Please help me no links!!!

Mathematics

1 answer:

vodka [1.7K]3 years ago

3 0

Answer:

y=4

Step-by-step explanation:

y = mx+b

The slope of the line is 0 and the graph crosses the y-axis at 4. The point crossing the y-axis is the y-intercept or aka "b"

y=mx+b

y = 0*x +4

y = 0+4

y= 4

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Solve the differential equation dy/dx+4xy=x

Irina-Kira [14]

$\dfrac{\mathrm dy}{\mathrm dx}+4xy=x$
$\dfrac{\mathrm dy}{\mathrm dx}=x(1-4y)$

This ODE is separable, so you can write

$\dfrac{\mathrm dy}{1-4y}=x\,\mathrm dx$

Integrating both sides gives

$-\dfrac14\ln|1-4y|=\dfrac12x^2+C$
$\ln|1-4y|=-2x^2+C$
$1-4y=e^{-2x^2+C}$
$1-4y=Ce^{-2x^2}$
$y=\dfrac{1-Ce^{-2x^2}}4$

3 0

3 years ago

The time between arrivals of customers at an automatic teller machine is an exponential random variable with a mean of 4 minutes

andre [41]

Answer:

0.7788 = 77.88% probability that more than three customers arrive in 10 minutes

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

In this question, we have that:

The time between arrivals of customers at an automatic teller machine is an exponential random variable with a mean of 4 minutes, and we have three customers, which means that $m = 3*4 = 12, \mu = \frac{1}{12} = 0.0833$