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3 years ago

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Which is the solution set of the compound inequality 3.5 x -10> -3 and 8x -9 <39

2 answers:

aivan3 [116]3 years ago

7 0

3.5x-10>-3 add 10 to both sides

3.5x>13 divide both sides by 3.5

x>26/7

x=(26/7, +oo)

...

8x-9<39 add 9 to both sides

8x<48 divide both sides by 8

x<6

x=(-oo,6)

Since this is a compound inequality with AND the solution set will be the union of the two intervals found above.

x=(26/7, 6)

Zielflug [23.3K]3 years ago

7 0

Answer:

2<x<6

Step-by-step explanation:

I graphed it

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(b) 0.36909

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Step-by-step explanation:

Given information:

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(b)Three or four will be drunken drivers.

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$P(x=3\text{ or }x=4)=P(x=3)+P(x=4)$

Using binomial we get

$P(x=3\text{ or }x=4)=^{12}C_{3}(0.2)^{3}(0.8)^{12-3}+^{12}C_{4}(0.2)^{4}(0.8)^{12-4}$

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Therefore, the probability that three or four will be drunken drivers is 0.3691.

(c)

At least 7 will be drunken drivers.

$P(x\geq 7)=1-P(x$

$P(x\leq 7)=1-[P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)+P(x=6)]$

$P(x\leq 7)=1-[0.06872+0.20616+0.28347+0.23622+0.13288+0.05315+0.0155]$

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$P(x\leq 7)=0.0039$

Therefore, the probability of at least 7 will be drunken drivers is 0.0039.

(d) At most 5 will be drunken drivers.

$P(x\leq 5)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)$

$P(x\leq 5)=0.06872+0.20616+0.28347+0.23622+0.13288+0.05315$

$P(x\leq 5)=0.9806$

Therefore, the probability of at most 5 will be drunken drivers is 0.9806.

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