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Mathematics II. (GT_AGMNE013, GT_AKMNE014-17) 2024/2025_2

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Find the inverse, if it exists, for the matrix.

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Provide an appropriate response.

If S = is a sample space of an experiment with events E = and then E F' =
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Solve the problem.

Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3.00 for rolling 4 or 5. What is your expected payback?
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Solve the system of equations below. For the answer provide only the value of  x1 !

table row cell x subscript 1 end cell minus cell x subscript 2 end cell plus cell 3 x subscript 3 end cell cell equals 5 end cell end table
table row cell negative 2 x subscript 1 end cell cell plus space space end cell cell 5 x subscript 2 end cell plus cell 2 x subscript 3 end cell cell equals 1 end cell end table
table row cell space space space space space space end cell blank cell x subscript 2 end cell plus cell 3 x subscript 3 end cell cell equals 4 end cell end table

 

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Use the Gauss-Jordan method to solve the system of equations.

5x - y + z = 8

7x + y + z = 6

12x + 2z = 14
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Find the probability.

Assuming that boy and girl babies are equally likely, find the probability that a family with four children has all boys given that the first two are boys.
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Solve the problem.

In a lottery, players must pick 6 different numbers from 1 to 21. How many ways are there to choose the 6 numbers if order is important?
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Use the Gauss-Jordan method to solve the system of equations.

x + y + z = 7

x - y + 2z = 7

2x + 3z = 14
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Solve the system of equations below. For the answer provide only the value of  x1 !

table row cell x subscript 1 end cell minus cell x subscript 2 end cell plus cell 3 x subscript 3 end cell cell equals 3 end cell end table
table row cell negative 2 x subscript 1 end cell plus cell 5 x subscript 2 end cell plus cell 5 x subscript 3 end cell cell equals 2 end cell end table
table row cell negative 2 x subscript 1 end cell plus cell 2 x subscript 2 end cell minus cell 2 x subscript 3 end cell cell equals 1 end cell end table

 

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Provide an appropriate response.

A building contractor can order lumber from 5 suppliers, bricks from 4 suppliers, and hardware from 8 suppliers. If the contractor chooses one supplier for each item, how many choices are available for the three items?
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