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Sonbull [250]
3 years ago
7

Of the students in your class, 12% are left-handed. What fraction of the students are left-handed? Are there more right-handed o

r left-handed students? Explain. Write your answers in simplest form.
Mathematics
1 answer:
kvv77 [185]3 years ago
4 0
The left-handed students
12% are left handed, percent means per hundred. Change percent into per 100.
12% = \dfrac{12}{100}

Then simplify the fraction by dividing the numerator and denominator by 4
\dfrac{12}{100}
= \dfrac{12:4}{100:4}
= \dfrac{3}{25}
This is the fraction showing the proportion of the left-handed students

The right-handed students
Determine the fraction showing the proportion of the right-handed students
1 - the left-handed
= 1 - \dfrac{3}{25}

Equalize the denominator to 25
\dfrac{25}{25} - \dfrac{3}{25}

Simplify
\dfrac{21}{25}
This is the proportion of the right-handed students

<span>Are there more right-handed or left-handed students?
There are more right-handed students than the left-handed students, because 21/25 is more than 3/25</span>
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Read 2 more answers
Using properties of sets show that : a) A ∩ (A’ U B) = A ∩ B b) A ∩ (A U B )’ = Ф
asambeis [7]

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a) From A ∩ A' = ∅, we have;

A ∩ (A' ∪ B) = A ∩ B

b) From A ∩ (A' ∩ B') = (A ∩ A') ∩ B' and A ∩ A' = ∅, we have;

A ∩ (A ∪ B)' = ∅

Step-by-step explanation:

a) By distributive law of sets, we have;

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

From the complementary law of sets, we have;

A ∩ A' = ∅

Therefore, for A ∩ (A' ∪ B) = A ∩ B, we have

A ∩ (A' ∪ B) = (A ∩ A') ∪ (A ∩ B) (distributive law of sets)

A ∩ A' = ∅ (complementary law of sets)

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(A ∩ A') ∪ (A ∩ B) = ∅ ∪ (A ∩ B)  = (A ∩ B) (Addition to zero identity property)

∴  A ∩ (A' ∪ B) = A ∩ B

b) By De Morgan's law

(A ∪ B)' = A' ∩ B'

Therefore, A ∩ (A ∪ B)' = A ∩ (A' ∩ B')

By associative law of sets, we have;

A ∩ (A' ∩ B') = (A ∩ A') ∩ B'

A ∩ A' = ∅ (complementary law of sets)

Therefore, (A ∩ A') ∩ B' = ∅  ∩ B' = ∅

Which gives;

A ∩ (A ∪ B)' = ∅.

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3 years ago
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