Answer: 14,515,200
Note: this is a single number (not an ordered triple or a collection of three different numbers) roughly equal to about 14.5 million if you round to the nearest hundred thousand.
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Explanation:
There are 13 people. Let's call them person A, person B, person C, ... all the way up to person M. The first four people are given who we'll call A through D. The rest (E through M) aren't really important since they aren't named.
A = Monsier Thenardier
B = Madame Thenardier
C = Cosette
D = Marius
Peron's E through M = remaining 9 people
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A and B must stick together. Because of this, we can consider "AB" as one "person".
So we go from 13 people to 13-2+1 = 12 "people".
Likewise, C and D must stick together. We can consider "CD" as one "person". So we go from 12 "people" to 12-2+1 = 11 "people"
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The question is now: how many ways can we arrange these 11 "people" around a circular table? The answer is (n-1)! ways where n = 11 in this case
So, (n-1)! = (11-1)! = 10! = 10*9*8*7*6*5*4*3*2*1 = 3,628,800
We're almost at the answer. We need to do two adjustments.
First off, for any single permutation, there are two ways to arrange "AB". The first is "AB" itself and the second is the reverse of that "BA". So we will multiply 3,628,800 by 2 to get 2*3,628,800 = 7,257,600
Using similar logic for "CD", we double 7,257,600 to get 2*7,257,600 = 14,515,200
The final answer is 14,515,200
I'll use arithmetic series to find it.
First two-digit number divisible by 3 is 12, last such number is 99. Every 3rd number is divisible by 3.
So,
<u>There are 30 such numbers.</u>
Answer: The final answer in proper fraction is 169/9
Step-by-step explanation:
Given the expression
-6 4/9-3 2/9-82/9
Firstly let us convert all mixed fraction to proper fraction to further simplify the expression
-58/9 - 29/9 - 82/9
We now have all terms in proper fraction, we can continue by finding the LCM which is 9
= (- 58-29-82)/9
= 169/9
(x+(x+2)+(x+4)+(x+6))=4x+12=212
x+x+x+x(2+4+6)=4x+12=212
4x (2+4+6)=4x+12=212
4x(6+6)=4x+12=212
12+4x=4x+12=212
<u>-12 -12 -12</u>
4x=4x=200
<u>/4 /4 /4</u>
<u>x=x=50</u>
<u>x=50</u>
Divide the total amount charged by the number of hours worked, and you have $/hour
$168÷14 hours = $12/hour
