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3 years ago

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There are 3 yellow, 3 green, and 3 red pens in a jar. Each day Michelle selects a pen without looking, uses the pen, and then re

places it in the jar. Over 14 days she selects a red pen 6 times. Compare the theoretical and experimental probabilities of this experiment.
(Hint: Calculate the theoretical probability and experimental probability
separately)

1 answer:

Anni [7]3 years ago

3 0

Theoretical Probability: she will pick the red pen 4-5 times in the 14 days (14days/3options=4.667times picked over the duration of the time allotted).

Experimental Probability: she picks the red pen 6/14 times

So the experimental is 1-2 times more than predicted via theoretical probability

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Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area: where V = volume (mm3

Alex

Answer:

V = 20.2969 mm^3 @ t = 10

r = 1.692 mm @ t = 10

Step-by-step explanation:

The solution to the first order ordinary differential equation:

$\frac{dV}{dt} = -kA$

Using Euler's method

$\frac{dVi}{dt} = -k *4pi*r^2_{i} = -k *4pi*(\frac {3 V_{i} }{4pi})^(2/3)\\ V_{i+1} = V'_{i} *h + V_{i} \\$

Where initial droplet volume is:

$V(0) = \frac{4pi}{3} * r(0)^3 = \frac{4pi}{3} * 2.5^3 = 65.45 mm^3$

Hence, the iterative solution will be as next:

i = 1, ti = 0, Vi = 65.45

$V'_{i} = -k *4pi*(\frac{3*65.45}{4pi})^(2/3) = -6.283\\V_{i+1} = 65.45-6.283*0.25 = 63.88$

i = 2, ti = 0.5, Vi = 63.88

$V'_{i} = -k *4pi*(\frac{3*63.88}{4pi})^(2/3) = -6.182\\V_{i+1} = 63.88-6.182*0.25 = 62.33$

i = 3, ti = 1, Vi = 62.33

$V'_{i} = -k *4pi*(\frac{3*62.33}{4pi})^(2/3) = -6.082\\V_{i+1} = 62.33-6.082*0.25 = 60.813$

We compute the next iterations in MATLAB (see attachment)

Volume @ t = 10 is = 20.2969

The droplet radius at t=10 mins

$r(10) = (\frac{3*20.2969}{4pi})^(2/3) = 1.692 mm\\$

The average change of droplet radius with time is:

Δr/Δt = $\frac{r(10) - r(0)}{10-0} = \frac{1.692 - 2.5}{10} = -0.0808 mm/min$

The value of the evaporation rate is close the value of k = 0.08 mm/min

Hence, the results are accurate and consistent!

5 0

3 years ago

Write 90,523 in Word form

azamat

Ninety thousand five hundred twenty three

3 0

3 years ago

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How do you write “twice a number less than 3 is 17” as an equation?

ki77a [65]

Answer:

2 x 3 < 17

Step-by-step explanation:

Greater than and/or less than step by step equasion.

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3 years ago

Find what n equals 8(2n-2) = 4 - 4n (explanation please)

slavikrds [6]

Answer:

$\huge\boxed{n=1}$

Step-by-step explanation:

In order to find the value of n that satisfies this equation, we can perform a series of algebraic steps on it to solve for n.

$8(2n-2) = 4- 4n$
<em>Distribute in the 8 on the left side:</em>
<em /> $16n-16=4-4n$ <em> </em>
<em>Add 4n to both sides</em>
$20n-16=4$
<em>Add 16 to both sides</em>
$20n = 20$
<em>Divide both sides by 20</em>
$n=1$

Therefore, n=1 is the value of n that satisfies this equation.

Hope this helped!

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3 years ago

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For which rational expression is 8 an excluded value ? check all that apply

denis23 [38]

<u>Answer:</u>

The correct answer options are C. $\frac{x^2+5}{x-8}$ and D. $\frac{x^2-x-56}{x^2-64}$ .

<u>Step-by-step explanation:</u>

The values which make the denominator equal to zero are called the excluded values.

Here, we can substitute 8 for x and check if it makes the denominator 0.

$\frac{x-8}{x+8} = \frac{8-8}{8+8} =\frac{0}{16} =0$

$\frac{x-2}{x^2-4} = \frac{8-2}{8^2-4} =\frac{6}{60} =\frac{1}{10}$

$\frac{x^2+5}{x-8} = \frac{8^2+5}{8-8} =\frac{69}{0}$

$\frac{x^2-x-56}{x^2-64} = \frac{8^2-8-56}{8^2-64} = \frac{0}{0} =0$

$\frac{8x^2-2}{x^2-16} = \frac{8(8)^2-2}{8^2-16} =\frac{510}{48}$

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3 years ago