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steposvetlana [31]
3 years ago
15

In a class of 6, there are 2 students who forgot their lunch.

Advanced Placement (AP)
1 answer:
Daniel [21]3 years ago
7 0

Answer: 1/15

Explanation:

Since it's a class of 6, and there are 2 students who forgot their lunch. The probability of firs choosing a student who forget their lunch will be 2 out of 6 which is 2/6.

When the next student who forget their lunch is picked there'll be 5 students left which means the probability then will be 1 out of 5 which is 1/5.

Therefore, the if the teacher chooses 2 students, the probability that both of them forgot their lunch will be 1/3 multiplied by 1/5 which will be:

= 1/3 × 1/5

= 1/15

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For the answer to the question above asking in what way were Auguste Comte and Immanuel Kant alike? I` think the answer here is Auguste Comte and Immanuel Kant was alike in the fact that they both felt like science would improve the world. 
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What is the net primary productivity of an algal bed if the gross primary productivity in an algal bed is 7 kcal/m2/yr and respi
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Answer:

NPP = 4\ kcal/m^2/yr

Explanation:

Given

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A presidential candidate emerges from a new minor party that supports radical changes to the national government. This candidate
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Surface Area of a can is 517.8 cm^2. Maximize the volume of this can using the measured surface area.
mafiozo [28]

Answer:

r = 5.24 --- Radius

h = 10.48 --- Height

Explanation:

Given

Object: Can (Cylinder)

Surface\ Area = 517.8cm^2

Required

Maximize the volume

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S.A = 2\pi r^2 + 2\pi rh

Substitute 517.8 for S.A

517.8 = 2\pi r^2 + 2\pi rh

Divide through by 2

258.9 = \pi r^2 + \pi rh

Factorize:

258.9 = \pi r(r + h)

Divide through by \pi r

\frac{258.9}{\pi r} = r + h

Make h the subject

h = \frac{258.9}{\pi r} - r --- (1)

Volume (V) is calculated as:

V = \pi r^2h

Substitute (1) for h

V = \pi r^2(\frac{258.9}{\pi r} - r)

Open Bracket

V = 258.9r - \pi r^3

Differentiate V

V' = 258.9 - 3\pi r^2

Set V' to 0

0 = 258.9 - 3\pi r^2

Collect Like Terms

3\pi r^2 = 258.9

Divide through by 3

\pi r^2 = 86.3

Divide through by \pi

r^2 = \frac{86.3}{\pi}

r^2 = \frac{86.3*7}{22}

r^2 = \frac{604.1}{22}

Take square root of both sides

r = \sqrt{\frac{604.1}{22}

r = 5.24

Recall that:

h = \frac{258.9}{\pi r} - r

Substitute 5.24 for r

h = \frac{258.9}{\pi * 5.24} - 5.24

h = \frac{258.9*7}{22 * 5.24} - 5.24

h = \frac{1812.3}{115.28} - 5.24

h = 15.72 - 5.24

h = 10.48

Hence, the dimension that maximize the volume is:

r = 5.24 --- Radius

h = 10.48 --- Height

7 0
3 years ago
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