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kakasveta [241]
3 years ago
13

Express 356 miles in 8 hours as a unit rate

Mathematics
2 answers:
natulia [17]3 years ago
3 0
356/8 = 44.5

44.5 miles/hour
44.5 miles per hour
Lelechka [254]3 years ago
3 0
The unit is miles per hour
so you would divide 356 by 8 
answer is 44.5 mph which can also be written as 44.5 mi/hr
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3 years ago
For each statement, write what would be assumed and what would be proven in a proof by contrapositive of the statement. Then wri
Anna007 [38]

Answer:

a)

Given Statement - If x and y are a pair of consecutive integers, then x and y have opposite parity.

Proof by Contrapositive:

Assumed statement: Suppose that integers x and y do not have opposite parity.

Proven Statement: x and y are not a pair of consecutive integers.

Proof -

x = 2u₁ , y = 2u₂

Then

(x, x+1) = (2u₁ , 2u₁ + 1) = (Even, odd)

If y = 2u₁ + 1

Not possible

⇒x and y are not a pair of consecutive integers.

Hence proved.

Proof by Contradiction:

Assumed statement: Suppose x and y are not a pair of consecutive integers.

Proven Statement: Suppose x and y do not have opposite parity.

Proof -

If x and y are not a pair of consecutive integers.

⇒ either x and y are odd or even

If x and y are odd

⇒x and y have same parity

Contradiction

If x and y are even

⇒x and y have same parity

Contradiction

(b)

Proof by Contrapositive:

Assumed statement: Let n be an integer such that n is not odd (i.e. n is an even integer)

Proven Statement: n² is not odd (i.e n² is even)

Proof -

Let n is even

⇒n = 2m

⇒n² = (2m)² = 4m²

⇒n² is even

Hence proved.

Proof by Contradiction:

Assumed statement: Let n be an integer such that n² be odd.

Proven Statement:  suppose that n is not odd (i.e n is even)

Proof -

Let n² is odd

⇒n² is even

⇒n² = 2m

⇒2 | n²

⇒2 | n

⇒n = 2x

⇒ n is even

Contradiction

8 0
3 years ago
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