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3 years ago

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The graph of a linear function passes through the points (2, 4) and (8, 10).

1 answer:

taurus [48]3 years ago

7 0

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -2}}\quad ,&{{ 4}})\quad 
% (c,d)
&({{ 8}}\quad ,&{{ 10}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{10-4}{8-(-2)}\implies \cfrac{10-4}{8+2}\implies \cfrac{6}{10}
\\\\\\
\cfrac{3}{5}$

$\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-4=\cfrac{3}{5}[x-(-2)]\implies y-4=\cfrac{3}{5}(x+2)
\\\\\\
y-4=\cfrac{3}{5}x+\cfrac{6}{5}\implies y=\cfrac{3}{5}x+\cfrac{6}{5}+4\implies y=\cfrac{3}{5}x+\cfrac{26}{5}$

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3 years ago

6 = -5 -x solve for x

makkiz [27]

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<h2>x = -11</h2>

Step-by-step explanation:

In algebra, the goal is always to isolate the variable, so that its value can be determined.

<h3>Step 1: Add x</h3>

6 + x = -5

<h3>Step 2: Subtract 6</h3>

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<h3>Step 3: Check</h3>

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I'm always happy to help :)

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3 years ago

In one town, the number of burglaries in a week has a poisson distribution with a mean of 1.9. find the probability that in a ra

tester [92]

Let X be the number of burglaries in a week. X follows Poisson distribution with mean of 1.9

We have to find the probability that in a randomly selected week the number of burglaries is at least three.

P(X ≥ 3 ) = P(X =3) + P(X=4) + P(X=5) + ........

= 1 - P(X < 3)

= 1 - [ P(X=2) + P(X=1) + P(X=0)]

The Poisson probability at X=k is given by

P(X=k) = $\frac{e^{-mean} mean^{x}}{x!}$

Using this formula probability of X=2,1,0 with mean = 1.9 is

P(X=2) = $\frac{e^{-1.9} 1.9^{2}}{2!}$

P(X=2) = $\frac{0.1495 * 3.61}{2}$

P(X=2) = 0.2698

P(X=1) = $\frac{e^{-1.9} 1.9^{1}}{1!}$

P(X=1) = $\frac{0.1495 * 1.9}{1}$

P(X=1) = 0.2841

P(X=0) = $\frac{e^{-1.9} 1.9^{0}}{0!}$

P(X=0) = $\frac{0.1495 * 1}{1}$

P(X=0) = 0.1495

The probability that at least three will become

P(X ≥ 3 ) = 1 - [ P(X=2) + P(X=1) + P(X=0)]

= 1 - [0.2698 + 0.2841 + 0.1495]

= 1 - 0.7034

P(X ≥ 3 ) = 0.2966

The probability that in a randomly selected week the number of burglaries is at least three is 0.2966

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3 years ago