题干

经销商经销某种农产品,在一个销售季度内,每售出1t该产品获利润500元,未售出的产品,每1t亏损300元.根据历史资料,得到销售季度内市场需求量的频率分布直方图,如图所示.经销商为下一个销售季度购进了130t该农产品.以X(单位:t,100≤X≤150)表示下一个销售季度内的市场需求量,T(单位:元)表示下一个销售季度内经销该农产品的利润.

(I)将T表示为X的函数;

(II)根据直方图求利润T不少于57 000元的频率;

(Ⅲ)在直方图的需求量分组中,以各组的区间中点值代表该组的各个值 (例如:若需求量X∈[100,110),则取X=105),估计T的平均值.

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答案(点此获取答案解析)

解:(I)由题意得,当X∈100,130)时,

T=500X﹣300(130﹣X)=800X﹣39000,

当X∈130,150时,T=500×130=65000,

∴T= {800X39

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    Four days after Dad's 67th birthday, he had a heart attack. Luckily, he survived. But something inside him had died. His enthusiasm for life was gone. He refused to follow doctor's orders, and his sour attitude made everyone upset when they visited him. Dad was left alone.

    So I asked Dad to come to live with me on my small farm, hoping the fresh air would help him adjust. Within a week after he moved in, I regretted the invitation. He criticized everything I did. I became frustrated. Something had to be done.

    One day I read an article which said when given dogs, depressed patients would be better off. So I drove to the animal shelter that afternoon. As soon as I got there, a pointer's eyes caught my attention. They watched me calmly.

A staff member said: “He got here two weeks ago and we've heard nothing. His time is up tomorrow.”

    I turned to the man in horror. “You mean you're going to kill him”

    “Ma'am,” he said gently. “We don't have room for every unclaimed dog.”

    The police's calm brown eyes awaited my decision. “I'll take him,” I said.

    I drove home with the dog on the front seat beside me. I was helping it out of the car when Dad walked onto the front porch. “Look what I got you!” I said excitedly.

Dad wrinkled his face. “I don't want it,” he muttered, turning back towards the house. Then, suddenly, the dog pulled free from my grasp. He sat down in front of my Dad.

    Dad's anger melted, and soon he was hugging the dog.

    This was the beginning of a warm friendship. Dad named the dog Cheyenne. Together they spent long hours walking down dusty lanes and relaxing on the banks of streams.

    Dad's bitterness faded, and he and Cheyenne went on to make many friends. Then, late one night two years later, I felt Cheyenne's cold nose burrowing (搜寻) through my bed covers. He had never before come into my bedroom at night. I ran into my father's room and found that he had passed away.

    Two days later, my shock and grief deepened when I discovered Cheyenne lying dead beside Dad's bed. As I buried him near their favorite stream, I silently thanked the dog for restoring Dad's peace of mind.