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2 years ago

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According to a report for veterinarians in the United States, 36.5 percent of households in the United States own dogs and 30.4

percent of households in the United States own cats. If one household in the United States is selected at random, what is the probability that the selected household will own a dog or a cat?(A)0.111(B) 0.331(C) 0.558(D) 0.669(E) Not enough information is given to determine the probability.

1 answer:

aleksandrvk [35]2 years ago

3 0

Answer :E) Not enough information is given to determine the probability.

Step-by-step explanation:

Le A denotes the event that households in the United States own dogs .

and B denotes the event that households in the United States own cats.

As per given , we have

P(A)=36.5%= 0.365

P(B)=30.4% = 0.304

To find the probability that the selected household will own a dog or a cat, we apply the following formula :

P(A or B)=P(A)+P(B)+P(A and B)

But P(A and B) is not given to us.

i..e the probability that a house hold own both a cat and adg is not given to us.

Therefore, The correct option is (E) Not enough information is given to determine the probability.

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The area of a shape is the amount of space a shape can occupy, while the perimeter is the sum of its lengths.

<em>The perimeter is </em> $18 + 3\sqrt 5 + 3\sqrt 2$ <em>units</em>
<em>The area of the sanctuary is 27 square units</em>

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$A = (5,7)\\B=(8, 7)\\C=(8, 1)\\D=( 1, 1)\\E=( 1, 4)\\F= ( 5,4)$

<u>Perimeter</u>

See attachment for the layout of the sanctuary

$BC = \sqrt{(8 - 8)^2 + (7 - 1)^2} = 6$

$EF = \sqrt{(1 - 5)^2 + (4 - 4)^2} = 4$

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From the attachment, the sides are

<em>AB, BF, FC, CD, DE and EA</em>

Start by calculating the length of each side using the following distance formula:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_2)^2}$

So, we have:

$AB = \sqrt{(5 - 8)^2 + (7 - 7)^2} = 3$

$BF = \sqrt{(8 - 5)^2 + (7 -1)^2} = \sqrt{45} = 3\sqrt 5$

$FC = \sqrt{(8 - 5)^2 + (1 -4)^2} = \sqrt{18} = 3\sqrt 2$

$CD = \sqrt{(8 - 1)^2 + (1 - 1)^2} = 7$

$DE = \sqrt{(1 - 1)^2 + (1 - 4)^2} = 3$

$EA = \sqrt{(1 - 5)^2 + (4 -7)^2} = 5$

So, the perimeter (P) is:

$P = AB + BF + FC + CD + DE + EA$

$P = 3 + 3\sqrt 5 + 3\sqrt 2 + 7 + 3 + 5$

$P = 18 + 3\sqrt 5 + 3\sqrt 2$

<em>Hence, the perimeter is </em> $18 + 3\sqrt 5 + 3\sqrt 2$ <em>units</em>

<u />

<u>Area</u>

To calculate the area, we need to divide the sanctuary into three.

<em>Triangle ABF</em>
<em>Triangle EFA</em>
<em>Trapezium CDEF</em>

The area of ABF is:

$Area = \frac 12 \times AB \times FA$

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$AB = 3$

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$Area = \frac 12 \times 3 \times 3$

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$Area = \frac 12 \times EF \times FA$

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$FA = 3$

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$Area = \frac 12 \times 4 \times 3$

$Area = 6$

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$Area = \frac 12(CD + EF) \times DE$

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$CD = 7$

$EF = 4$

$DE = 3$

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$Area = \frac 12 (7 + 4) \times 3$

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$Area = \frac 92 + 6 + \frac {33}2$

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<em>Hence, the area of the sanctuary is 27 square units</em>

Read more about areas and perimeters at:

brainly.com/question/11957651

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