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In a support system in the U.S. space program, a single crucial component works only 85% of the time. In order to enhance the reliability of the system, it is decided that 3 components will be installed in parallel such that the system fails only if they all fail. Assume the components act independently and that they are equivalent in the sense that all 3 of them have an 85% success rate. Consider the random variable X as the number of components out of 3 that fail.
(a) Write out a probability function for the random variable X.
(b) What is E(X) (i.e., the mean number of components out of 3 that fail)?
(c) What is Var(X)?
(d) What is the probability that the entire system is successful?
(e) What is the probability that the system fails?
(f) If the desire is to have the system be successful with probability 0.99, are three components sufficient? If not, how many are required?
The car's position is defined by the position vector, where . The image below shows the system projected onto the x-y plane. What are the car's velocity and acceleration vectors at this position
A ferrari with 808 hp has a max. speed of 211 mph at 6,300 rpm. the Ferrari weighs 4,155 lb/ton and is operated over a smooth concrete road with a rolling resistance of 40 lb/ton and a slope of 3%.
The x-component of a velocity field is ax+b.If the flow is steady, two-dimentional and incompressible; generate an expression for velocity component in the y-direction as a function of x and y.
A rapid sand filter has a loading rate of 8.00 m/h, surface dimension of 10m x 8m, an effective filtration rate of 7.70 m/h, and a production efficiency of 96 percent.
The continuity equation is just the water balance for the slope or any small portion of the slope and can be given as: p - fp = RO where i = rainfall rate, fp = infiltration capacity, and RO = runoff rate, all expressed as a depth per time
The reaction between 2-methyl-2-pentanol and HBr to yield 2-methyl-2-pentene is probably: A) an E1-type reaction involving the protonated alcohol as the substrate. B) an SN2-type reaction involving the protonated alcohol as the substrate.
The velocity of propagation, c of surface waves is assumed to depend on the water depth, y, the water density, and the acceleration due to gravity, g. Express these variables as a dimensionless group.
the three forces of magnitude P can be replaced by a single, equivalent force R acting at point A. Determine the distance x and the magnitude and direction of R
In a certain community 36% of the families own a dog, and 22 percent of the families that own a dog also own a cat. In addition 30 percent of the families own a cat. a.) what percentage of families own both a dog and a cat
FeCl3 is added to remove excess phosphate. The following reactions occur (the charges are in parentheses): FeCl3 -> Fe(3+) + 3Cl(-) Fe(3+) + PO4(3-) -> FePO4 The equilibrium constant for the second reaction is 10^26.4.
A pile resists the tension developed by three stay cables for a major tent (Membrane) Structure. Assuming no bending is desired in the pile (no resultant horizontal component), what is the magnitude of the force S if the angle \thetaS = 30 degrees
Vehicles A and B are traveling toward each other in the opposing lanes on a straight segment of a two-lane highway at 35 and 40 mph respectively. If the critical rates of angular change of the two drivers are 0.0065 and 0.0055 rad/s,
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