The probability density function of the time to failure of an electronic component in a copier (in hours) is f left-parenthesis x right-parenthesis equals StartFraction e Superscript negative x divided by 1054 Baseline Over 1054EndFraction for x greater-than 0. Determine the probability that a) A component lasts more than 3000 hours before failure. (Round the answer to 3 decimal places.)

Acompany manufactures three types of cabinets. it makes 110 cabinets each week. in the first week, the sum of the number of type-1 cabinets and twice the number of type-2 cabinets produced was 10 more than the number of type-3 cabinets produced. the next week, the number of type-1 cabinets produced was three times more than in the first week, no type-2 cabinets were produced, and the number of type-3 cabinets produced was the same as in the previous week.