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vekshin1
4 years ago
10

Solve x: 9x - 6/5 = -12

Mathematics
2 answers:
tiny-mole [99]4 years ago
3 0
9x - 6/5 = -12
Convert -12 to -60/5
9x - 6/5 = -60/5
Add 6/5 to both sides
9x - 6/5 + 6/5 = -60/5 + 6/5
9x = -54/5
divide both sides by 9
x = -6/5
mrs_skeptik [129]4 years ago
3 0

9x-\dfrac{6}{5}=-12\qquad\text{multiply both sides by 5}\\\\45x-6=-60\qquad\text{add 6 to both sides}\\\\45x=-54\qquad\text{divide both sides by 45}\\\\x=-\dfrac{54:9}{45:9}\\\\\boxed{x=-\dfrac{6}{5}}\to\boxed{x=-1\dfrac{1}{5}}

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Answer:

12,13 and 14

Step-by-step explanation:

Let the three consecutive integers be n, n+1 and n+2

ATQ,

The sum of twice the second integer and 4 times the third integer is two less than seven times the first integer.

[2(n+1)+4(n+2)] = 7n-2

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2n+2+4n+8=7n-2

Taking like terms together,

6n-7n = -2-8-2

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So,

First integer = 12

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3 years ago
A tobacco company claims that the nicotine content of its "light" cigarettes has a mean of milligrams and a standard deviation o
valina [46]

The missing values in the given question is shown below.

A tobacco company claims that the nicotine content of its "light" cigarettes has a mean of 1.5 milligrams and a standard deviation of 0.52 milligrams. What is the probability that 50 randomly selected light cigarettes from this company will have a total combined nicotine content of 81 milligrams or less, assuming the company's claims to be true? Carry your intermediate computations to at least four decimal places. Report your result to at least three decimal places.

Answer:

P(x ≤ 1.62) = 0.949    to three decimal places.

Step-by-step explanation:

From the question; given that:

The population mean = 1.5

The standard deviation = 0.52

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The sample mean \overline x = \dfrac{81}{50} = 1.62

Hence; we can calculate the required probability as:

P( x \leq 1.62) = P \bigg (\dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{\overline x -1.5 }{\dfrac{\sigma}{\sqrt{n}}} \bigg )

P( x \leq 1.62) = P \bigg (Z \leq \dfrac{1.62 -1.5 }{\dfrac{0.52}{\sqrt{50}}} \bigg )

P( x \leq 1.62) = P \bigg (Z \leq \dfrac{0.12 }{\dfrac{0.52}{\sqrt{50}}} \bigg )

P( x \leq 1.62) = P \bigg (Z \leq 1.632 \bigg )

From z - tables;

P(x ≤ 1.62) = 0.9486

P(x ≤ 1.62) = 0.949    to three decimal places.

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