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irina [24]
2 years ago
5

Solve the following 1) 2(x + 3) = x - 42) 4(5x-2) = 2(9x+3)PLS HELP ​

Mathematics
1 answer:
gayaneshka [121]2 years ago
6 0

Answer:

(1) x = -4 (2) x = 7

Step-by-step explanation:

From the first equation:

2(x + 3) = x - 4\\\implies x =  2(x + 3) + 4\\\implies x = 2x + 6 + 4\\\implies x = 2x + 4\\\implies -4 = 2x - x\\\implies x = -4

From the second equation,

4(5x - 2) = 2(9x + 3)\\\implies 20x - 8 = 18x +6\\\implies 20x - 18x - 8 -6 = 0\\\implies 2x -14 = 0\\\implies 2x = 14\\\implies x = \frac{14}{2} = 7

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Answer:

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Step-by-step explanation:

We are given that a soda bottling company’s manufacturing process is calibrated so that 99% of bottles are filled to within specifications, while 1% is not within specification.

Every hour, 12 random bottles are taken from the assembly line and tested. If 2 or more bottles in the sample are not within specification, the assembly line is shut down for recalibration.

Let X = <u><em>Number of bottles in the sample that are not within specification</em></u>.

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P(X=r)=\binom{n}{r} \times p^{r}\times (1-p)^{n-r};x=0,1,2,3,.....

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So, X ~ Binom (n = 12, p = 0.01)

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                 = 1-(1 \times 1\times 0.99^{12})-(12 \times 0.01^{1}\times 0.99^{11})

                 = <u>0.00617</u>

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