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mars1129 [50]
4 years ago
15

A bank requires that its customers create a PIN to access their account. The pin must be 2 letters followed by 2 numbers. How ma

ny unique PINS are there if letters can be repeated but digits cannot be repeated?
Mathematics
1 answer:
klio [65]4 years ago
5 0

Answer:

There are 60840 unique PINS if letters can be repeated but digits cannot be repeated

Step-by-step explanation:

In total, there are 26 letters and 10 digits.

The PIN has the following format:

L - L - N - N

The letters can be repeated, so for both letters, there are 26 options.

The digits cannot be repeated. So for the first digits there are 10 options. For the second there are 9, since the first digit used cannot be repeated.

In total:

26 - 26 - 10 - 9

26*26*10*9 = 60840

There are 60840 unique PINS if letters can be repeated but digits cannot be repeated

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7x+100+68.25 Let me know if you want me to explain it to you
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3 years ago
Help with matrices please? Any wrong/not applicable answers will be reported and BLOCKED
marin [14]

m x H = \left[\begin{array}{ccc}-25&37.5&-12.5\\\9\end{array}\right]

Step-by-step explanation:

Step 1; Multiply 5 with this matrix  \left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right] and we get a matrix \left[\begin{array}{ccc}-5&10\\20&40\\\end{array}\right]

Multiply the fraction  \frac{2}{5} with the matrix  \left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right] and we get \left[\begin{array}{ccc}-\frac{2m}{5} &\frac{4m}{5} \\\frac{8m}{5} &\frac{16m}{5} \\\end{array}\right]

Step2; Now equate corresponding values of the matrices with each other.

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Step 3; Add the matrices to get the value of matrix m.

Adding the three matrices on the RHS we get  \left[\begin{array}{ccc}2&9&-9\\\end{array}\right].

Step 4; Adding the matrices on the LHS we get the resulting matrix as H +

\left[\begin{array}{ccc}4&6&-8\\\9\end{array}\right]. Equating the matrices from step 3 and 4 we get the value of H as \left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right]

Step 5; Now to find the value of m x H we need to multiply the value of \frac{25}{2} with the matrix \left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right]

Step 6; Multiplying we get the matrix m x H = [ -25  \frac{75}{2}  \frac{-25}{2} ]

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3 years ago
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Answer: x^{2} +23x+49

Step-by-step explanation:

To find the area of the shaded region, you must find the area of the larger rectangle [(x+10)×(2x+5)] and subtract the area of the smaller rectangle [(x+1)×(x+1)] from it.

First, you simplify the larger rectangle's area:

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Then, simplify the smaller rectangle's area:

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Finally, subtract the smaller rectangle's area from the larger rectangle's area:

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Therefore, the final answer is x^{2} +23x+49.

I hope this helps!

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2 years ago
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Answer:

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4 years ago
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