Are the expressions 12a + (6+3a) and 3(5a + 2) equivalent show your work and explain

Mathematics

2 answers:

bezimeni [28]3 years ago

8 0

12a + 6 + 3a = 15a + 2
15a = 15a - 4
0 = - 4

Eduardwww [97]3 years ago

3 0

I’m pretty sure it’s -4

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A company must select 4 candidates to interview from a list of 12, which consist of 8 men and 4 women.

Radda [10]

Part A

If 4 candidates were to be selected regardless of gender, that means that 4 candidates is to be selected from 12.

The number of possible selections of 4 candidates from 12 is given by

$^{12}C_4= \frac{12!}{4!(12-4)!}= \frac{12!}{4!\times8!} =11\times5\times9=495$

Therefore, the number of selections of 4 candidates regardless of gender is 495.

Part B:


If 4 candidates were to be selected such that 2 women must be selected, that means that 2 men candidates is to be selected from 8 and 2 women candidates is to be selected from 4.

The number of possible selections of 2 men candidates from 8 and 2 women candidates from 4 is given by

 $^{8}C_2\times ^{4}C_2= \frac{8!}{2!(8-2)!}\times 
\frac{4!}{2!(4-2)!} \\ \\ = 
\frac{8!}{2!\times6!}\times\frac{4!}{2!\times2!} 
=4\times7\times2\times3=168$

Therefore, the number of selections of 4 candidates such that 2 women must be selected is 168.

Part 3:

If 4 candidates were to be selected such that at least 2 women must be selected, that means that 2 men candidates is to be selected from 8 and 2 women candidates is to be selected from 4 or 1 man candidates is to be selected from 8 and 3 women candidates is to be selected from 4 of no man candidates is to be selected from 8 and 4 women candidates is to be selected from 4.

The number of possible selections of 2 men candidates from 8 and 2 women candidates from 4 of 1 man candidates from 8 and 3 women candidates from 4 of no man candidates from 8 and 4 women candidates from 4 is given by

$^{8}C_2\times ^{4}C_2+ ^{8}C_1\times ^{4}C_3+ ^{8}C_0\times ^{4}C_4 \\ \\ = \frac{8!}{2!(8-2)!}\times \frac{4!}{2!(4-2)!}+\frac{8!}{1!(8-1)!}\times \frac{4!}{3!(4-3)!}+\frac{8!}{0!(8-0)!}\times \frac{4!}{4!(4-4)!} \\ \\ = \frac{8!}{2!\times6!}\times\frac{4!}{2!\times2!}+\frac{8!}{1!\times7!}\times\frac{4!}{3!\times1!}+\frac{8!}{0!\times8!}\times\frac{4!}{4!\times0!} \\ \\ =4\times7\times2\times3+8\times4+1\times1=168+32+1=201$

Therefore, the number of selections of 4 candidates such that at least 2 women must be selected is 201.

7 0

3 years ago

Read 2 more answers

Trying to at least find the point slope form of a line

daser333 [38]

I think the third option is correct.

8 0

3 years ago

Please help me. Are my answers right?

V125BC [204]

I’m sorry but I don’t see the paper or the homework that you have

3 0