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2 years ago

How many rectangles (including squares) are there in a 4x4 square

Mathematics

2 answers:

saul85 [17]2 years ago

7 0

Answer:

Hello,

100

Step-by-step explanation:

a square 4*4 : wide=4 , lenght=4

number of rectangles= wide*(wide+1)*lenght*(lenght+1) /4 = 4*5*4*5/4=100

Proof:

1 per 1 : 16 (rectangles )

1 per 2: 3*4=12

1 per 3: 2*4=8

1 per 4: 1*4=4 so 4*(4+3+2+1)=4*10=40

2 per 1: 4*3

2 per 2: 3*3

2 per 3: 2*3

2 per 4: 1*3 so 3*(4+3+2+1)=30

3 per 1: 4*2

3 per 2: 3*2

3 per 3: 2*2

3 per 4: 1*2 so 2*(4+3+2+1)=20

4 per 1: 4

4 per 2: 3

4 per 3: 2

4 per 4: 1 so 1*(4+3+2+1)=10

Total=40+30+20+10=(4+3+2+1)*(4+3+2+1)=100

ale4655 [162]2 years ago

3 0

Answer:

70 squares

Step-by-step explanation:

this is my answer to your question

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John and Annie have two distinguishable ponds. Initially, each of the ponds contains four ducks and five geese. John first picks

Sladkaya [172]

Answer: 4/9

Step-by-step explanation:

The probability that annie picks a duck Pt= the probability of picking a duck without accounting for the added one (Po)+ probability of picking the added bird and it's a duck(Pi)

Pt = Po+Pi

Since the total number of birds in the right pond is 10 after the addition of one by john

Po= 4/10

Pi= the of john adding a duck × the probability of annie picking the added bird

Pi= 4/9 × 1/10

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Pt= 4/9

(This implies that the probability of picking a duck remain the same even after the addition of one bird from the left ponds because they both have equal proportions of duck and geese i.e the initial number of duck and geese in both right and left ponds are 4 and 5 respectively)

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