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Sati [7]
3 years ago
10

Tina is planning to fence in an area for her dog. She wants to create a rectangular area of 1,600 square feet for her pet and ca

n afford to purchase 160 feet of fence. In two or more complete sentences, explain the algebraic model, calculations and reasoning necessary to determine the dimensions of the rectangular area.
Mathematics
1 answer:
castortr0y [4]3 years ago
4 0

The dimensions of the rectangular area of Tina's fence is 40 ft by 40 ft

<h3 />

<h3>Area of a rectangle:</h3>
  • area = lw

where

l = length

w = width

She wants to create a rectangular area of 1,600 square feet for her pet . Therefore,

  • area = 1600 ft²

lw = 1600

Therefore,

perimeter = 160 ft

Then,

perimeter of rectangle = 2(l + w)

160 = 2(l + w)

l + w = 80

Let's combine the equations

lw = 1600

l + w = 80

l = 80 - w

Therefore,

w(80 - w) = 1600

80w - w² = 1600

Therefore,

w² - 80w + 1600 = 0

w² - 40w - 40w + 1600 = 0

w(w - 40) - 40(w - 40) = 0

(w - 40)(w - 40) = 0

w = 40 or 40

Therefore, the dimensions can be calculated as follows:

lw = 1600

40l = 1600

l = 1600 / 40

l = 40 ft

Therefore, the dimensions are 40ft by 40 ft

learn more on algebraic model here: brainly.com/question/4151078

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Answer:

(a)

S = \{GGG, GGB, GBG, GBB, BBG, BGB, BGG, BBB\}

(b)

i.

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ii.

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Step-by-step explanation:

Given

Children = 3

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Solving (a): List all possible elements using set-roster notation.

The possible elements are:

S = \{GGG, GGB, GBG, GBB, BBG, BGB, BGG, BBB\}

And the number of elements are:

n(S) = 8

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From the list of possible elements, we have:

1\ girl = \{GBB, BBG, BGB\}

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The probability is calculated as;

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P(1\ girl) = \frac{3}{8}

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Solving (bi) At least 2 are girls

From the list of possible elements, we have:

Atleast\ 2 \ girls = \{GGG, GGB, GBG, BGG\}

And the number of the list is;

n(Atleast\ 2 \ girls) = 4

The probability is calculated as;

P(Atleast\ 2 \ girls) = \frac{n(Atleast\ 2 \ girls)}{n(S)}

P(Atleast\ 2 \ girls) = \frac{4}{8}

P(Atleast\ 2 \ girls) = 0.5

Solving (biii) No girl

From the list of possible elements, we have:

No\ girl = \{BBB\}

And the number of the list is;

n(No\ girl) = 1

The probability is calculated as;

P(No\ girl) = \frac{n(No\ girl)}{n(S)}

P(No\ girl) = \frac{1}{8}

P(No\ girl) = 0.125

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