There are 105 comparisons made with 15 statistically independent scenarios.
According to the statement
we have given value of n is 15.
Then r = 2. so,
we use the formula NcR then
Substitute the values in it then
15c2
we open it according to ncr formula
In this formula we arrange the terms according to the following
NcR formula = n! /r! * (n-r)!
then the terms will arrange in this way.
So,
ncr = 15! / 2! * 13!
After solving the statement some terms will be cancel with each other and remaining terms are
ncr = 15*14/2
ncr = 210/2
ncr = 105
here the value becomes 105.
So, There are 105 comparisons made with 15 statistically independent scenarios.
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Let's say the point is C, so C partitions AB into two pieces, where AC is at a ratio of 3 and CB is at a ratio of 7, thus 3:7,
![\bf \left. \qquad \right.\textit{internal division of a line segment} \\\\\\ A(5,10)\qquad B(20,25)\qquad \qquad 3:7 \\\\\\ \cfrac{AC}{CB} = \cfrac{3}{7}\implies \cfrac{A}{B} = \cfrac{3}{7}\implies 7A=3B\implies 7(5,10)=3(20,25)\\\\ -------------------------------\\\\ { C=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}\\\ -------------------------------](https://tex.z-dn.net/?f=%5Cbf%20%5Cleft.%20%5Cqquad%20%20%5Cright.%5Ctextit%7Binternal%20division%20of%20a%20line%20segment%7D%0A%5C%5C%5C%5C%5C%5C%0AA%285%2C10%29%5Cqquad%20B%2820%2C25%29%5Cqquad%0A%5Cqquad%203%3A7%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7BAC%7D%7BCB%7D%20%3D%20%5Ccfrac%7B3%7D%7B7%7D%5Cimplies%20%5Ccfrac%7BA%7D%7BB%7D%20%3D%20%5Ccfrac%7B3%7D%7B7%7D%5Cimplies%207A%3D3B%5Cimplies%207%285%2C10%29%3D3%2820%2C25%29%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A%7B%20C%3D%5Cleft%28%5Ccfrac%7B%5Ctextit%7Bsum%20of%20%22x%22%20values%7D%7D%7B%5Ctextit%7Bsum%20of%20ratios%7D%7D%5Cquad%20%2C%5Cquad%20%5Ccfrac%7B%5Ctextit%7Bsum%20of%20%22y%22%20values%7D%7D%7B%5Ctextit%7Bsum%20of%20ratios%7D%7D%5Cright%29%7D%5C%5C%5C%0A-------------------------------)
Total money=$120
on shirt=$25.65
on socks=$7.98
on a cd=$16.23
on snack=$4.58
so total money left=total money-total money spent
=$120-($25.65+$7.98+$16.23+$4.58)
=$120-$54.44
so total money left=$65.56
Answer:
4.24
Step-by-step explanation:
First, let's set up the equation: ![\frac{2+x^2}{2}=10](https://tex.z-dn.net/?f=%5Cfrac%7B2%2Bx%5E2%7D%7B2%7D%3D10)
Next, clear the fraction by multiplying both sides by 2:![2*(\frac{2+x^2}{2}=10)=2+x^2=20](https://tex.z-dn.net/?f=2%2A%28%5Cfrac%7B2%2Bx%5E2%7D%7B2%7D%3D10%29%3D2%2Bx%5E2%3D20)
Then, subtract 2 from both sides: ![x^2=18](https://tex.z-dn.net/?f=x%5E2%3D18)
Finally, take a square root of both sides and round:
(Rounded to the nearest hundredth) 4.24