Solve the inequality. 5 - 4x > 3x - 9

Mathematics

2 answers:

azamat3 years ago

7 0

Answer:

x < 2

Step-by-step explanation:

I took the test.. got it correct!

Olegator [25]3 years ago

6 0

Answer:

2 >x

Step-by-step explanation:

5 - 4x > 3x - 9

Add 4x to each side

5 - 4x+4x > 3x+4x - 9

5 > 7x-9

Add 9 to each side

5+9> 7x-9+9

14>7x

Divide each side by 7

14/7 >7x/7

2 >x

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Plastic parts produced by an injection-molding operation are checked for conformance to specifications. Each tool contains 15 ca

Rainbow [258]

Answer:

(A) 0.006593 or 0.6593%

(B) 0.01538 or 1.538%

Step-by-step explanation:

The total number of possibilities to pick 3 parts out of 15 possible parts is given by the following combination:

$n=\frac{15!}{(15-3)!3!}=\frac{15*14*13}{3*2*1}\\n=455\ ways\\$

(A) There are only three possibilities for which the inspector finds exactly one nonconforming part (NCC, CNC, CCN). Therefore, the probability is:

$P(N=1) = \frac{3}{455}=0.006593 =0.6593\%$

(B) There are three possibilities for which the inspector finds exactly one nonconforming part, three possibilities for two nonconforming parts (NNC, CNN, NCN), and one possibility for all nonconforming parts (NNN). The probability that the inspector finds at least one nonconforming part is:

$P(N>0) =P(N=1)+P(N=2)+P(N=3) \\P(N>0) = \frac{3}{455}+ \frac{3}{455}+ \frac{1}{455}\\P(N>0) =0.01538 =1.538\%$