The failure time of an electronic component is represented by random variable x, which is continuous and exponentially distributed with mean 8 years. find the probability density function (pdf) x. derive the probability (cumulative) distribution function of x and use it to find pr(2yrs ≤ x ≤ 4yrs).

Given the points a(-2, 1) and b(8, 6), find the coordinates of the point c on directed line segment ab, that partitions ab in the ration 2: 3.

Answer this two poles, ab and ed, are fixed to the ground with the of ropes ac and ec, as shown: two right triangles abc and edc have a common vertex c. angle abc and edc are right angles. ab is labeled 13 feet, ac is labeled 15 feet, ec is labeled 10 feet, and ed is labeled 4 feet.what is the approximate distance, in feet, between the two poles? 11.14 feet16.65 feet14.35 feet15.59 feet

Use the ratio test to determine whether ∑n=14∞n+2n! converges or diverges. (a) find the ratio of successive terms. write your answer as a fully simplified fraction. for n≥14, limn→∞∣∣∣an+1an∣∣∣=limn→∞.