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Semmy [17]
2 years ago
5

I NEEEDDDD HELPPP ASAPPPP!!! it’s urgentttttt

Mathematics
1 answer:
Artist 52 [7]2 years ago
4 0

Answer:

(x + 14)² + (y – 21/2)² = 1

Step-by-step explanation:

The equation of a circle can be written as seen below

(x – h)² + (y – k)² = r²

Where (h,k) is at the center and r = radius

We are given that the radius is 1

We are also given that the center is at (-14,21/2)

So we know that r = 1, h = -14, and k = 21/2

So to find the equation of the circle we simply substitute these values into the equation of a circle

Equation of a circle: (x – h)² + (y – k)² = r²

r = 1, h = -14, and k = 21/2

Substitute values

(x – (-14))² + (y – 21/2)² = 1²

1^2 = 1

The two negative signs before the 14 cancel out and it changes to + 14

The equation of a circle with a center at (-14,21/2) and a radius of 1 is (x + 14)² + (y – 21/2)² = 1

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A sociologist wishes to estimate the percentage of the United States population living in poverty. What size sample should be ob
andriy [413]

Answer:

a) We need a sample size of at least 705.

b) We need a sample size of at least 1692.

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}.

The margin of error is:

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

90% confidence level

So \alpha = 0.1, z is the value of Z that has a pvalue of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

a) If she uses 1999 estimate of 11.8% obtained from the Current Population Survey.

We need a sample of size at least n

n is found when M = 0.02, \pi = 0.118.

So

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

0.02 = 1.645\sqrt{\frac{0.118*0.882}{n}}

0.02\sqrt{n} = 1.645\sqrt{0.118*0.882}

\sqrt{n} = \frac{1.645\sqrt{0.118*0.882}}{0.02}

(\sqrt{n})^{2} = (\frac{1.645\sqrt{0.118*0.882}}{0.02})^{2}

n = 704.08

Rounding up

We need a sample size of at least 705.

b) She does not use any estimate.

Same thing as above, we just use \pi = 0.5 when do not use any estimate.

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

0.02 = 1.645\sqrt{\frac{0.5*0.5}{n}}

0.02\sqrt{n} = 1.645\sqrt{0.5*0.5}

\sqrt{n} = \frac{1.645\sqrt{0.5*0.5}}{0.02}

(\sqrt{n})^{2} = (\frac{1.645\sqrt{0.5*0.5}}{0.02})^{2}

n = 1691.2

Rounding up

We need a sample size of at least 1692.

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