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Alex17521 [72]
3 years ago
8

Select the correct answer. Which expression is equivalent to this polynomial? 15x − 24 A. 5(3x − 8) B. 3(5x − 5) C. 3(5x − 24) D

. 3(5x − 8)
Mathematics
2 answers:
Scilla [17]3 years ago
6 0

15x-24

the answer is not B because 3*-5= -15, we need -24

the answer is not C because 3*-24= -72

the answer is not A because 5*8= 40

Answer :

D. 3(5x − 8)

(3)(5x)(3)(-8)

15x-24= 15x-24

muminat3 years ago
5 0

Answer: OPTION D.

Step-by-step explanation:

Given the following polynomial:

15x - 24

You can find an equivalent expression by factoring out the Greatest Common Factor (GCF).

In order to find the Greatest Common Factor, you need to descompose the coefficients 15 and 24 into their prime factors:

15=3*5\\24=2*2*2*3=2^3*3

You can observe that the Greatest Common Factor is:

GCF=3

Then, factoring out 3, you get:

3(5x-8)

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We're told that

P(A\cap B)=0.15

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where the last fact is due to the law of total probability:

P(A)=P(A\cap B)+P(A\cap B^C)

\implies P(A)=P(B\mid A)P(A)+P(B^C\mid A)P(A)

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so that B\mid A and B^C\mid A are complementary.

By definition of conditional probability, we have

P(B\mid A)=P(B^C\mid A)

\implies\dfrac{P(A\cap B)}{P(A)}=\dfrac{P(A\cap B^C)}{P(A)}

\implies P(A\cap B)=P(A\cap B^C)

We make use of the addition rule and complementary probabilities to rewrite this as

P(A\cap B)=P(A\cap B^C)

\implies P(A)+P(B)-P(A\cup B)=P(A)+P(B^C)-P(A\cup B^C)

\implies P(B)-[1-P(A\cup B)^C]=[1-P(B)]-P(A\cup B^C)

\implies2P(B)=2-[P(A\cup B)^C+P(A\cup B^C)]

\implies2P(B)=[1-P(A\cup B)^C]+[1-P(A\cup B^C)]

\implies2P(B)=P(A\cup B)+P(A\cup B^C)^C

\implies2P(B)=P(A\cup B)+P(A^C\cap B)\quad(*)

By the law of total probability,

P(B)=P(A\cap B)+P(A^C\cap B)

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and substituting this into (*) gives

2P(B)=P(A\cup B)+[P(B)-P(A\cap B)]

\implies P(B)=P(A\cup B)-P(A\cap B)

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