Answer:
The length of the interval during which no messages arrive is 90 seconds long.
Step-by-step explanation:
Let <em>X</em> = number of messages arriving on a computer server in an hour.
The mean rate of the arrival of messages is, <em>λ</em> = 11/ hour.
The random variable <em>X</em> follows a Poisson distribution with parameter <em>λ</em> = 11.
The probability mass function of <em>X</em> is:
![P(X=x)=\frac{e^{-11}11^{x}}{x!};\ x=0,1,2,3....](https://tex.z-dn.net/?f=P%28X%3Dx%29%3D%5Cfrac%7Be%5E%7B-11%7D11%5E%7Bx%7D%7D%7Bx%21%7D%3B%5C%20x%3D0%2C1%2C2%2C3....)
It is provided that in <em>t</em> hours the probability of receiving 0 messages is,
P (X = 0) = 0.76
Compute the value of <em>t</em> as follows:
![P(X=0)=\frac{e^{-11\times t}(11\times t)^{0}}{0!}\\0.76=e^{-11\times t}\\\ln(0.76)=-11\times t\\t=-\frac{\ln(0.76)}{11} \\=0.025\ hours\\\approx90\ seconds](https://tex.z-dn.net/?f=P%28X%3D0%29%3D%5Cfrac%7Be%5E%7B-11%5Ctimes%20t%7D%2811%5Ctimes%20t%29%5E%7B0%7D%7D%7B0%21%7D%5C%5C0.76%3De%5E%7B-11%5Ctimes%20t%7D%5C%5C%5Cln%280.76%29%3D-11%5Ctimes%20t%5C%5Ct%3D-%5Cfrac%7B%5Cln%280.76%29%7D%7B11%7D%20%5C%5C%3D0.025%5C%20hours%5C%5C%5Capprox90%5C%20seconds)
Thus, the length of the interval during which no messages arrive is 90 seconds long.
.. Please... Please tell me you know fractions at least well enough to know this ;_;
3/4 is like 0.75, yeh?
3/8 is like.. 0.365
Change the Denominator (Bottom Number in Fraction) so they're the same:
6/8 3/8.
Now d'you see?
Answer:
36%
Step-by-step explanation:
Jeans: 14
Shorts: 9
Capris: 2
Total number of students = Number of Jeans + Number of Shorts + Number of Capris
Total number of students = 14 + 9 + 2 = 25
% of students wearing shorts = Number of shorts / Total number of students * 100
% of students wearing shorts = 9 / 25 * 100 = 0.36 * 100 = 36%
Answer:
8.29
Step-by-step explanation:
It is 8.29 because the 3 is not greater than a 5, therefore it does not get rounded up.
Answer:
24mph
Step-by-step explanation:
24 mph times 5 hours = 120 miles
24 mph + 36 mph = 60 mph
60 mph × 2 hours = 120 miles