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An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
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Response:
An electric device delivers a current of [tex]15.0 \, \text{A}[/tex] for 30 seconds. How many electrons flow through it?



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Fix any grammar or spelling errors.
Remove phrases that are not part of the question.
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Which best explains why Irving sets "The Adventure of the Mysterious Stranger" in a land of "masks and gondolas"? The setting is symbolic of the idea that a life of quiet study is the ideal pursuit. The setting is symbolic of the idea that innocence cannot be outgrown. The setting is symbolic of the idea that ease and affluence are available to all. The setting is symbolic of the idea that appearances can be deceiving.
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Response:
Which best explains why Irving sets "The Adventure of the Mysterious Stranger" in a land of "masks and gondolas"?

A. The setting is symbolic of the idea that a life of quiet study is the ideal pursuit.
B. The setting is symbolic of the idea that innocence cannot be outgrown.
C. The setting is symbolic of the idea that ease and affluence are available to all.
D. The setting is symbolic of the idea that appearances can be deceiving.



Format the following question or task so that it is easier to read.
Fix any grammar or spelling errors.
Remove phrases that are not part of the question.
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Do not change or remove [tex] [/tex] tags.
If the question is nonsense, rewrite it so that it makes sense.
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Read the lines from "The Tide Rises, The Tide Falls."
Darkness settles on roofs and walls,
But the sea, the sea in darkness calls;
The imagery in these lines evokes a sense of
Olaziness.O fear.
O mystery
O despair. .
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Response:
Read the lines from "The Tide Rises, The Tide Falls."

"Darkness settles on roofs and walls,
But the sea, the sea in darkness calls;"

The imagery in these lines evokes a sense of:
A. laziness
B. fear
C. mystery
D. despair



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Fix any grammar or spelling errors.
Remove phrases that are not part of the question.
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WARM-UP
Solve for x.
3x = 6x - 2
O
||
X=
2/3
DONE
312
x=2
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Response:
Solve for x.

[tex]\[ 3x = 6x - 2 \][/tex]



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[tex]$(2 p+q)^3$[/tex]
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Response:
Simplify the expression:

[tex]\[ (2p + q)^3 \][/tex]



Answer :

GinnyAnswer
Sure, let's expand the expression [tex]\((2p + q)^3\)[/tex] step-by-step.

To expand [tex]\((2p + q)^3\)[/tex], we can use the binomial theorem which states:

[tex]\[ (a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k \][/tex]

Here, [tex]\(a = 2p\)[/tex], [tex]\(b = q\)[/tex], and [tex]\(n = 3\)[/tex].

First, identify the binomial coefficients for [tex]\(n = 3\)[/tex]:
- [tex]\(\binom{3}{0} = 1\)[/tex]
- [tex]\(\binom{3}{1} = 3\)[/tex]
- [tex]\(\binom{3}{2} = 3\)[/tex]
- [tex]\(\binom{3}{3} = 1\)[/tex]

Now, apply the binomial theorem:

[tex]\[ (2p + q)^3 = \binom{3}{0} (2p)^3 q^0 + \binom{3}{1} (2p)^2 q^1 + \binom{3}{2} (2p)^1 q^2 + \binom{3}{3} (2p)^0 q^3 \][/tex]

Simplify each term:

1. For [tex]\(k = 0\)[/tex]:
[tex]\[ \binom{3}{0} (2p)^{3} q^0 = 1 \cdot (2p)^3 \cdot q^0 = 8p^3 \][/tex]

2. For [tex]\(k = 1\)[/tex]:
[tex]\[ \binom{3}{1} (2p)^2 q^1 = 3 \cdot (2p)^2 \cdot q = 3 \cdot 4p^2 \cdot q = 12p^2q \][/tex]

3. For [tex]\(k = 2\)[/tex]:
[tex]\[ \binom{3}{2} (2p)^1 q^2 = 3 \cdot (2p) \cdot q^2 = 3 \cdot 2p \cdot q^2 = 6pq^2 \][/tex]

4. For [tex]\(k = 3\)[/tex]:
[tex]\[ \binom{3}{3} (2p)^0 q^3 = 1 \cdot (2p)^0 \cdot q^3 = q^3 \][/tex]

Combining all these terms, we get the expanded form of [tex]\((2p + q)^3\)[/tex]:

[tex]\[ (2p + q)^3 = 8p^3 + 12p^2q + 6pq^2 + q^3 \][/tex]

So, the expanded expression is:

[tex]\[ 8p^3 + 12p^2q + 6pq^2 + q^3 \][/tex]

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