Task: Table-QA (source dataset: FinQA)

Task: 
You are given a table containing structured data and a natural language question referring to the table. Your goal is to analyze the table and provide an accurate and concise answer based on the given data.

Instructions:
1. Understand the Table: Examine the structure, headers, and data in the table. Identify relevant columns and rows related to the question.
2. Interpret the Question: Determine whether the question requires direct retrieval, aggregation, comparison, sorting, filtering, or inference.
3. Extract the Answer: Use logical reasoning and numerical operations (if necessary) to derive the correct response from the table.
4. Format the Answer: No explanation, return the answer in a structured JSON format: {"answer": <answer>}. If the question cannot be answered due to missing or ambiguous data, return a JSON response with {"answer": null}.

Table:
| ( $ in millions )                             | 2011     | 2010     | 2009     |
|:----------------------------------------------|:---------|:---------|:---------|
| net sales                                     | $ 8630.9 | $ 7630.0 | $ 6710.4 |
| net earnings attributable to ball corporation | 444.0    | 468.0    | 387.9    |

Question:
the contracted backlog at december 31 , 2011 contained how much in million dollars for fixed price contracts?


pre_text: begin production in early 2012 .
the output from the first line has been contracted for sale under a long-term agreement .
additionally , in march 2011 we entered into a joint venture agreement with thai beverage can limited to construct a beverage container manufacturing facility in vietnam that will begin production in the first quarter of 2012 .
we have also made recent strategic acquisitions .
in october 2011 , we acquired our partners 2019 interests in qmcp and recorded a gain of $ 9.2 million related to our previously held interest in the joint venture .
additionally , we are constructing a new expanded beverage container facility for qmcp that will begin production in the first quarter of 2012 .
in july 2010 , we entered the aluminum slug market by acquiring the leading north american manufacturer of aluminum slugs used to make extruded aerosol containers , beverage bottles , collapsible tubes and technical impact extrusions .
to further expand this new product line and broaden our market development efforts into a new customer base , in january 2011 , we acquired a leading european supplier of aluminum aerosol containers and bottles and the slugs used to make them .
further details of recent acquisitions are included in note 3 to the consolidated financial statements within item 8 of this report .
we recognize sales under long-term contracts in the aerospace and technologies segment using percentage of completion under the cost-to-cost method of accounting .
the 2011 contract mix consisted of approximately 60 percent cost-type contracts , which are billed at our costs plus an agreed upon and/or earned profit component , and 33 percent fixed-price contracts .
the remainder represents time and material contracts , which typically provide for the sale of engineering labor at fixed hourly rates .
the contracted backlog at december 31 , 2011 , of approximately $ 897 million consisted of approximately 50 percent fixed price contracts indicating a continuing trend towards more fixed price business .
throughout the period of contract performance , we regularly reevaluate and , if necessary , revise our estimates of aerospace and technologies total contract revenue , total contract cost and progress toward completion .
because of contract payment schedules , limitations on funding and other contract terms , our sales and accounts receivable for this segment include amounts that have been earned but not yet billed .
management performance measures management uses various measures to evaluate company performance such as return on average invested capital ( net operating earnings after tax over the relevant performance period divided by average invested capital over the same period ) ; economic value added ( net operating earnings after tax less a capital charge on average invested capital employed ) ; earnings before interest and taxes ( ebit ) ; earnings before interest , taxes , depreciation and amortization ( ebitda ) ; diluted earnings per share ; cash flow from operating activities and free cash flow ( generally defined by the company as cash flow from operating activities less additions to property , plant and equipment ) .
these financial measures may be adjusted at times for items that affect comparability between periods such as business consolidation costs and gains or losses on acquisitions and dispositions .
nonfinancial measures in the packaging businesses include production efficiency and spoilage rates ; quality control figures ; environmental , health and safety statistics ; production and sales volumes ; asset utilization rates ; and measures of sustainability .
additional measures used to evaluate financial performance in the aerospace and technologies segment include contract revenue realization , award and incentive fees realized , proposal win rates and backlog ( including awarded , contracted and funded backlog ) .
results of operations consolidated sales and earnings .
post_text: the increase in net sales in 2011 compared to 2010 was driven largely by the increase in demand for metal packaging in the prc , improved beverage container volumes in the americas , the consolidation of latapack-ball , the acquisition of two prc joint ventures and the extruded aluminum businesses , and improved aerospace program performance .
in addition to the business segment performance analyzed below , net earnings attributable to ball corporation included discontinued operations related to the sale of the plastics business in august 2010 , business consolidation costs , debt refinancing costs , and the equity earnings and gains on the acquisitions .
these items are detailed in the 201cmanagement performance measures 201d section below .
higher sales in 2010 compared to 2009 were due largely to sales associated with 2010 business acquisitions described above .
the higher net earnings from continuing operations in 2010 compared to 2009 included $ 105.9 million of equity gains on acquisitions associated with the acquisitions. .
label: 448.5
qa: answer: 448.5
ann_text_rows: 12
steps: op: divide1-1
arg1: 50
arg2: const_100
res: .5
op: multiply1-2
arg1: 897
arg2: #0
res: 448.5
program: divide(50, const_100), multiply(897, #0)
gold_inds: text_12: the contracted backlog at december 31 , 2011 , of approximately $ 897 million consisted of approximately 50 percent fixed price contracts indicating a continuing trend towards more fixed price business .
exe_ans: 448.5
tfidftopn: text_10: the 2011 contract mix consisted of approximately 60 percent cost-type contracts , which are billed at our costs plus an agreed upon and/or earned profit component , and 33 percent fixed-price contracts .
text_18: additional measures used to evaluate financial performance in the aerospace and technologies segment include contract revenue realization , award and incentive fees realized , proposal win rates and backlog ( including awarded , contracted and funded backlog ) .
program_re: multiply(897, divide(50, const_100))
model_input: text_10
the 2011 contract mix consisted of approximately 60 percent cost-type contracts , which are billed at our costs plus an agreed upon and/or earned profit component , and 33 percent fixed-price contracts .
text_11
the remainder represents time and material contracts , which typically provide for the sale of engineering labor at fixed hourly rates .
text_12
the contracted backlog at december 31 , 2011 , of approximately $ 897 million consisted of approximately 50 percent fixed price contracts indicating a continuing trend towards more fixed price business .