table of contents recoverability of goodwill is measured at the reporting unit level and begins with a qualitative assessment to determine if it is more likely than not that the fair value of each reporting unit is less than its carrying amount as a basis for determining whether it is necessary to perform the two-step goodwill impairment test prescribed by gaap . for those reporting units where it is required , the first step compares the carrying amount of the reporting unit to its estimated fair value . if the estimated fair value of a reporting unit exceeds its carrying amount , goodwill of the reporting unit is not impaired and the second step of the impairment test is not necessary . to the extent that the carrying value of the reporting unit exceeds its estimated fair value , a second step is performed , wherein the reporting unit's carrying value of goodwill is compared to the implied fair value of goodwill . to the extent that the carrying value exceeds the implied fair value , impairment exists and must be recognized . the calculation of estimated fair value is based on two valuation techniques , a discounted cash flow model ( income approach ) and a market adjusted multiple of earnings and revenues ( market approach ) , with each method being weighted in the calculation . the implied fair value of goodwill is determined in the same manner as the amount of goodwill recognized in a business combination . the estimated fair value of the reporting unit is allocated to all of the assets and liabilities of the reporting unit ( including any unrecognized intangible assets ) as if the reporting unit had been acquired in a business combination and the fair value of the reporting unit , as determined in the first step of the goodwill impairment test , was the price paid to acquire that reporting unit . recoverability of other intangible assets with indefinite useful lives ( i.e . trademarks ) is determined on a relief from royalty methodology ( income approach ) , which is based on the implied royalty paid , at an appropriate discount rate , to license the use of an asset rather than owning the asset . the present value of the after-tax cost savings ( i.e . royalty relief ) indicates the estimated fair value of the asset . any excess of the carrying value over the estimated fair value is recognized as an impairment loss equal to that excess . intangible assets such as patents , customer-related intangible assets and other intangible assets with finite useful lives are amortized on a straight-line basis over their estimated economic lives . the weighted-average useful lives approximate the following: .
what is the difference between the weighted average useful lives of trademarks and patents , in number of years?\\n
recoverability of intangible assets with finite useful lives is assessed in the same manner as property , plant and equipment as described above . income taxes : for purposes of the company 2019s consolidated financial statements for periods prior to the spin-off , income tax expense has been recorded as if the company filed tax returns on a stand-alone basis separate from ingersoll rand . this separate return methodology applies the accounting guidance for income taxes to the stand-alone financial statements as if the company was a stand-alone enterprise for the periods prior to the spin-off . therefore , cash tax payments and items of current and deferred taxes may not be reflective of the company 2019s actual tax balances prior to or subsequent to the spin-off . cash paid for income taxes for the year ended december 31 , 2015 was $ 80.6 million . the income tax accounts reflected in the consolidated balance sheets as of december 31 , 2015 and 2014 include income taxes payable and deferred taxes allocated to the company at the time of the spin-off . the calculation of the company 2019s income taxes involves considerable judgment and the use of both estimates and allocations . deferred tax assets and liabilities are determined based on temporary differences between financial reporting and tax bases of assets and liabilities , applying enacted tax rates expected to be in effect for the year in which the differences are expected to reverse . the company recognizes future tax benefits , such as net operating losses and tax credits , to the extent that realizing these benefits is considered in its judgment to be more likely than not . the company regularly reviews the recoverability of its deferred tax assets considering its historic profitability , projected future taxable income , timing of the reversals of existing temporary differences and the feasibility of its tax planning strategies . where appropriate , the company records a valuation allowance with respect to a future tax benefit . product warranties : standard product warranty accruals are recorded at the time of sale and are estimated based upon product warranty terms and historical experience . the company assesses the adequacy of its liabilities and will make adjustments as necessary based on known or anticipated warranty claims , or as new information becomes available. .