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4 years ago

Line CD passes through points C(3, –5) and D(6, 0). What is the equation of line CD in standard form?

1 answer:

5 0

Slope = (y₂- y₁) / (x₂- x₁)

Points C( 3, -5) and D (6, 0) compare to (x₁, y₁) and (x₂, y₂)

Slope = (0 - -5) / (6- 3) = (0+5) / (3) = 5/3

Slope = 5/3

Equation of line given a slope and point, y - y₁ = m(x - x₁)

m = 5/3,    let point C( 3, -5) = (x₁, y₁)

y - - 5 = (5/3) (x - 3)

y + 5 = (5/3)(x - 3)

   3(y + 5) = 5(x - 3)

3y + 15 = 5x - 15

   3y = 5x - 15 - 15

   3y = 5x - 30

Hence the equation of the line is 3y = 5x - 30

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Answer:

a) $P(X$

$P(X>14) = 1-P(X$

b) $P(7< X$

c) We want to find a value c who satisfy this condition:

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And using the cumulative distribution function we have this:

$P(x$

And solving for c we got:

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Step-by-step explanation:

For this case we define the random variable X as he amount of time (in minutes) that a particular San Francisco commuter must wait for a BART train, and we know that the distribution for X is given by:

$X \sim Unif (a=0, b =20)$

Part a

We want this probability:

$P(X$

And for this case we can use the cumulative distribution function given by:

$F(x) = \frac{x-a}{b-a} = \frac{x-0}{20-0}= \frac{x}{20}$

And using the cumulative distribution function we got:

$P(X$

For the probability $P(X>14)$ if we use the cumulative distribution function and the complement rule we got:

$P(X>14) = 1-P(X$

Part b

We want this probability:

$P(7< X$

And using the cdf we got:

$P(7< X$

Part c

We want to find a value c who satisfy this condition:

$P(x$

And using the cumulative distribution function we have this:

$P(x$

And solving for c we got:

$c = 20*0.9 = 18$

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