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sattari [20]
3 years ago
6

Question 1

Mathematics
1 answer:
zzz [600]3 years ago
5 0

Answer:

52

Step-by-step explanation:

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How many numbers between 1 and 2005 are integer multiples of 3 or 4 but not 12?
siniylev [52]

Count the number of multiples of 3, 4, and 12 in the range 1-2005:

⌊2005/3⌋ ≈ ⌊668.333⌋ = 668

⌊2005/4⌋ = ⌊501.25⌋ = 501

⌊2005/12⌋ ≈ ⌊167.083⌋ = 167

(⌊<em>x</em>⌋ means the "floor" of <em>x</em>, i.e. the largest integer smaller than <em>x</em>, so ⌊<em>a</em>/<em>b</em>⌋ is what you get when you divide <em>a</em> by <em>b</em> and ignore the remainder)

Then using the inclusion/exclusion principle, there are

668 + 501 - 2•167 = 835

numbers that are multiples of 3 or 4 but not 12. We subtract the number multiples of 12 twice because the sets of multiples of 3 and 4 both contain multiples of 12. Subtracting once removes the multiples of 3 <em>and</em> 4 that occur twice. Subtracting again removes them altogether.

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3 years ago
Which is the correct classificatio
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d

Step-by-step explanation:

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4 years ago
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The population of California grew at 3.5% per year from the year 1860 to 1990. The population in 1860 was about 400,000 people.
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Answer:

Step-by-step explanation:

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Answer:

3x - 20 = 5

Step-by-step explanation:

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3 years ago
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Rickey has been commissioned to paint a mural that is allowed to have an area of 50 square meters. To make the rectangle shape o
Leno4ka [110]

Answer:

12.808 meter is the length should Rickey use for the mural.

Step-by-step explanation:

Area of the mural = A = 50 m^2

Length of the mural = l

Width of the mural = w

l = 5 + 2w

Area of the rectangle = l × w

A=(5+2w)\times w

50 m^2=5w+2w^2

2w^2+5w-50=0

Solving above equation with the help of Completing squares method:

(\sqrt{2}w)^2+2\times \sqrt{2}w\times \frac{5}{2\sqrt{2}}+(\frac{5}{2\sqrt{2}})^2-50=(\frac{5}{2\sqrt{2}})^2

(a+b)^2=a^2+b^2+2ab

(\sqrt{2}w+\frac{5}{2\sqrt{2}})^2=(\frac{5}{2\sqrt{2}})^2+50

(\sqrt{2}w+\frac{5}{2\sqrt{2}})^2=\frac{25}{8}+50

(\sqrt{2}w+\frac{5}{2\sqrt{2}})^2=\frac{425}{8}

(\sqrt{2}w+\frac{5}{2\sqrt{2}})=\pm\sqrt{\frac{425}{8}}

w = 3.904 m (accept)

w = -6.404 m (reject)

l = (5 + 2w)m = 5 + 2 × (3.904) m= 12.808 m

12.808 meter is the length should Rickey use for the mural.

3 0
3 years ago
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