Get one x+y=3 to y=x+3 and plug it into x-y=1 and you get x-(x+3)=1. Destitute the x and solve. Once you get what x equals plug it to to either equation for the value of x and solve for y

7 0

3 years ago

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The number of accidents that occur at a busy intersection is Poisson distributed with a mean of 4.5 per week. Find the probabili

Mariana [72]

Answer:

a) 0.01111

b) 0.4679

c) 0.33747

Step-by-step explanation:

We are given the following in the question:

The number of accidents per week can be treated as a Poisson distribution.

Mean number of accidents per week = 4.5

$\lambda= 4.5$

Formula:

$P(X =k) = \displaystyle\frac{\lambda^k e^{-\lambda}}{k!}\\\\ \lambda \text{ is the mean of the distribution}$

a) No accidents occur in one week.

$P(x =0)\\\\= \displaystyle\frac{4.5^0 e^{-4.5}}{0!}= 0.01111$

b) 5 or more accidents occur in a week.

$P( x \geq 5) = 1-\displaystyle \sum P(x$

c) One accident occurs today.

The mean number of accidents per day is given by

$\lambda = \dfrac{4.5}{7} = 0.64$

$P(x =1)\\\\= \displaystyle\frac{0.64^1 e^{-0.64}}{1!}= 0.33747$

5 0

3 years ago

Whats the equation of the line that passes threw -4,4 and is parrell to the line y=1/2-4

vovangra [49]

Answer:

$y=\frac{1}{2}x+6$

Step-by-step explanation:

Given:

The equation of the known line is:

$y=\frac{1}{2}x-4$

A point on the unknown line is (-4, 4)

Now, since the two lines are parallel, their slopes must be equal.

Now, slope of the known line is the coefficient of 'x' which is $\frac{1}{2}$ .

Therefore, the slope of the unknown line is also $m=\frac{1}{2}$

Now, for a line with slope 'm' and a point on it $(x_1,y_1)$ is given as:

$y-y_1=m(x-x_1)$

Here, $m=\frac{1}{2}, x_1=-4,y_1=4$ . Therefore,

$y-4=\frac{1}{2}(x-(-4))\\\\y-4=\frac{1}{2}(x+4)\\\\y-4=\frac{1}{2}x+2\\\\y=\frac{1}{2}x+2+4\\\\y=\frac{1}{2}x+6$

Hence, the equation of the unknown line is $y=\frac{1}{2}x+6$ .

5 0

4 years ago