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alexgriva [62]
2 years ago
14

4. A fair, six-sided die has four green and two red faces. The die will be rolled several times. You

Advanced Placement (AP)
1 answer:
nalin [4]2 years ago
5 0

Considering the situation described above, the sequence most likely to occur is the <u>First Sequence.</u>

<h3>How did the first sequence become the most probable?</h3>

Given that the sequences are similar except for the order for the first five rolls. Thus, it is concluded that these sequences have the same probability in their first five rolls.

However, the second and third sequences are less probable to occur than the first because they have an additional roll making the probability less than the first sequence.

Hence, in this case, it is concluded that the correct answer is "<u>the first sequence</u>."

Learn more about probability here: brainly.com/question/25688842

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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

The surface area is:

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

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What is a tsunami definition?
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Answer:

A tsunami is a series of waves caused by earthquakes or undersea volcanic eruptions.

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