( 4/9 ) x ( 5/8 )  =  ( 4 x 5 ) / ( 9 x 8 )  =  20 / 72  =  10 / 36  =  5 / 18

Since  y = 2x  and  y = 4x + 12:

Setting these equal to each other:  y = y   --->   2x  =  4x + 12

                                                                        --->   -2x  =  12

                                                                        --->       x  =  -6

Since  y = 2x:  x = -12

Two lines are parallel if they have the same slope.

The formula for slope is:  ( y₂ - y₁ ) / ( x₂ - x₁ )

The slope for AB is:  ( -3 - 1 ) / ( 2 - x )

The slope for CD is:  ( 5 - 2 ) / ( -3 - -5 )

Setting these slopes equal to each other:  ( -3 - 1 ) / ( 2 - x )  =  ( 5 - 2 ) / ( -3 - -5 )

Simplifying:                                                                  -4 / (2 - x)  =  3 / 2

Cross-multiplying:                                                                     -8  =  6 - 3x

Solving:                                                                                      3x  =  14

                                                                                                       x  =  4 2/3

0.125  =  1/8

1 / 0.125  =  1 / (1/8)  =  1 x (8/1)  =  1 x 8  =  8

(When you are dividing by a fraction, multiply by the multiplicative inverse.)

a = a*r + 36  → a[ 1 - r ]  = 36   →   a = 36 / [ 1 - r ]    (1)

ar^2  = ar^3 + 324    (2)  →     ar^2 [1 - r] = 324   (2)

Sub(1) into (2)

(36 / [ 1 - r ] ) r^2 [1 - r] = 324

36r^2  =  324

r^2   = 9

r = ± 3

And a  = 36/ [ 1 - 3]  =  - 18     or a = 36 / [ 1 - -3 ]  = 36 / 4  = 9

And the two series are

[ a = 9 and r = -3]

9, - 27, 81, -243     and

[ a = -18 and r = 3  ]

-18, - 54 , -162, -486

THX soo much CPhill

9+10=19

10=5+5

9+5=14

14+5=19

t₁  = 4(1) –  1  = 3

t₂  = 4(2) –  1  = 7

t₃  = 4(3) –  1  = 11

t_n+1  = 4(n + 1) –  1  =  4n + 4  –  1  =  4n + 3

t_n+1   – t_{n  =}  [4n + 3] – [ 4(n) –  1]  =  4

–5^2  =  (–1)* 5^2  = ( – 1) * 25  = – 25  ...... but.....

( –5)^2  = (–1)^2 * (5)^2  =  1 * 25  = 25

This  ???

[778.75 - 414.99] / 5  = 72.752

EP's answer is the same.....just rounded.....

($ 778.75 mil  - 414.99 mil)/ 5 yr  = 72.75 million per year

Sorry for the typo in my previous answer

Now....if you know what the answer is, why are you asking questions??????

"At most"  means  "ess than or equal to 6" ....so we have.....

2 + (1 /3) N  ≤  6    where N is the number