Expressed a proper fraction in its simplest form, 0.79 is equal to 79/100, or this seventy-nine hundredths
Answer:
56
Step-by-step explanation:
If there can be only one 1 and only one 2, the remaining digits must all be 0. The digits 1 and 2 can be anywhere in the 8 digits, and can be in either order.
There are 8 possible locations in the sequence for the 1, then 7 possible locations for the 2. The total number of possibilities is 8·7 = 56.
12000000, 21000000, 10200000, 20100000, ..., 00000012, 00000021.
Answer is 7
Work
4C-8= 20
+8
4C=28
28/4=7
T= total cost= $3.30
c= cost of fruit per pound
x= # of pounds of fruit purchased
EQUATION
T= (c)(x) - $0.55 coupon
to find c, substitute $3.30 total for T
$3.30= cx - $0.55
add $0.55 to both sides
$3.85= cx
divide both sides by x
$3.85/x= c
Hope this helps! :)
Note that

,

,

, and so on. The function

is continuous and increasing for all

, so when

, we have

; when

,

; and so on.
This means

which means we can capture the number of digits of

with the function

.
So the problem is the same as finding positive integer solutions to

We know that

has one digit, so clearly this must be a solution. We need to show that this is the only solution.
Recall that
![\dfrac{\mathrm d}{\mathrm dx}[\log_{10}x+1]=\dfrac1{\ln10\,x}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5B%5Clog_%7B10%7Dx%2B1%5D%3D%5Cdfrac1%7B%5Cln10%5C%2Cx%7D)
, while
![\dfrac{\mathrm d}{\mathrm dx}[x]=1](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Bx%5D%3D1)
. This means

increases at a much slower rate than

as

. We know the two functions intersect when

. Therefore it's clear that

for all

.
Now, it's always the case that

, so we're essentially done:

which means there are no other solutions than

.