31² 10° 0≤t≤1000 hrs. A-What is the probability of failure within the 100-hour period? b- Find the average vacation time c- Find the determined age when the reliability is 0.99.
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- For which values of a does fo00 eax dx converge?The number N(t) of supermarkets throughout the country that are using a computerized checkout system is described by the initial-value problem, dN/dt=N(1-0.0005N), N(0)=1. How many supermarkets are expected to adopt the new technology when t = 10?Let F(s) = 1.1s + 0.05s2 be the stopping distance as in Example 3. Calculate F(65) and estimate the increase in stopping distance if speed is increased from 65 to 66 mph. Compare your estimate with the actualincrease.
- Can you find the amount of salt A in the tank at any time t?where p(t) is the proportion of the population that knows the rumor at time t and a and k are positive constants. (a) When would half the population have heard the rumor? (b) When is the rate of spread of the rumor greatest?a. At what time t does the cave's salamander population reach its maximum?
- What is the amount of salt in the tank at time t = 0?Consider the function E(x)=x2+6x-5. Compute the average rate of change of E(x) over the interval [a, a+ delta(x)], simplifying as much as possible. What happens to this expression for the average rate of change as x approaches zero?Suppose that when a sense organ receives a stimulus at time t, the total number of action potentials is P(t). If the rate at which action potentials are produced is 7t3+2t2+2, and if there are 0 action potentials when t=0, find the formula for P(t).
- An efficiency study of the morning shift at a factory (7:00 A.M. to 12:00 noon) indicates that an average worker who arrives on the job at 7:00 A.M. will have produced Qunits t hours later, whereQ(t) = -t3 + 9t2 + 15tWhen during the morning shift does the worker’s production reach the point of diminishing returns?Show that an investment that pays out R dollars per year continuously for T years has a PV of R(1 −e−rT )/r.A.) use a right hand sum with three rectangles to estimate the net change in population between t=1 and t=7 B.) how would you visualize the exact net change in population between t=1 and t=7? C.) was the population larger at time t=1 or time t=7? How do you know?