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UNO [17]
3 years ago
13

Find an equation of the line that passes through (3,4) and parallel to 4x-2y=5

Mathematics
1 answer:
Alex73 [517]3 years ago
4 0
       4x - 2y = 5
4x - 4x - 2y = -4x + 5
             -2y = -4x + 5
              -2         -2
                y = 2x - 2¹/₂

          y - y₁ = m(x - x₁)
           y - 4 = 2(x - 3)
           y - 4 = 2(x) - 2(3)
           y - 4 = 2x - 6
             + 4        + 4
                y = 2x - 2
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A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct the 95% confid
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Answer:

The 95% confidence interval for the true proportion of all voters in the state who favor approval is (0.4384, 0.5050).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

n = 865, \pi = \frac{408}{865} = 0.4717

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4717 - 1.96\sqrt{\frac{0.4717*0.5283}{865}} = 0.4384

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4717 + 1.96\sqrt{\frac{0.4717*0.5283}{865}} = 0.5050

The 95% confidence interval for the true proportion of all voters in the state who favor approval is (0.4384, 0.5050).

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3 years ago
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