"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant
that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow (sec). Suppose that in a particular traffic environment, the distribution of time headway has the following form.f(x) = k/(x^7) ; x > 1 0 ; x<1a) Determine the value of K for which f(x) is a legitimate pdfb) Obtain the cumulative distribution functionF(x) = [ Blank ] ; x > 1 0 ; x < 1c) Use the cdf from (b) to determine the probability that headway exceeds 2 sex. (Round your answer to three decimal places.)Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec (round your answer to three decimal places)d) Obtain the mean value of headway and the standard deviation of headway. (Roun to nearest 3 decimal places)mean [ blank ]standard deviation [ blank ]e) what is the probability that headway is within 1 standard deviation of the mean value
1 answer:
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Answer:
1 : 400,000
Step-by-step explanation:
A map scale is usually represented as a unit fraction, one with 1 in the numerator. It has no units, which is to say that it is the ratio of same units.
It can be found by dividing the map dimension by the ground dimension when both are expressed in the same units.
(8.4 cm) / (33.6 km) = (8.4×10^-2 m) / (33.6×10^3 m) = (8.4/33.6)×10^-5
= 0.25×10^-5 = 1/400,000
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<em>Additional comment</em>
Map scales are often expressed using the colon for the ratio unit separator:
1 : 400,000
<u>Given</u>:
The system of linear equations are and
We need to determine the solution to the system of equations using substitution method.
<u>Solution</u>:
The solution can be determined using the substitution method.
Let us substitute in the equation
Thus, we have;
Thus, the value of y is -17.
Substituting in the equation
, we get;
Thus, the value of x is -13.
Hence, the solution to the system of equations is (-13,-17)