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ddd [48]
3 years ago
8

Solving Two-Step Inequalities

Mathematics
1 answer:
Nuetrik [128]3 years ago
6 0

Answer:

x > \frac{9}{5}

Step-by-step explanation:

Given

\frac{2}{3} x - \frac{1}{5} > 1

Multiply through by 15 to clear the fractions

10x - 3 > 15 ( add 3 to both sides )

10x > 18 ( divide both sides by 10 )

x > \frac{18}{10} , that is

x > \frac{9}{5}

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3 years ago
A national survey of companies included a question that asked whether the company had at least one bilingual telephone operator.
nirvana33 [79]

Answer:

The first option is correct. Option A is correct.

LCL = 0.270, and UCL = 0.397

80% Confidence interval = (0.270, 0.397)

Step-by-step explanation:

The data for Y and N for the 90 companies is attached to this solution provided.

Y represents companies with at least 1 bilingual operator and N represents companies with no bilingual operator.

The number of Y in the data = 30

Hence, sample proportion of companies with at least one bilingual operator = (30/90) = 0.3333

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion = 0.3333

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 80% confidence level for sample size of 90 is obtained from the z-tables.

Critical value = 1.280

Standard error of the mean = σₓ = √[p(1-p)/n]

p = sample proportion

n = sample size = 90

σₓ = √[0.3333×0.6667)/90] = 0.0496891568 = 0.04969

80% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.3333 ± (1.28 × 0.04969)

CI = 0.3333 ± 0.0636021207

80% CI = (0.2696978793, 0.3969021207)

80% Confidence interval = (0.270, 0.397)

Hope this Helps!!!

3 0
3 years ago
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