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Andreas93 [3]
4 years ago
7

Plot the points in the coordinate plane. Then find the perimeter and area of the polygon.

Mathematics
1 answer:
anyanavicka [17]4 years ago
7 0

Answer:

The answer to your question is below

Step-by-step explanation:

See the graph below

Process

1.- Find the distance from A to B, B to C, C to D, A to D

Formula

d = \sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}

d AB = \sqrt{(1 + 3)^{2} + (6 - 5)^{2}}  = \sqrt{17}

dBC = \sqrt{(-2 -6)^{2} + (3 - 1)^{2}}  = \sqrt{68}

dCD = \sqrt{(-1 - 3)^{2} + (-3 +2)^{2}}  = \sqrt{17}

dAD = \sqrt{(-1 + 3)^{2} + (-3 - 5)^{2}}  = \sqrt{68}

2.- Find the perimeter

Perimeter = 2\sqrt{17} + 2\sqrt{68} = 6\sqrt{17} u

3.- Find the area

Area = \sqrt{17} x \sqrt{68}

Area = \sqrt{17x68} = \sqrt{1156} = 34 u^{2}

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b)  0.501\leq p

Step-by-step explanation:

Given : Sample size of respondents in the exit polls  : n= 2020

Number of respondents voted for George Bush = 412

Sample proportion: \hat{p}=\dfrac{412}{768}\approx0.536

a) Critical value for 99% confidence level : z_{\alpha/2}=2.576

Confidence interval for proportion:-

\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

=0.536\pm (2.576)\sqrt{\dfrac{0.536(1-0.536)}{768}}\\\\=0.536\pm0.046\\\\=(0.490,\ 0.582)

Hence, the 99% confidence interval for the proportion of college graduates in Ohio that voted for George Bush: 0.490\leq p\leq0.582

b) Critical value for 95% confidence level : z_{\alpha/2}=1.96

Lower confidence bound for the proportion :

\hat{p}- z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.536-(1.96)\sqrt{\dfrac{0.536(1-0.536)}{768}}\\\\=0.536-0.035=0.501

Hence,  a 95% lower confidence bound for the proportion of college graduates in Ohio that voted for George Bush : 0.501\leq p

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A cube is packed with decorative pebbles. If the cube has a side length of 6 inches, and each pebble weighs on average 0.5 lb pe
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