For dialysis membranes the lp was determined to be 6.34 x 10-7 cm min-1 mm hg-1. a cylindrical hole 1 cm in diameter was cut in two lexan pieces that were then bolted together with the membrane between. fluid entered one side through a pump and a pressure transducer was affixed. the flow was adjusted until the pressure (above atmospheric) was 2 pascals. the pressure on the opposite side was atmospheric (zero). what was the flow through the membrane?

Which lists the main components of darwin’s theory of evolution? a. random mutations drive evolution; the evolution of a population happens slowly; organisms have common ancestors; organisms do not change. b. natural selection drives evolution; the evolution of a population happens slowly; organisms have common ancestors; organisms change over time. c. natural selection drives evolution; the evolution of a population happens rapidly; organisms have common ancestors; organisms change over time. d. random mutations drive evolution; the evolution of a population happens rapidly; organisms have common ancestors; organisms do not change.

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒

The number of passengers who arrive at the platform of a subway station for the 10 am train is a random variable with a mean of 120 and a variance of 16. find the lower bound of the probability that there will be between 100 and 140 passengers (round off to second decimal place).