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Reil [10]
3 years ago
11

0%5Cfrac%7B4%7D%7Bx%20%2B%203%7D%20%20" id="TexFormula1" title="3 + \frac{x - 3}{9 - {x}^{2} } \div 3 - \frac{4}{x + 3} " alt="3 + \frac{x - 3}{9 - {x}^{2} } \div 3 - \frac{4}{x + 3} " align="absmiddle" class="latex-formula">

Mathematics
1 answer:
malfutka [58]3 years ago
7 0

\frac{3 +  \frac{x - 3}{9 -  {x}^{2} } }{3 -\frac{4}{x + 3} }  \\  =  \frac{ \frac{3(9 -  {x}^{2} ) + x - 3}{9 -  {x}^{2} } }{ \frac{3(x + 3) - 4}{x + 3} }  \\  =  \frac{27 - 3 {x}^{2}  + x - 3}{9 -  {x}^{2} }  \times  \frac{x + 3}{3x + 12 - 4}  \\  =  \frac{ - 3 {x}^{2} + x + 24 }{ - (x - 3)(x + 3)}  \times  \frac{x + 3}{3x + 8}  \\  =   \frac{ - (3x + 8)(x - 3)}{ - (x - 3)}  \times  \frac{1}{3x + 8}  \\  =   \frac{ - (x - 3)}{ - (x - 3)}  \\  = 1

Hope this helps. - M
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Write the equation of the parabola in vertex form.
givi [52]

Answer: -9 = a(1 - 3)² + 3

Step-by-step explanation:

Vertex Form Equation:

y = a(x - h)² + k

vertex: (h, k) which means

h = 3

k = 3

because your vertex is (3, 3).

Your point is (1, -9) which is (x, y).

This means

x = 1

y = -9

Now, plug everything into your Vertex Form Equation:

-9 = a(1 - 3)² + 3

That’s your equation and final answer, but of course, if you need to, you can solve for a if you need to.

If a is positive, the parabola opens up. If a is negative, the parabola opens down.

Hope this helps!

3 0
3 years ago
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Grace [21]
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5 0
2 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!!!

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