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3 years ago

8

There are 8 feet and 4 heads in Ms. Wilson’s class. If 4 feet belong to boys and 4 feet belong to girls, what is the ratio of bo

ys to girls in the class?

1 answer:

yarga [219]3 years ago

8 0

1to 3am obviously lolololololol

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A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is

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10/54 = 0.185

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3 years ago

A drilling machine can drill 12 holes in 6 minutes. If the machine drills holes at a constant speed, it can drill ______ holes i

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An international company has 27,100 employees in one country. If this represents 22.6% of the company's employees, how many empl

Step2247 [10]

Answer:

The total employee of the company is 11912

Step-by-step explanation:

The employee in one country = 27,100

Let the total population be P

$\frac{ 22.6}{100} *P = 27,100$

P = $\frac{27100*100}{22.6}$

P = 11911.5

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So the total employee of the company is 11912

7 0

3 years ago

A piece of cardboard is 15 inches by 30 inches. A square is to be cut from each corner and the sides folded up to make an open-t

solmaris [256]

Answer:

Maximum volume = 649.519 cubic inches

Step-by-step explanation:

A rectangular piece of cardboard of side 15 inches by 30 inches is cut in such that a square is cut from each corner. Let x be the side of this square cut. When it was folded to make the box the height of box becomes x, length becomes (30-2x) and the width becomes (15-2x).

Volume is given by

V = $V = Length\times Width\times Height\\V = (30 - 2x)(15-2x)x= 4x^3-90x^2+450x\\So,\\V(x) = 4x^3-90x^2+450x$

First, we differentiate V(x) with respect to x, to get,

$\frac{d(V(x))}{dx} = \frac{d(4x^3-12x^2+9x)}{dx} = 12x^2 - 180x +450$

Equating the first derivative to zero, we get,

$\frac{d(V(x))}{dx} = 0\\\\12x^2 - 180x +450 = 0$

Solving, with the help of quadratic formula, we get,

$x = \displaystyle\frac{5(3+\sqrt{3})}{2}, \frac{5(3-\sqrt{3})}{2}$ ,

Again differentiation V(x), with respect to x, we get,

$\frac{d^2(V(x))}{dx^2} = 24x - 180$

At x =

$\displaystyle\frac{5(3-\sqrt{3})}{2}$ ,

$\frac{d^2(V(x))}{dx^2} < 0$

Thus, by double derivative test, the maxima occurs at

x = $\displaystyle\frac{5(3-\sqrt{3})}{2}$ for V(x).

Thus, largest volume the box can have occurs when $x = \displaystyle\frac{5(3-\sqrt{3})}{2}}$ .

Maximum volume =

$V(\displaystyle\frac{5(3-\sqrt{3})}{2}) = (30 - 2x)(15-2x)x = 649.5191\text{ cubic inches}$

8 0

3 years ago