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Darina [25.2K]
3 years ago
15

There are 2 red pens, 3 blue pens, 1 black pen, and 4 green pens in a desk drawer. You randomly choose one. Find each probabilit

y as a FRACTION in SIMPLEST FORM. Total Pens: __________ 1) P (red) ____________ 2) P (black) ____________ 3) P (purple) ____________ 4) P (not green) ____________ 5) P (black or red) __________ 6) P (orange) _________
Mathematics
1 answer:
zheka24 [161]3 years ago
5 0

Answer:

total = 10

1. 1/5

2. 1/10

3. 0/10

4. 3/5

5. 3/10

6. 0/10

Step-by-step explanation:

total;

The sum of all pen types is: 2 + 3 + 1 + 4 = 10

Pen types are:

   red

   blue

   black

   green

1. P (red)

There are 2 red pens, so the fraction is 2/10 which when simplified is 1/5

2. P (black)

There is one black pen, so simplified it will be 1/10

3. P (purple)

There are no purple pens, so its just 0/10

4. P (not green)

There are ten pens total. 4 of them are green, so we subtract the number of green pens to the number of pens total, 10 - 4 = 6

So 6/10 which simplified is 3/5

5. P (black or red)

We find the sum of red and black pens, so its 3/10 which cannot be simplified any further

6. P (orange)

There are no green pens, so its 0/10

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Answer:

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Step-by-step explanation:

(a) Initial amount of salt in tank

The tank initially contains 60 kg of salt.

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\text{Let A = mass of salt after t min}\\\text{and }r_{i} = \text{rate of salt coming into tank}\\\text{and }r_{0} =\text{rate of salt going out of tank}

(i) Set up an expression for the rate of change of salt concentration.

\dfrac{\text{d}A}{\text{d}t} = r_{i} - r_{o}\\\\\text{The fresh water is entering with no salt, so}\\ r_{i} = 0\\r_{o} = \dfrac{\text{3 L}}{\text{1 min}} \times \dfrac {A\text{ kg}}{\text{1000 L}} =\dfrac{3A}{1000}\text{ kg/min}\\\\\dfrac{\text{d}A}{\text{d}t} = -0.003A \text{ kg/min}

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(iv) Solve for A as a function of time.

\text{The integrated rate expression is}\\\ln A = -0.003t +  \ln(0.060)\\\text{Solve for } A\\A = 0.060e^{-0.003t}

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b.Calculate the concentration

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The volume added in 4.5 h is  

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\text{As t $\longrightarrow \, -\infty,\, e^{-\infty} \longrightarrow \, 0$, so A $\longrightarrow \, 0$.}

This makes sense, because the salt is continuously being flushed out by the fresh water coming in.

The graph below shows how the concentration of salt varies with time.

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