The given equation shows the number of possible distinct passwords, p, of length, L, where each character is selected from n permitted characters. p=n^(L) How does the number, p, of possible distinct passwords change if the length is increased by 3 characters? Choose 1 answer: (A) p is multiplied by n^(3). (B) p is multiplied by 3n. (C) p is cubed. (D) p is multiplied by 3 .

Original Formula Explanation: The original formula for the number of possible distinct passwords is p = n^(L). We need to determine the new number of passwords when the length L is increased by 3.New Length Denotation: Let's denote the new length as L_new = L + 3. The new number of possible passwords will be p_new = n^(L_new).Substitution of New Length: Substitute L_new into the formula: p_new = n^(L + 3).Rewriting Using Exponents: Using the properties of exponents, we can rewrite n^(L + 3) as n^L * n^3.Substitution of Original Number: Since n^L is the original number of passwords p, we can substitute p back into the equation: p_new = p * n^3.Final Conclusion: This shows that the new number of passwords is the original number of passwords multiplied by n^3. Therefore, the correct answer is (A) p is multiplied by n^(3).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The given equation shows the number of possible distinct passwords,
p, of length,
L, where each character is selected from
n permitted characters.

p=n^(L)
How does the number,
p, of possible distinct passwords change if the length is increased by 3 characters?
Choose 1 answer:
(A)
p is multiplied by
n^(3).
(B)
p is multiplied by
3n.
(C)
p is cubed.
(D)
p is multiplied by 3 .

The given equation shows the number of possible distinct passwords, $p$ , of length, $L$ , where each character is selected from $n$ permitted characters. $\newline$ $p=n^{L}$ $\newline$ How does the number, $p$ , of possible distinct passwords change if the length is increased by $3$ characters? $\newline$ Choose $1$ answer: $\newline$ (A) $p$ is multiplied by $n^{3}$ . $\newline$ (B) $p$ is multiplied by $3 n$ . $\newline$ (C) $p$ is cubed. $\newline$ (D) $p$ is multiplied by $3$ .

View step-by-step help

Home

Math Problems

Grade 6

Find a value using two-variable equations: word problems

Full solution

Q. The given equation shows the number of possible distinct passwords,

p

, of length,

L

, where each character is selected from

n

permitted characters.

\newline

p=n^{L}

\newline

How does the number,

p

, of possible distinct passwords change if the length is increased by

3

characters?

\newline

Choose

1

answer:

\newline

(A)

p

is multiplied by

n^{3}

\newline

(B)

p

is multiplied by

3 n

\newline

(C)

p

is cubed.

\newline

(D)

p

is multiplied by

3

Original Formula Explanation: The original formula for the number of possible distinct passwords is $p = n^{L}$ . We need to determine the new number of passwords when the length $L$ is increased by $3$ .
New Length Denotation: Let's denote the new length as $L_{\text{new}} = L + 3$ . The new number of possible passwords will be $p_{\text{new}} = n^{L_{\text{new}}}$ .
Substitution of New Length: Substitute $L_{\text{new}}$ into the formula: $p_{\text{new}} = n^{(L + 3)}$ .
Rewriting Using Exponents: Using the properties of exponents, we can rewrite $n^{L + 3}$ as $n^L \cdot n^3$ .
Substitution of Original Number: Since $n^L$ is the original number of passwords $p$ , we can substitute $p$ back into the equation: $p_{\text{new}} = p \times n^3$ .
Final Conclusion: This shows that the new number of passwords is the original number of passwords multiplied by $n^3$ . Therefore, the correct answer is (A) $p$ is multiplied by $n^{3}$ .