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kobusy [5.1K]
2 years ago
7

Solve each system by the addition method.

Mathematics
1 answer:
Aneli [31]2 years ago
7 0
-4x + 7y = 9  ⇒ -4x + 7y = 9  ⇒     8x - 14y = -18
2y = -5x - 22 ⇒ -5x - 2y = 22 ⇒ <u>-35x - 14y = 154</u>
                                                               <u>43x</u> = <u>-172</u>
                                                                43       43
                                                                   x = -4
                                                        -4x + 7y = 9
                                                     -4(-4) + 7y = 9
                                                          16 + 7y = 9
                                                        <u>- 16        - 16</u>
                                                                  <u>7y</u> = <u>-7</u>
                                                                   7      7
                                                                    y = -1
                                                              (x, y) = (-4, -1)
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Answer:

a) z = 2.327

b) The margin of error is of 0.065.

c) The 98% confidence interval for the true population proportion of all New York State union members who favor the Republican candidate is (0.3083, 0.4383).

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}}

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The margin of error is:

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

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M = 2.327\sqrt{\frac{0.3733(1-0.3733)}{300}} = 0.065

The margin of error is of 0.065.

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The 98% confidence interval for the true population proportion of all New York State union members who favor the Republican candidate is (0.3083, 0.4383).

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