What is the answer 3.3010 x 10^23=

An aquarium with a square base has no top. There is a metal frame. Glass costs 8 dollars/m^2 and the frame costs 7 dollars/m. Th

Irina-Kira [14]

Given that the volume of the aquarium is 20m^3.

Volume = Area of Base x height

Area of Base = Volume / height = 20/h

Given that the aquarium has a square base.

Area of square = l^2

Thus, the length of the base of the aquarium is $\sqrt{area \ of \ base} = \sqrt{ \frac{20}{h} }$

The frame is to cover 8 sides with the length equal to the length of the base and 4 sides with the length of the height.

Thus, the total perimeter of the frame is given by $8\sqrt{\frac{20}{h}}+4h= \sqrt{64\left(\frac{20}{h}\right)}+4h = \sqrt{\frac{1,280}{h}}+4h$

Area of the four side faces of the aquarium is 4 times the length of the base times the height = $4\times\sqrt{ \frac{20}{h} }\times h=\sqrt{16\left(\frac{20}{h}\right)h^2}=\sqrt{320h}$

Total area to be covered by grass is the base and the four side faces and is given by $\frac{20}{h}+\sqrt{320h}$

Cost of the entire metal frame = $7\left(\sqrt{\frac{1,280}{h}}+4h\right)= \sqrt{49\left(\frac{1,280}{h}\right)}+7(4h) = \sqrt{\frac{62,720}{h}}+28h$

Cost of the entire grass = $8\left(\frac{20}{h}+\sqrt{320h}\right)=\frac{160}{h}+\sqrt{64(320h)}=\frac{160}{h}+\sqrt{20,480h$

Therefore, total cost in terms of the height, h, is given by

$C=\sqrt{\frac{62,720}{h}}+28h+\frac{160}{h}+\sqrt{20,480h$

3 0

3 years ago

A supplier delivers an order for 20 electric toothbrushes to a store. By accident, three of the electric toothbrushes are defect

Vladimir79 [104]

The probability that the first two electric toothbrushes sold are defective is 0.016.

The probability of an event, say E occurring is:

$P(E)=\frac{n(E)}{N}$

Here,

n (E) = favorable outcomes

N = total number of outcomes

Let X = the number of defective electric toothbrushes sold.

The number of electric toothbrushes that were delivered to a store is n = 20.

The number of defective electric toothbrushes is x = 3.

The number of ways to select two toothbrushes to sell from the 20 toothbrushes is:

$(\left {{20} \atop {2}} \right. )$ $=\frac{20!}{2!(20-2)!} =\frac{20!}{2!18!} =\frac{20*19*18!}{2!*18!} = 190$

The number of ways to select two defective toothbrushes to sell from the 3 defective toothbrushes is:

$(\left {{3} \atop {2}} \right. )$ $=\frac{3!}{2!(3-2)!} =\frac{3!}{2!1!} =\frac{3*2!}{1!2!} =3$

Compute the probability that the first two electric toothbrushes sold are defective as follows:

P (Selling 2 defective toothbrushes) = Favorable outcomes ÷ Total no. of outcomes

$\frac{3}{190}\\ =0.01579\\=0.016$

Thus, the probability that the first two electric toothbrushes sold are defective is 0.016.

Learn more about probability here brainly.com/question/27474070

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4 0

1 year ago

Volume of cylinder diameter 10 inches height of 20 inches

stiks02 [169]

$\sf{Volume~of~a~cylinder=\pi r^2h}\\\\V = \pi (\frac{10}{2})^2(20)\\\\V = 5^2 \pi (20)\\\\V = 25 \times 20 \pi\\\\\boxed{\bf{V = 500 \pi\approx1570.8}}$