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2 years ago

What is 9| - z/3| + 6 < 30

2 answers:

4 0

9|⁻¹/₃z| + 6 < 30
9|⁻¹/₃z| + 6 < ±30
9|⁻¹/₃z| + 6 < 30 or 9|⁻¹/₃z| + 6 > -30
9(¹/₃z) + 6 < 30 or 9(¹/₃z) + 6 > -30
3z + 6 < 30 or 3z + 6 > -30
- 6 - 6 - 6 - 6
3z < 24 or 3z > -24
3 3 3 3
z < 8 or z > -8

Solution Set: {z|z < 8 or z > -8} and (-∞, 8) or (-8, ∞)

Aleks [24]2 years ago

4 0

$9|- \frac{z}{3} | + 6 \ \textless \ 30 \\ \\ 9 \times \frac{z}{3} + 6 \ \textless \ 30 \\ \\ 3z + 6 \ \textless \ 30 \\ \\ 3z \ \textless \ 30 - 6 \\ \\ 3z \ \textless \ 24 \\ \\ z \ \textless \ \frac{24}{3} \\ \\ z \ \textless \ 8 \\ \\ Answer: z \ \textless \ 8$

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Step-by-step explanation:

Given the following expression shown in the picture:

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Then, in order to simplify the expression, you can follow the following steps:

Step 1. You need to multiply the numerator and the denominator of the fraction by $3+\sqrt{2}$ , which is the conjugate of the denominator $3-\sqrt{2}$ .

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Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

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$Z = \frac{X - \mu}{\sigma}$

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