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maksim [4K]
3 years ago
12

How do I do this? f(a)=4a+5; Find f(2)

Mathematics
1 answer:
Mariana [72]3 years ago
6 0
F(2)=4(2)+5
f(2)=8+5
f(2)=13
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The time between telephone calls to a cable television service call center follows an exponential distribution with a mean of 1.
Ulleksa [173]

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0.52763 is the probability that the time between the next two calls will be 54 seconds or​ less.

0.19285 is the probability that the time between the next two calls will be greater than 118.5 ​seconds.

Step-by-step explanation:

We are given the following information in the question:

The time between telephone calls to a cable television service call center follows an exponential distribution with a mean of 1.2 minutes.

The distribution function can be written as:

f(x) = \lambda e^{-\lambda x}\\\text{where lambda is the parameter}\\\\\text{Mean} = \mu = \displaystyle\frac{1}{\lambda}\\\\\Rightarrow 1.2 = \frac{1}{\lambda}\\\\\lambda = 0.84 \\f(x) = 0.84 e^{0.84 x}

The probability for exponential distribution is given as:

P( x \leq a) = 1 - e^{\frac{-a}{\mu}}\\\\P(a \leq x \leq b) = e^{\frac{-a}{\mu} -\frac{-b}{\mu}}

a) P( time between the next two calls will be 54 seconds or​ less)

P( x \leq 0.9)\\= 1 - e^{\frac{\frac{-54}{60}}{1.2}} = 0.52763

0.52763 is the probability that the time between the next two calls will be 54 seconds or​ less.

b) P(time between the next two calls will be greater than 118.5 ​seconds)

p( x > \frac{118.5}{60}) = P(x > 1.975)\\\\ = 1 - P(x \leq 1.975) \\\\= 1 -1+ e^{\frac{-1.975}{1.2}}\\\\= 0.19285

0.19285 is the probability that the time between the next two calls will be greater than 118.5 ​seconds.

6 0
3 years ago
A 31 foot board is cut in two pieces so that the longer piece is 1 foot less than three times the shorter piece
strojnjashka [21]
X is the short piece
(3•x-1)+x=31
4x=31+1
X=32/4=8

Short piece is 8
Long piece is 3•8-1=23

Check 8+23=31 ✔️
8 0
3 years ago
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