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Mazyrski [523]
3 years ago
7

Juanita has a storage closest at her shop with extra bottles of lotion and shower gel. Some are scented and some are unscented.

If she reaches into the closest and grabs a bottle without looking, she has 42% chance of grabbing a bottle of shower gel.
For the events "shower gel" and "scented" to be independent, what must be shown to be true?
Mathematics
2 answers:
Eddi Din [679]3 years ago
7 0
<span>P(shower gel | scented) = 42%</span>
Kisachek [45]3 years ago
7 0

Answer:

The probability of choosing a shower gel given the item is scented must be the same as grabbing shower gel, or 42%.

Step-by-step explanation:

To determine if two events are independent using their probabilities, we look for:

P(A|B) = P(A);

P(B|A) = P(B);

or P(A∩B) = P(A)·P(B)

We know that the probability she chooses a shower gel is 42%.  Letting this be event A, we have:

P(shower gel | scented) = P(shower gel) = 42%

This must be true for the events to be independent.

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The product of <em>z₁ =</em> 3 · (cos 14π/15 + i · sin 14π/15) and <em>z₂ =</em> 3 √3 · (cos 11π/15 + i · sin 11π/15) in <em>rectangular</em> form with fully simplified expressions is <em>z₁ · z₂ =</em> 7.794 - i · 13.5.

<h3>How to determine the product of two complex numbers</h3>

Let be two numbers of the form <em>z = a + i · b</em>, where <em>i =</em> √-1, the product of two of these numbers in <em>rectangular</em> form is described by the following formula:

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If we know that a = 3 · cos 14π/15, b = 3 · sin 14π/15, c = 3√3 · cos 11π/15, d = 3√3 · sin 11π/15, then the result in rectangular form is:

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The product of <em>z₁ =</em> 3 · (cos 14π/15 + i · sin 14π/15) and <em>z₂ =</em> 3 √3 · (cos 11π/15 + i · sin 11π/15) in <em>rectangular</em> form with fully simplified expressions is <em>z₁ · z₂ =</em> 7.794 - i · 13.5. \blacksquare

<h3>Remark</h3>

The statement presents typing mistakes and is poorly formatted, the correct form is introduced below:

<em>Given the complex number z₁ = 3 · (cos 14π/15 + i · sin 14π/15) and z₂ = 3 √3 · (cos 11π/15 + i · sin 11π/15), express the result of z₁ · z₂ in rectangular form with fully simplified fractions and radicals.</em>

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