Set up and solve an equation for the following business situation.

Mathematics

1 answer:

evablogger [386]3 years ago

3 0

Answer:

Step-by-step explanation:

5(x)-600=800

x=280

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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]

Answer:

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

Jon caught four fish that weighed a total of 252 pounds. The kingfish weighed twice as much as the amberjack and the white marli

Allushta [10]

Answer:

amberjack, 21 lbs
kingfish, 42 lbs
white marlin, 84 lbs
tarpon, 105 lbs

Step-by-step explanation:

Let k, a, m, t represent the weights of the kingfish, amberjack, marlin, and tarpon, respectively. The problem statement tells us ...

k = 2a
m = 2k
t = 5a
k + a + m + t = 252

Using substitution, we can rewrite the last equation as ...

... (2a) + (a) + 2(2a) + (5a) = 252

... 12a = 252 . . . . . collect terms

... a = 21 . . . . . . . . .divide by 12

Then k = 2a = 42; m = 2k = 84; t = 5a = 105.

8 0

3 years ago

Frands collects marbles. In her collection are:

Vilka [71]

Answer:

Step-by-step explanation:

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