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viva [34]
3 years ago
9

Samuel measured three ropes as 3and 63/80 feet, 3and 1/5 feet, and 3and 11/20feet. Put the measurements of the ropes in order fr

om lease to greatest.
Mathematics
2 answers:
S_A_V [24]3 years ago
7 0
3 1/5, 3 11/20, 3 63/80
Sauron [17]3 years ago
7 0
The measurements in the order given are:
3 63/80, 3 1/5, 3 11/20
We can make the common denominator 80 so:
3 63/80 stays the same, 3 1/5 both sides of the fraction are multiplied by 16 so it becomes 3 16/80, 3 11/20 both sides of the fraction are multiplied by 4 so it becomes 3 44/80
In ascending order the new fractions are:
3 16/80, 3 44/80, 3 63/80.
So in order from least to greatest, the fractions are:
3 1/5, 3 11/20, 3 63/80

Hope this helps :)
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Let <em>S</em> be the sum of the integers 25-210:

<em>S</em> = 25 + 26 + 27 + … + 208 + 209 + 210

Let <em>S₃</em>, <em>S₄</em>, and <em>S₁₂</em> denote the sums of the integers in <em>S</em> that are multiples of 3, 4, or 12, respectively. We'll also count how many terms each sum involves; it'll be useful later.

<em>S₃</em> = 27 + 30 + 33 + … + 204 + 207 + 210 … … … (<u>62</u> terms)

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<em>S₄</em> = 28 + 32 + 36 + … + 200 + 204 + 208 … … … (<u>46</u> terms)

<em>S₄</em> = 4 (7 + 8 + 9 + … + 50 + 51 + 52)

<em>S₁₂</em> = 36 + 48 + 60 + … + 180 + 192 + 204 … … … (<u>15</u> terms)

<em>S₁₂</em> = 12 (3 + 4 + 5 + … + 15 + 16 + 17)

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<em>S₃</em> = 3 (9 + 10 + 11 + … + 68 + 69 + 70)

By reversing the order of the sum, we get

<em>S₃</em>* = 3 (70 + 69 + 68 + … + 11 + 10 + 9)

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9 + 70 = 79

10 + 69 = 79

11 + 68 = 79

and so on. Then

<em>S₃</em> + <em>S₃</em>* = 3 (79 + 79 + 79 + … + 79 + 79 + 79)

or

2<em>S₃</em> = 3 × <u>62</u> × 79   ==>   <em>S₃</em> = 7,347

We can compute the other two sums in the same way.

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<em>S₄</em>* = 4 (52 + 51 + 50 + … + 9 + 8 + 7)

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Answer:

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Step-by-step explanation:

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C. Operators:

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