## Find the relative uncertainty in the half-life.

1.  The flow rate of water through a cylindrical pipe is given by Q = πr 2v, where r is the radius of the pipe and v is the flow velocity.

a.  Assume that r = 3.00 ± 0.03 m and v = 4.0 ± 0.2 m/s. Estimate Q, and find the uncertainty in the estimate.

b.   Assume that r = 4.00 ± 0.04 m and v = 2.0 ± 0.1 m/s. Estimate Q, and find the uncertainty in the estimate.

c.    If r and v have not been measured, but it is known that the relative uncertainty in r is 1% and that the relative uncertainty in v is 5%, is it possible to compute the relative uncertainty in Q? If so, compute the relative uncertainty. If not, explain what additional information is needed.

2.    The conversion of cyclobutane (C4H8 ) to ethylene (C2H4 ) is a first-order reaction. This means that the concentration of cyclobutane at time t is given by ln C = ln C0 − kt, where C is the concentration at time t, C0 is the initial concentration, t is the time since the reaction started, and k is the rate constant. Assume that C0 = 0.2 mol/L with negligible uncertainty. After 300 seconds at a constant temperature, the concentration is measured to be C = 0.174 ± 0.005 mol/L. Assume that time can be measured with negligible uncertainty.

a.   Estimate the rate constant k, and find the uncertainty in the estimate.

b.  The units of k will be s−1 . Find the relative uncertainty in k. The half-life t1/2 of the reaction is the time it takes for the concentration to be reduced to one-half its initial value.

c.   The half-life is related to the rate constant by t1/2 = (ln 2)/k. Using the result found in part (a), find the uncertainty in the half-life.

d.  Find the relative uncertainty in the half-life.

### What is the probability that the parcel was shipped express and arrived the next day?

1.  In a lot of n components, 30% are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective,….

### Given that the test is positive, what is the probability that the person has the disease?

1.  Refer to Exercise 28. Assume that both inspectors inspect every item and that if an item has no flaw, then neither inspector will detect a flaw. a.  Assume that….

### If a man tests negative, what is the probability that he actually has the disease?

1.  Refer to Example 2.26. a.  If a man tests negative, what is the probability that he actually has the disease? b.  For many medical tests, it is standard procedure….