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The mass-to-light ratio will be used to determine the mass of the galaxy in question. Further, we need the rotation curves for this galaxy and will need to fit the data with the curves. Now disk rotation curve alone will not fit the data and we will also have to use the halo parameters, which correspond to the dark matter. Fitting the curve to the available data can be easily done by using an online applet (http://burro.astr.cwru.edu/JavaLab/RotcurveWeb/lab_MAIN.html) developed at Case Western Reserve University. It seems that's where you got the question from.
Now, as per enotes policy we can not solve your assignments for you, but give you enough information to get you started on the right path. So that is what I will do and provide you with the relevant information.
Use the applet to fit both the disk rotation and halo parameters to the data and determine the optimal mass-to-light ratio. Use that M/L ratio in conjunction with the luminosity given in the question and calculate the total mass (Matter + Dark Matter). Use the Mass-to-light ratio for disk rotation curve and get the luminous mass and subtract it from the total disk mass to get the estimate of dark matter in the galaxy. Use the luminous mass and dark matter mass to get the desired ratio.
The total mass of the galaxy is calculated as per the link: http://www.enotes.com/homework-help/measuring-out-last-datapoint-what-total-mass-476540#answer-678634
And the model fit for disk rotation will give you the best mass-to-light ratio and you can use that ratio to determine the luminous mass.
Now subtract the luminous mass from the total mass and obtain the dark matter mass.
Hope this helps.
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