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2 years ago

Multiply. {}=3\dfrac{1}{2} \times 3\dfrac12=3 2 1 ×3 2 1

Mathematics

1 answer:

Inessa [10]2 years ago

4 0

I assume you mean the product of mixed numbers,

3 1/2 × 3 1/2

If we write this as

(3 + 1/2) × (3 + 1/2) = (3 + 1/2)²

we can use the identity

(a + b)² = a² + 2ab + b²

so that

3 1/2 × 3 1/2 = 3² + (2 × 3 × 1/2) + (1/2)²

3 1/2 × 3 1/2 = 9 + 3 + 1/4

3 1/2 × 3 1/2 = 12 1/4

Alternatively, we can first write 3 1/2 as a mixed number:

3 + 1/2 = 6/2 + 1/2 = (6 + 1)/2 = 7/2

Then

3 1/2 × 3 1/2 = 7/2 × 7/2 = (7 × 7) / (2 × 2) = 49/4

and

49/4 = (48 + 1)/4 = ((4 × 12) + 1)/4 = 12 + 1/4

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g If there are 52 cards in a deck with four suits (hearts, clubs, diamonds, and spades), how many ways can you select 5 diamonds

dezoksy [38]

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The number of ways to select 5 diamonds and 3 clubs is 368,082.

Step-by-step explanation:

In a standard deck of 52 cards there are 4 suits each consisting of 13 cards.

Compute the probability of selecting 5 diamonds and 3 clubs as follows:

The number of ways of selecting 0 cards from 13 hearts is:

${13\choose 0}=\frac{13!}{0!\times(13-0)!} =\frac{13!}{13!}=1$

The number of ways of selecting 3 cards from 13 clubs is:

${13\choose 3}=\frac{13!}{3!\times(13-3)!} =\frac{13!}{13!\times10!}=286$

The number of ways of selecting 5 cards from 13 diamonds is:

${13\choose 5}=\frac{13!}{5!\times(13-5)!} =\frac{13!}{13!\times8!}=1287$

The number of ways of selecting 0 cards from 13 spades is:

${13\choose 0}=\frac{13!}{0!\times(13-0)!} =\frac{13!}{13!}=1$

Compute the number of ways to select 5 diamonds and 3 clubs as:

${13\choose0}\times{13\choose3}\times{13\choose5}\times{13\choose0} = 1\times286\times1287\times1=368082$

Thus, the number of ways to select 5 diamonds and 3 clubs is 368,082.

6 0

3 years ago

Multiply. {}=3\dfrac{1}{2} \times 3\dfrac12=3 2 1 ​ ×3 2 1 ​

Multiply. {}=3\dfrac{1}{2} \times 3\dfrac12=3 2 1 ×3 2 1