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Yes that is right.

Thanks Alan, 

Alan's method is obviously the best way to so this problem.

Well if you know how to do it on the calculator and you wanted to know how to do it by hand you should have stated that in your question and not wasted people's time.

You should also have given the calculator answer so that people could easily see if their answer was correct.

Let's have a look at it again.

The first term is 1, you should automatically know that

The second term is 13 you should know that too.

You can work the rest out by hand but it is messy.

there are 14 terms in the entire Pascal triangle row.

You have half the row and it is symmetrical

If the sum of the entire row is 2^13 as you say (I did not know that - You could/should have mentioned this in your original question.

Then the sum of your terms is half that = 2^12

If I had read your last response properly I would know that you already worked this out. 

I wasted my own time it was not your fault this time.

Isn't it great when you work things out for yourself !

Good work!

h = hot dogs            money from hot dogs   =   $1.50 h

87 - h = sodas         money from sodas       =   $ .5 (87-h)        add money amount to total 78.50

1.50 h       +    .5 (87-h)       =  78.50      solve for 'h' the number of hot dogs   then sodas =  87-h

180 m / 5 hr   =   B - C       or    180 = 5B - 5C

260 m/  5 hr   =   B + C      or    260 = 5B + 5C

Add the two red equations to solve for  'B'  ..... you should be able to solve for 'C'   from there.....   

x = adult tix                 13x     =        money from adult tix

238 - x = child tix         4 ( 238-x)  = money from child tix        add money amounts together to equal  $ 1330

13x    +    4 (238-x) = `1330      solve for 'x' , the number of adults, then number of child =   238-x

x +2 = 2x     and    x+2 = -2x

2= x             and    2= -3x       x = -2/3

Square both sides: (x + 2)^2 = 4x^2 => x^2 + 4x + 4 = 4x^2 => 3x^2 - 4x - 4 = (3x + 2)(x - 2) = 0.  Solutions are x = -3/2, x = 2.

(a) I'm getting a_5 = 1*5 + 2*4 + 4*3 + 8*2 + 16*1 = 57.

The distance is 3/2.

There are 8*6 ways of seating A and B, then 6! ways of seating the other 6 people, so the answer is 8*6*6! = 34560.

33,700 =19,000 x 1.045^N, solve for N

33,700 / 19,000 =1.045^N

1.7736842 = 1.045^N

N = Log(1.7736842) / Log(1.045)

N =~13.0 years

there aren't any. 

Let x be the number of adult tickets, and let y be the number of children's tickets.  You can then write down the equations, and solve.

Because of the tangency, arc AS = 39 + 116/2 = 97 degrees.

The number of possible sequences is C(9,7) + C(9,8) + C(9,9) = 72 + 9 + 1 = 82.

20% of $15 is \(\frac{1}{5} \cdot 15 = $3\) tip. 15%= \(\frac{3}{20}\). \(\frac{3}{20} x = 3\Rightarrow \frac{1}{20} x = 1\Rightarrow x=20\)

Liam's dinner cost $20.

-MPS101

Set the other cyclist's speed as x miles per hour. Therefore the slower cyclist's speed is x-8. Their total distance apart each hour is x+x-8=2x-8. Therefore after 4 hours, their speed is 4(2x-8) which is 8x-32. We can set an equation: \(8x-32=144\) since they are 144 miles apart after 4 hours. We add 32 to both sides and divide by 8 into both sides, and we get x= 22mph for the faster bicyclist and 22-8=14 mph for the slower bicyclist.

Answer:

22 mph for faster bicyclist

14 mph for slower bicyclist

-MPS101

P.S. That speed is FAST! I mean, 22mph? How tiring would that be for FOUR hours! 

12 inches = 1 foot

4  is   to   1      as      x   is to  118

4/1   =  x/118

x = 472 ft                 (THAT is a really tall cell tower!)

10 c / 1 L     x    7 L / 10 v   =  70 c / 10 v   = 7 c / 1 v

7 c / 1 v     * 50 v   = 350 cars 

4 pi r^2   is the surface area of a sphere

r = 10                                                             this is all given

1/2   of a sphere would be   2 pi r^2

2 pi (10)^2

= 200 pi                 done

.4 h  *  7 m/h   +  .8 h  *  x  m/h

_________________________

       .4  +  .8      hr                                       = 5 m/h

2.8  + .8x   = (1.2) 5

.8x = 3.2

x= 4 m/hr

Need picture.