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user100 [1]
2 years ago
5

There are 10 pens in a box. There are x red pens in the box. All the other pens are blue. Jack takes at random two pens from the

box. Find an expression, in terms of x, for the probability that Jack takes one pen of each colour. Give your answer in its simplest form.​
Mathematics
1 answer:
expeople1 [14]2 years ago
4 0

The probability that one of each color is selected is \frac{10x - x^2}{45}

<h3>Probabilities</h3>

The probability of an event is the chances of the said event

The given parameters are:

  • Total  = 10
  • Red = x
  • Blue = 10 - x

<h3>Calculating the required probability</h3>

The probability that one of each color is selected is calculated as follows:

P = P(Blue) \times P(Red) + P(Red) \times P(Blue)

So, we have:

P = \frac{10 - x}{10} \times \frac{x}{9} + \frac{x}{10} \times \frac{10 - x}{9}

This gives

P = \frac{x(10 - x)}{90} +\frac{x(10 - x)}{90}

Take LCM

P = \frac{2x(10 - x)}{90}

Simplify the above expression

P = \frac{x(10 - x)}{45}

Expand

P = \frac{10x - x^2}{45}

Hence, the probability that one of each color is selected is P = \frac{10x - x^2}{45}

Read more about probabilities at:

brainly.com/question/7965468

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3 years ago
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CaHeK987 [17]

(C)

Step-by-step explanation:

The volume of the conical pile is given by

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Taking the derivative of V with respect to time, we get

\dfrac{dV}{dt} = \dfrac{\pi}{3}\dfrac{d}{dt}(r^2h)

\:\:\:\:\:\:\:= \dfrac{\pi}{3}\left(2rh\dfrac{dr}{dt} + r^2\dfrac{dh}{dt}\right)

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\:\:\:\:\:\:\:= \dfrac{1}{9\pi\:\text{m}^2}(36\:\text{m}^3\text{/s})

\:\:\:\:\:\:\:= \dfrac{4}{\pi}\:\text{m/s}

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3 years ago
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