so, what we do is, we multiply the value by a power of 10, that moves the recurring numbers to the left of the dot, in this case we want moved the "15", so we'll need two zeros, so we'll be using 100.
![\bf 0.151515\overline{15}~\hspace{7em}x=0.151515\overline{15} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{array}{|lll|ll} \cline{1-3} &&\\ 100\cdot x&=&15.1515\overline{15}\\ &&15+0.1515\overline{15}\\ &&15+x \\&&\\ \cline{1-3} \end{array}\implies 100x=15+x \\\\\\ 99x=15\implies x=\cfrac{15}{99}\implies \stackrel{simplified}{x=\cfrac{5}{33}}](https://tex.z-dn.net/?f=%5Cbf%200.151515%5Coverline%7B15%7D~%5Chspace%7B7em%7Dx%3D0.151515%5Coverline%7B15%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7B%7Clll%7Cll%7D%20%5Ccline%7B1-3%7D%20%26%26%5C%5C%20100%5Ccdot%20x%26%3D%2615.1515%5Coverline%7B15%7D%5C%5C%20%26%2615%2B0.1515%5Coverline%7B15%7D%5C%5C%20%26%2615%2Bx%20%5C%5C%26%26%5C%5C%20%5Ccline%7B1-3%7D%20%5Cend%7Barray%7D%5Cimplies%20100x%3D15%2Bx%20%5C%5C%5C%5C%5C%5C%2099x%3D15%5Cimplies%20x%3D%5Ccfrac%7B15%7D%7B99%7D%5Cimplies%20%5Cstackrel%7Bsimplified%7D%7Bx%3D%5Ccfrac%7B5%7D%7B33%7D%7D)
First of all, sorry for not including a picture - I hope I can describe this well enough:
Call the centre of the circle O, the chord AB (touching the circumference at A and B) and the midpoint of AB M. From circle theorems, we know that a radius, passing through the midpoint of a chord, will be perpendicular to it. Therefore we have a right-angled triangle OMA, with the hypotenuse OA forming the radius of length 13in, the line OM being 5in as stated in the question, and the side AM being an unknown.
By Pythagoras' theorem, AM = <span>√(13^2 - 5^2) = 12in (it's a 5,12,13 Triple)
Because M is the midpoint of AB, this value needs to be doubled to get the length of AB as 24in. One inch is 2.54cm (3sf), so the length of the chord is:
24 * 2.54 = 60.96cm, which rounds to 61.0cm (3sf)
I hope this helps
</span>
Answer:
Option d: $0
Step-by-step explanation:
Parking penalties arent deductible from expenses, so Andrew cant deduct neither the 250 for his delivery van nor the 75 for the rock concert. Dui tickets definetely arent deductable from expenses, so Andrew cant deduct the 500 from the ticket either. That gives us only 2 options: Andrew can deduct $600 (if he is able to deduct from attoeney's fee), else he cant deduct anything.
However, the attorney's fee shoudn't be deductible, because as a general rule, personal legal fees are not deductible. So the answer is option d, $0
The interest earned in 2 years is:
$15000 x 5.5%= $825
Step-by-step explanation:
s.i= P×T×R/100
=2000×0.25×2/100
= 1000/100
= 10
