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monitta
3 years ago
14

1. A senator is thinking about running for president. But she will only do so if more than 60% of the voters view her favorably.

She gathers some data to see if she has this level of support. Which statistical method would be best for her to use?
Mathematics
1 answer:
OLga [1]3 years ago
7 0

The senator is faced with the making a decision to run for President, based

on the conclusion she can make from the data she gathers.

The statistical method that would be best for her to use is <u>inferential </u>

<u>statistic method</u> such as finding the percentage of supporters she has to a

given <u>confidence level</u>.

Reason:

The two main types of statistical methods are;

Inferential statistics methods; Theses are methods used to reach a

conclusion that extends past the given or available data.

Descriptive statistics methods; Theses are statistical method used as a

summary of a data set.

Given that the senator is trying to draw conclusion based on the data she

gathers, she should use inferential statistic method.

The type inferential statistic method that can be used is the confidence

interval.

From the data collected, the proportion of voters that view her favorably is

used at a given confidence level to determine the true proportion of voters

that view her favorably.

Therefore;

The statistical method that would be best for her to use is the

finding of the <u>confidence interval which is a inferential statistic method</u>.

Learn more here:

brainly.com/question/15873157

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Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant below the line y=5 and betw
vfiekz [6]

First, complete the square in the equation for the second circle to determine its center and radius:

<em>x</em> ² - 10<em>x</em> + <em>y</em> ² = 0

<em>x</em> ² - 10<em>x</em> + 25 + <em>y </em>² = 25

(<em>x</em> - 5)² + <em>y</em> ² = 5²

So the second circle is centered at (5, 0) with radius 5, while the first circle is centered at the origin with radius √100 = 10.

Now convert each equation into polar coordinates, using

<em>x</em> = <em>r</em> cos(<em>θ</em>)

<em>y</em> = <em>r</em> sin(<em>θ</em>)

Then

<em>x</em> ² + <em>y</em> ² = 100   →   <em>r </em>² = 100   →   <em>r</em> = 10

<em>x</em> ² - 10<em>x</em> + <em>y</em> ² = 0   →   <em>r </em>² - 10 <em>r</em> cos(<em>θ</em>) = 0   →   <em>r</em> = 10 cos(<em>θ</em>)

<em>y</em> = 5   →   <em>r</em> sin(<em>θ</em>) = 5   →   <em>r</em> = 5 csc(<em>θ</em>)

See the attached graphic for a plot of the circles and line as well as the bounded region between them. The second circle is tangent to the larger one at the point (10, 0), and is also tangent to <em>y</em> = 5 at the point (0, 5).

Split up the region at 3 angles <em>θ</em>₁, <em>θ</em>₂, and <em>θ</em>₃, which denote the angles <em>θ</em> at which the curves intersect. They are

<em>θ</em>₁ = 0 … … … by solving 10 = 10 cos(<em>θ</em>)

<em>θ</em>₂ = <em>π</em>/6 … … by solving 10 = 5 csc(<em>θ</em>)

<em>θ</em>₃ = 5<em>π</em>/6  … the second solution to 10 = 5 csc(<em>θ</em>)

Then the area of the region is given by a sum of integrals:

\displaystyle \frac12\left(\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\}\left(10^2-(10\cos(\theta))^2\right)\,\mathrm d\theta+\int_{\frac\pi6}^{\frac{5\pi}6}\left((5\csc(\theta))^2-(10\cos(\theta))^2\right)\,\mathrm d\theta\right)

=\displaystyle 50\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\} \sin^2(\theta)\,\mathrm d\theta+\frac12\int_{\frac\pi6}^{\frac{5\pi}6}\left(25\csc^2(\theta) - 100\cos^2(\theta)\right)\,\mathrm d\theta

To compute the integrals, use the following identities:

sin²(<em>θ</em>) = (1 - cos(2<em>θ</em>)) / 2

cos²(<em>θ</em>) = (1 + cos(2<em>θ</em>)) / 2

and recall that

d(cot(<em>θ</em>))/d<em>θ</em> = -csc²(<em>θ</em>)

You should end up with an area of

=\displaystyle25\left(\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\}(1-\cos(2\theta))\,\mathrm d\theta-\int_{\frac\pi6}^{\frac{5\pi}6}(1+\cos(2\theta))\,\mathrm d\theta\right)+\frac{25}2\int_{\frac\pi6}^{\frac{5\pi}6}\csc^2(\theta)\,\mathrm d\theta

=\boxed{25\sqrt3+\dfrac{125\pi}3}

We can verify this geometrically:

• the area of the larger circle is 100<em>π</em>

• the area of the smaller circle is 25<em>π</em>

• the area of the circular segment, i.e. the part of the larger circle that is bounded below by the line <em>y</em> = 5, has area 100<em>π</em>/3 - 25√3

Hence the area of the region of interest is

100<em>π</em> - 25<em>π</em> - (100<em>π</em>/3 - 25√3) = 125<em>π</em>/3 + 25√3

as expected.

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Which equation is represented by the graph below?
gregori [183]

Answer:

y = e^x - 4

Step-by-step explanation:

The missing options are

y = ln x - 3

y = ln x - 4

y = e^x - 3

y = e^x - 4

The function is defined in quadrant 3 and increases exponentially, then it is not a logarithm.

f(x) crosses the y-axis at (0, -3). Replacing x = 0 the last option, we get:

y = e^0 - 4 = 1 - 4 = -3

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A square piece of plywood has sides that are 10 feet long. What is the piece of plywood's area
Anuta_ua [19.1K]
I don’t really understand the question, but if you’re looking for the area, it would be 100 feet since you have to do “Side x Side”. Hope this helps!
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7 is equal to 1 in this ratio.

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