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Vanyuwa [196]
3 years ago
14

There are `15` pieces of fruit in a bowl, and `6` of them are apples.

Mathematics
2 answers:
zalisa [80]3 years ago
5 0

Answer:

40% of the pieces of fruit in the Bowl are apples.

Step-by-step explanation:

Given the statement:- There are 15 pieces of fruit in a bowl and six of them are apples.

⇒ Total number of pieces of fruit in a bowl = 15 pieces

and

Number of pieces of apple in a bowl = 6 pieces.

To find the percentage of the pieces of fruit in the Bowl are apples.

=

Therefore, 40% of the pieces of fruit in the Bowl are apples.

Advocard [28]3 years ago
4 0

Answer:

percent of apples = 40%

percent that is not apple = 60%

Step-by-step explanation:

percent of apples = 6/15 × 100% = 40%

percent that is not apple = 9/15 × 100% = 60%

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3 years ago
Using properties of sets show that : a) A ∩ (A’ U B) = A ∩ B b) A ∩ (A U B )’ = Ф
asambeis [7]

Answer:

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)

Therefore;

(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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Step-by-step explanation:

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