Answer:
1.28 m
Step-by-step explanation:
The speed at which water rises in the tank is proportional to the speed of the water in the pipe and inversely proportional to the ratio of the tank area to the pipe area.
The ratio of tank area to pipe area is the square of the ratio of their diameters:
((150 cm)/(4 cm))² = 1406.25
Then the rate of rise of water in the tank is ...
(0.5 m/s)/(1406.25)
After 1 hour = 3600 seconds, the height of the water will be ...
rise = (time)(rate of rise)
(3600 s)(0.5 m/s)/1406.25 = 1.28 m
Answer:
22 miles per hour
Step-by-step explanation:
Against the current, the boat's rate of travel is ...
(120 mi)/(6 h) = 20 mi/h
With the current, the boat's rate of travel is ...
(120 mi)/(5 h) = 24 mi/h
___
The sum of boat speed (b) and current speed (c) is 24 mph. The difference is 20 mph. This lets us write the equations ...
b + c = 24
b - c = 20
Adding these two equations together, we get ...
2b + 0c = 44
b = 22 . . . . . . . . divide by 2
The rate of the boat in still water is 22 miles per hour.
Answer:
Answer for the question:
The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 69 and standard deviation 2.7.
a. If a specimen is acceptable only if its hardness is between 67 and 75, what is the probability that a randomly chosen specimen has an acceptable hardness?
b. If the acceptable range of hardness is (69-C, 69+C), for what value of C would 95% of all specimens have acceptable hardness?
c. If the acceptable range is as in part (a) and the hardness of each of ten randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the ten?
d. What is the probability that at most eight of ten independently selected specimens have a hardness of less than 72.84(HINT Y=number among the ten specimens with hardness less than72.84 is a binomial variable; what is p?)
is given in the attachment.
Step-by-step explanation:
The answer is to this problem is 2.2
