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3 years ago

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CODES Use the following information to solve. A bank gives each new customer a 4-digit code number which allows the new customer

to create
their own password. The code number is assigned randomly from the digits 1, 3, 5, and 7, and no digit is repeated.
• What is the probability that the code number will start with 371?
a 1/3
b 1/4
с 1/12
d 1/24

1 answer:

MaRussiya [10]3 years ago

7 0

<h3>Answer: D) 1/24</h3>

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Explanation:

There are 4 digits to pick from and 4 slots to fill, so there are 4! = 4*3*2*1 = 24 different codes possible.

If we want the code to start with 371, then that must mean 5 is the only thing left for that fourth slot. In short, there's only one code that starts with 371 and that code is 3715

We have one code we want (3715) out of 24 total, which is why the answer is 1/24 (choice D)

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The given system of equations is consistent and independent so, $\fbox{\begin\\\ \bf option (3)\\\end{minispace}}$ is correct.

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A system of equations is said to be a consistent system if the solution exists and if the solution does not exist then it is an inconsistent system.

If a consistent system has a unique solution then it is an independent system of equations but if the number of solutions is infinite then it is a dependent system of equations.

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The augmented matrix for the above equations is, as follows:

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Here, the first option is inconsistent and dependent.

There exists a solution of the given system of equations so it is consistent.

Therefore, option (1) is incorrect.

Option (2)

Here, the second option is consistent and dependent.

There exists a solution of the given system of equations so it is consistent.

Also, the solution is unique therefore the system of equations is independent.

Therefore, option (2) is incorrect.

Option (3)

Here, the third option is consistent and independent.

There exists a solution of the given system of equations so it is consistent.

Also, the solution is unique therefore the system of equations is independent.

Therefore, option (3) is correct.

Option (4)

Here, the fourth option is inconsistent and independent.

There exists a solution of the given system of equations so it is consistent.

Therefore, option (4) is incorrect.

Learn more:

1. A problem on circle brainly.com/question/9510228.

2. A problem on general equation of a circle brainly.com/question/1506955.

Answer details

Grade: High school

Subject: Mathematics

Chapter: System of linear equations

Keywords: Equations, unique solution, independent, dependent, consistent, inconsistent, infinite solutions, homogeneous equation, non- homogeneous equation, determinant.

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