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emmainna [20.7K]
1 year ago
6

A company gives each worker a cash bonus every Friday, randomly giving a worker an amount with these probabilities: $10 - 0.75,

$50 - 0.25. Over many weeks, what is a worker's expected weekly bonus?
1. 10 x 0.25 + 50 x 0.75 = $40
2. (10 + 50) x (0.75 x 0.25) = $11.5
3. 10 x 0.75 + 50 x 0.25 = $20
4. Cannot say as the number of weeks is not provided.
Mathematics
1 answer:
vredina [299]1 year ago
4 0

Answer:

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Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse
Drupady [299]

Answer:

a'(d) = \frac{d}{5} + \frac{3}{5}

a(a'(d)) = a'(a(d)) = d

Step-by-step explanation:

Given

a(d) = 5d - 3

Solving (a): Write as inverse function

a(d) = 5d - 3

Represent a(d) as y

y = 5d - 3

Swap positions of d and y

d = 5y - 3

Make y the subject

5y = d + 3

y = \frac{d}{5} + \frac{3}{5}

Replace y with a'(d)

a'(d) = \frac{d}{5} + \frac{3}{5}

Prove that a(d) and a'(d) are inverse functions

a'(d) = \frac{d}{5} + \frac{3}{5} and a(d) = 5d - 3

To do this, we prove that:

a(a'(d)) = a'(a(d)) = d

Solving for a(a'(d))

a(a'(d))  = a(\frac{d}{5} + \frac{3}{5})

Substitute \frac{d}{5} + \frac{3}{5} for d in  a(d) = 5d - 3

a(a'(d))  = 5(\frac{d}{5} + \frac{3}{5}) - 3

a(a'(d))  = \frac{5d}{5} + \frac{15}{5} - 3

a(a'(d))  = d + 3 - 3

a(a'(d))  = d

Solving for: a'(a(d))

a'(a(d)) = a'(5d - 3)

Substitute 5d - 3 for d in a'(d) = \frac{d}{5} + \frac{3}{5}

a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}

Add fractions

a'(a(d)) = \frac{5d - 3+3}{5}

a'(a(d)) = \frac{5d}{5}

a'(a(d)) = d

Hence:

a(a'(d)) = a'(a(d)) = d

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2 years ago
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A small company plans to invest in a new advertising campaign. There is a 20% chance that the company will lose $5,000, a 50% ch
Viktor [21]

A small company plans to invest in a new advertising campaign.

There is a 20% chance that the company will lose $5,000 ,

50% chance of a break even, and a 30% chance of a $10,000 profit


So the expected value from the advertisement campaign is calculated as - 20% of 5000 + 0% of 5000 + 30% of 10,000

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The expected value from the advertisement campaign is $2000.

So the Company must go ahead with the campaign.


Answer : Option A


Hope it helps.


Thank you ..!!

3 0
3 years ago
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