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beks73 [17]
3 years ago
10

Andrew is creating a rectangular dog run in his back yard. The length of the dog run is 18 feet. The perimeter of the dog run mu

st be at least 42 feet and no more than 72 feet. Use a compound inequality to find the range of values for the width of the dog run
Mathematics
1 answer:
ale4655 [162]3 years ago
6 0

Answer: 3\leq x \leq 18

Step-by-step explanation:

Given, the length of the rectangular dog run is 18 feet.

Formula: Perimeter = 2 ( length + width)

Let width be x.

Then, Perimeter = 2 (18 + x ) feet

The perimeter of the dog run must be at least 42 feet and no more than 72 feet.

That is  

42\leq 2 (x+18)\leq 72

Divide inequality by 2, we get

21\leq 18+x\leq 36

Subtract 18 from each side, we get

3\leq x \leq 18

Required inequality : 3\leq x \leq 18

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A.
In the first generation we have 2 ancestors.
In the second generation we have 4 ancestors or 2^{2} ancestors.
In the third generation we have 8 ancestors ot 2^{3} ancestors.

We can see that each succesive generation has two times more members. The sum is:
2+4+8+16+...+ 2^{40}

To calculate number of ancestors we can use formula <span>for the sum of a geometric sequence. Geometric sequence is sequence of numbers that differ by a certain factor. This factor is called ratio. Formula is:
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For this question:
a1 = 2
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</span>S= 2* \frac{1- 2^{40} }{1-2} =2 199 023 255 550
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b.
1 generation = 25 years
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c.
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The number of ancestors is greater than total number of people who have ever lived. This means that not all ancestors were distinct and that in each generation both men and women had children with more than one partner.
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