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Let me add something to Alan's answer.....

Note that  -1/24000 is very close to 0

And e^0  = 1

So

e^(-1/24000)  should be close to 1  ..   !!!   (and, as Alan showed...it is  !!!)

15 / 17 = 0.8823529411764706

e is the number

$${\mathtt{e}} = {\mathtt{2.718\: \!281\: \!828\: \!459\: \!045\: \!2}}$$ ... except that it goes on forever.

If you raise this number to the power of -1/24000 you get:

$${{\mathtt{e}}}^{{\mathtt{\,-\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{24\,000}}}}\right)} = {\mathtt{0.999\: \!958\: \!334\: \!201\: \!376\: \!8}}$$ ... which also goes on forever!

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This isn't as dark and deep as you might think....!!!

6 mod 3   just means ... "What is the remainder when we divide 6 by 3??"

The answer   ..    0   !!!

See???.... not too mysterious, is it???

Here's another approach....find the circle's center as Alan did  = (5,11)

And the distance from a line to a point not on that line is given by

d = abs ( Ax + By + C) / √(A² + B²)       where (x,y) is the given point and Ax + By + C = 0 is the equation of the line.....so we have....

d = abs (12(5) + 5(11) + 54 ) / √(12² + 5²) = abs(169) / 13 = 13

Here's the graph ...

Very nice, Alan....!!!

I really like that one....a definite "Daily Wrap" candidate

The average speed will be 355/7.5 miles per hour

Let N be the number of weeks that she will need to save

125 + 15N = 245    subtract 125 from both sides

15N  = 120      divide both sides by 15

N = 8 weeks

Let N be the number of passes....so we have

7 + 1.50N = 29.50    subtract 7  from both sides

1.50N = 22.50         divide both sides by 1.50

N = 15 passes

Let S be the number of years in a score....so we have

1963 - 1863 = 5S    simplify

100 = 5S       divide both sides by 5

20 = S     ...  thus, there are 20 years in a score

And   60 / 20  = 3 score

It's just 1 followed by 23 zeroes

-(x - 1) = 5   simplify

-x + 1  = 5    subtract 1 from both sides

-x = 4           which implies that x = -4

Therefore   -4x =  -4(-4) = 16

known E = m.c^2, if m=0.0024 and c=0.2*10^-5, so the value of E is ?

$$\small{\text{$\boxed{E = m c^2}$}}$$

$$\small{\text{$m= 0.0024 = \frac{24}{10000} = \frac{2.4}{1000}= \frac{2.4}{10^3} = 2.4 * 10^{-3} $}}$$

$$\small{\text{$
c= 0.2*10^{-5} = \frac{2}{10}*10^{-5} = \frac{2}{10*10^5}= \frac{2}{10^6} = 2*10^{-6} $
}}$$

$$\small{\text{
$
E=m*c^2 = 2.4*10^{-3} \ * \ (2*10^{-6})^2 =2.4*10^{-3} \ * \ 2^2*(10^{-6})^2
$
}}\\
\small{\text{
$
=2.4*10^{-3} \ * \ 2^2*10^{-12}=2.4*10^{-3} \ * \ 4*10^{-12} = 2.4*4*10^{-3} 10^{-12} = 9.6 * 10^{-3} 10^{-12} $
}}\\
\small{\text{
$
= 9.6 * 10^{-15}
$
}}$$

So we have

√(n - 1) =  ⁸√ n      

Here's the graphical solution to this using x instead of n

LOL!!!!

This is (nbr of ways of arranging 3 people in a group of 3 + nbr of ways of arranging 3 people in a group of 4 + nbr of ways of arranging 3 people in a group of 8)/(nbr of ways of arranging 3 people in a group of 15):

$${\frac{\left({\left({\frac{{\mathtt{3}}{!}}{({\mathtt{3}}{\mathtt{\,-\,}}{\mathtt{3}}){!}}}\right)}{\mathtt{\,\small\textbf+\,}}{\left({\frac{{\mathtt{4}}{!}}{({\mathtt{4}}{\mathtt{\,-\,}}{\mathtt{3}}){!}}}\right)}{\mathtt{\,\small\textbf+\,}}{\left({\frac{{\mathtt{8}}{!}}{({\mathtt{8}}{\mathtt{\,-\,}}{\mathtt{3}}){!}}}\right)}\right)}{{\left({\frac{{\mathtt{15}}{!}}{({\mathtt{15}}{\mathtt{\,-\,}}{\mathtt{3}}){!}}}\right)}}} = {\frac{{\mathtt{61}}}{{\mathtt{455}}}} = {\mathtt{0.134\: \!065\: \!934\: \!065\: \!934\: \!1}}$$

.

helppp the options are

a.9.6 * 10^-15 

helppppppppppp

pi=3.14 or equal to 22/7

Or do you mean  

$$2^{n-1}=8^n$$

in which case, because 8 = 2³

$$2^{n-1} = 2^{3n}$$

so n-1 = 3n 

-1 = 2n

n = -1/2

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