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kakasveta [241]
2 years ago
7

If ƒ(x ) = 3x + 1 and and ƒ -1 = , then the ordered pair of ƒ -1(10) = (10, 31) (10, 3) (3, 10)

Mathematics
1 answer:
MAXImum [283]2 years ago
6 0
        f(x) = 3x + 1
           y = 3x + 1
      y - 1 = 3x + 1 - 1
      <u>y - 1</u> = <u>3x</u>
         3       3
¹/₃y - ¹/₃ = x
           y = ¹/₃x - ¹/₃
      f⁻¹(x) = ¹/₃x - ¹/₃
    f⁻¹(10) = ¹/₃(10) - ¹/₃
    f⁻¹(10) = 3¹/₃ - ¹/₃
    f⁻¹(10) = 3
It is equal too (10, 3).
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For the random variable N_1 we define the possible values for this variable on this case [1,2,3,4,5] . We know that we have 2 defective transistors so then we have 5C2 (where C means combinatory) ways to select or permute the transistors in order to detect the first defective:

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We want the first detective transistor on the ath place, so then the first a-1 places are non defective transistors, so then we can define the probability for the random variable N_1 like this:

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And if we want to find the joint probability we just need to do this:

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And if we multiply the probabilities founded we got:

P(N_1 = a , N_2 = b)= \frac{1}{5-a C 1} * \frac{5-a C 1}{5C2} = \frac{1}{5C2}=\frac{1}{10}

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