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3 years ago

Write a mathmatical proof showing the algebraic equivalency of the following equation: (2x)(3y)(4z) = 24xyz

Mathematics

2 answers:

Blababa [14]3 years ago

8 0

Answer:

We have to evaluate

→ (2x)×(3y)×(4z)

Using Commutativity property of numbers,which states ----a b=ba

→ (x×2×3×y)×(4z)

→x×(6y)×(4z)

→x ×(y×6×4×z)----Again used Commutative property

→x × (y×24×z)

Using associativity property of numbers,which states

---a×(b×c)=(a×b)×c=(a×c)×b

→x ×(24 yz)--------(1)

Using commutative Property between x and 24 ,that is

(x)×(24)=24 x

Expression 1, can be written as

→24 xyz

Hence Proved

RSB [31]3 years ago

4 0

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Answer with Step-by-step explanation:

We are given that

P(A)=0.4 and P(B)=0.7

We know that

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We know that

Maximum value of $P(A\cup B)$ =1 and minimum value of $P(A\cup B)$ =0

$0\leq P(A\cup B )\leq 1$

$0\leq P(A)+P(B)-P(A\cap B)\leq 1$

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$0\leq 1.1-P(A\cap B)\leq 1$

$0\leq 1.1-P(A\cap B)$

$P(A\cap B)\leq 1.1$

It is not possible that $P(A\cap B)$ is equal to 1.1

$1.1-P(A\cap B)\leq 1$

$-P(A\cap B)\leq 1-1.1=-0.1$

Multiply by (-1) on both sides

$P(A\cap B)\geq 0.1$

Again, $P(A\cup B)\geq P(B)$

$0.4+0.7-P(A\cap B)\geq 0.7$

$1.1-P(A\cap B)\geq 0.7$

$-P(A\cap B)\geq -1.1+0.7=-0.4$

Multiply by (-1) on both sides

$P(A\cap B)\leq 0.4$

Hence, $0.1\leq P(A\cap B)\leq 0.4$

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