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user100 [1]
3 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]3 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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Answer:

x = a(c-b)

Step-by-step explanation:

x/a + b = c

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Which are counterexamples?<br> Look at the picture below. <br> Choose all that apply.
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Answer:

x^4/(2x^6)

Explanation:

In the first example the division results in a radical, not a polynomial.

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8 0
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8x + 6 - 2x = 34 x= ?
e-lub [12.9K]
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Subtract 6x from both sides:
6 = 34x- 6x

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Now switch sides and the answer is:

x = \frac{3}{14}

:) <3

5 0
3 years ago
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There are 12 donuts in a box 1/3 of them are chocolate, 1/4 of them are sprinkles, and the rest are glazed. How many donuts are
zmey [24]

Answer:

3 donuts are sprinkles

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1/4 of 12 is 3

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5 0
2 years ago
In a lab experiment, a student is trying to apply the conservation of momentum. Two identical balls, each with a mass of 1.0 kg.
muminat

Answer:

Trial- 2 shows the conservation of momentum in a closed system.

Step-by-step explanation:

Given: Mass of balls are m= 1.0\ kg

Conservation of momentum in a closed system occurs when momentum before collision is equal to momentum after collision.

  • Let initial velocity of ball A\ is\ u_1
  • Initial velocity of ball B\ is\ u_2
  • Final velocity of ball A\ is\ v_1
  • Final velocity of ball B\ is\ v_2
  • Momentum before collision = mu_1+mu_2
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Now, According to conservation of momentum.

Momentum before collision = Momentum after collision

mu_1+mu_2=mv_1+mv_2

We will plug each trial to this equation.

Trial 1

mu_1+mu_2=mv_1+mv_2\\1.0(1)+1.0(-2)=1.0(-2)+1.0(-1)\\1-2=-2-1\\-1=-3

Trial 2

mu_1+mu_2=mv_1+mv_2\\1.0(.5)+1.0(-1.5)=1.0(-.5)+1.0(-\.5)\\.5-1.5=-.5-.5\\-1=-1

Trial 3

mu_1+mu_2=mv_1+mv_2\\1.0(2)+1.0(1)=1.0(1)+1.0(-2)\\2+1=1-2\\3=-1

Trial 4

mu_1+mu_2=mv_1+mv_2\\1.0(.5)+1.0(-1)=1.0(1.5)+1.0(-1.5)\\.5-1=1.5-1.5\\-.5=0

We can see only Trial 2 satisfies the princple of conservation of momentum. That is momentum before collison should equal to momentum after collision.

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