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laila [671]
3 years ago
5

An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California. Suppose that

the mean income is found to be $22.7$⁢22.7 for a random sample of 183183 people. Assume the population standard deviation is known to be $6.3$⁢6.3. Construct the 85%85% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
Mathematics
1 answer:
sergiy2304 [10]3 years ago
7 0

Answer:

(22.0297, 23.3703)

Step-by-step explanation:

Given that an economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California.

Let X be per capita income (in thousands of dollars) for a major city in California.

Mean = 22.7

n = 183

Population std dev = 6.3

Since population std dev is known we can use Z critical value.

Std error = \frac{6.3}{\sqrt{183} } \\=0.4657

Z critical =1.44

Marginof error = ±1.44*0.4657=0.6706

Confidence interval 85%

=(22.7-0.6703, 22.7+0.6703)\\= (22.0297, 23.3703)

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an ellipse has a center at the origin , a vertex along the major axis at (13,0), and a focus at (12,0). What is the equation of
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Answer:

The answer to your question is below

Step-by-step explanation:

Data

Center = (0, 0)

Vertex = (13, 0)

Focus = (12, 0)

Process

From the data we know that it is a horizontal ellipse.

1.- Calculate "a", the distance from the center to the vertex.

                  a = 13

2.- Calculate "c", the distance from the center to the focus

                  c = 12

3.- Calculate b

Use the Pythagorean theorem to find it

                  a² = b² + c²

-Solve for b

                  b² = a² - c²

-Substitution

                  b² = 13² - 12²

-Simplification

                  b² = 169 - 144

                  b² = 25

                  b = 5

4.- Find the equation of the ellipse

                       \frac{x^{2} }{13^{2}} + \frac{y^{2}}{5^{2}} = 1    or \frac{x^{2} }{169} + \frac{y^{2}}{25} = 1

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3 years ago
I need this urgently!! I need by 7:15!!
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The question is telling you that the length of the rectangle is 3 metres more than twice the width.

So let:

<em>w= width</em>

<em>L= length</em>

Because the length is 3 metres more than twice<em> </em>the width: <em>L= </em><em>2</em><em>w+</em><em>3</em>


They also tell you the perimeter is 48 metres.

<em>P= L+L+w+w</em>

So the equation of the perimeter is:

<em>48= (2w+3)+(2w+3)+2w +2w</em>

<em>48= 2(2w+3) + 4w</em>


To find w, expand and simplify.

<em>48= 4w+6+4w</em>

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Now that you know the width, plug in the value into the length equation:

<em>L= 2w+3</em>

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