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

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Use the multiplication principle to solve the problem.

A biologist is attempting to classify plant species by assigning 5 initials to each species. How many classifications are possible using this method?
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Find the inverse, if it exists, for the matrix.

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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 4 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 3 end cell end table

 

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Solve the problem.

If 2 cards are drawn from a deck of 52 cards, what is the expected number of spades?
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The table shows, for some particular year, a listing of several income levels and, for each level, the proportion of the population in the level and the probability that a person in that level bought a new car during the year. Given that one of the people who bought a new car during that year is randomly selected, find the probability that that person was in the indicated income category. Round your answer to the nearest hundredth.

$40,000 - $49,999
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Solve the problem.

How many ways can a committee of 6 be selected from a club with 10 members?
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Use the Gauss-Jordan method to solve the system of equations.

x - y + 3z = -8

x + 5y + z = 40

5x + y + 13z = 10
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The table shows, for some particular year, a listing of several income levels and, for each level, the proportion of the population in the level and the probability that a person in that level bought a new car during the year. Given that one of the people who bought a new car during that year is randomly selected, find the probability that that person was in the indicated income category. Round your answer to the nearest hundredth.

$50,000 and over
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Evaluate.

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Solve the problem.

Find the expected number of girls in a family of 7 children.
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