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Viefleur [7K]
3 years ago
8

Inverse Function: f-¹ (- 3) f(x) = 6x - 12

Mathematics
1 answer:
sp2606 [1]3 years ago
7 0
       f(x) = 6x - 12
          y = 6x - 12
  y + 12 = 6x - 12 + 12
  <u>y + 12</u> = <u>6x</u>
      6         6
¹/₆y + 2 = x
          y = ¹/₆x + 2
     f⁻¹(x) = ¹/₆x + 2
    f⁻¹(-3) = ¹/₆(-3) + 2
    f⁻¹(-3) = -¹/₂ + 2
    f⁻¹(-3) = 1¹/₂
(x, f⁻¹(x)) = (-3, 1¹/₂)
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Two ballpoint pens are selected at random from a box that contains 3 blue pens, 2 red pens, and 3 green pens. If X is the number
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Answer:

a) f(x,y) =\frac{\binom{3}{x}\binom{2}{y}\binom{3}{2-x-y}}{\binom{8}{2}} ;   x = 0, 1 , 2;  y = 0, 1 , 2; 0 ≤ x+y ≥ 2

b) = \frac{9}{14}

Step-by-step explanation:

joint probability is a function that characterizes the distribution of a random variable. If X and Y be two random variables then the joint probability will be P(X = x, Y=y)

Given Data,

X = The number of blue Pens

Y = The number of red Pens

a)

possible outcomes(X, Y) are (0, 0), (0, 1), (1, 0), (1, 1), (0, 2), (2,0)

Please refer fig. also

total number ways of selecting any 2 pens = \binom{8}{2}= \frac{8!}{2! 6!} =28

f(x,y) = \frac{\binom{3}{x}\binom{2}{y}\binom{3}{2-x-y}}{\binom{8}{2}} ;   x = 0, 1 , 2;  y = 0, 1 , 2; 0 ≤ x+y ≥ 2

b)

P(X,Y)∈A = P(X + Y ≤ 1)

= P(0,0) + P(1,0) + P(0,1)

= \frac{3}{28} + \frac{3}{14} + \frac{9}{28}

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A regular polygon has an interior angle of approximately 158.8°.
Step2247 [10]

Answer:

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Step-by-step explanation:

<u>Property of regular polygons:</u>

  • Sum of Interior Angles = (n−2) × 180°, where n is number of sides

<u>In our case we have:</u>

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5 0
3 years ago
Q.2 - What is the value of y in the equation 3(4y - 12) = 0 ? Show your work.
Alex

Hey there!

3(4y - 12) = 0

3(4y) + 3(-12) = 0

12y - 36 = 0

Add 36 to both sides

12y - 36 + 36 = 0 + 36

Cancel out: -36 + 36 because it give you 0

Keep: 0 + 36 because it help solve for the equation

New equation: 12y = 0 + 36

Simplify it

12y = 36

DIVIDE 12 to both sides

12y/12 = 36/12

Cancel out: 12/12 because that give you 1

Keep: 36/12 because it give you the y-value (also known as your overall result)

New equation: y = 36/12

Simplify it

y = 3


Therefore, your answer should be:

y = 3


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

5 0
2 years ago
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