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3 years ago

If p(a) = 1/3, p(b) = 2/5, and p(a ∪ b) = 3/5, then p(a ∩ b) =

Mathematics

1 answer:

Mumz [18]3 years ago

8 0

P(a ∪ b) = p(a) + p(b) - p(a ∩ b)
p(a ∩ b) = p(a) + p(b) - p(a ∪ b)
p(a ∩ b) = 1/3 + 2/5 - 3/5
p(a ∩ b) = 2/15

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Help me please!

telo118 [61]

Answer:

$f^{-1}(6) = 50$

Step-by-step explanation:

Given

$f(x) = \sqrt{2x} - 4$

Required

Find $f^{-1}(6)$

First, we calculate the inverse function

$f(x) = \sqrt{2x} - 4$

Express f(x) as y

$y = \sqrt{2x} - 4$

Swap the positions of x and y

$x = \sqrt{2y} - 4$

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$4 + x = \sqrt{2y}$

Square both sides

$(4 + x)^2 = 2y$

Divide both sides by 2

$y = \frac{(4 + x)^2}{2}$

Express y as an inverse function

$f^{-1}(x) = \frac{(4 + x)^2}{2}$

Next, solve for: $f^{-1}(6)$

Substitute 6 for x

$f^{-1}(6) = \frac{(4 + 6)^2}{2}$

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50 point HELP ASAP Question: A rectangle has sides measuring (3x + 8) units and (6x + 5) units.

cluponka [151]

Answer:

see below

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(3x + 8) units by (6x + 5) units.

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= (3x+8)(6x+5)

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Answer: No, New York students are not truly more nerdy than the California students.

Step-by-step explanation:

Since we have given that

Number of students in a group = 50

Mean score of New York psychology = 530

Mean score of California psychology = 515

Standard deviation = 80

So, we will find t-distribution first.

$t=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\t=\dfrac{530-515}{\dfrac{80}{\sqrt{50}}}\\\\t=1.32$

Let α = 5% = 0.05

So, $t_{\alpha,2}=2.920$

Since t < t(critical value)

No, New York students are not truly more nerdy than the California students.

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Answer:

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Elanso [62]

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