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const2013 [10]
3 years ago
10

A sheet of standard size copy paper measures 8.5 inches by 11 inches. If a ream is 500 sheets of paper has a volume of 187 inche

s cube. How thick is the ream?
Mathematics
1 answer:
AURORKA [14]3 years ago
7 0

Answer:

\large \boxed{\text{2.00 in}}  

Step-by-step explanation:

The formula for the volume of a rectangular solid is  

V = lwh

\begin{array}{rcl}V & = & lwh\\187 & = & 8.5 \times 11 \times h\\& = & 93.5h\\h & = &\dfrac{187}{93.5}\\\\& = & \textbf{2.00 in}\\\end{array}\\\text{The ream is $\large \boxed{\textbf{2.00 in}}$ thick.}

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Hey guys I need some help with #7 so if anyone could help that would be great THANK YOU!!
iVinArrow [24]

The average rate of change obtained from the ratio of change in y to the change in x is 27

The average rate of change can be obtained using the relation :

Rate of change = (y2 - y1) ÷ (x2 - x1)

at; x1 = -3

y1 can be calculated from the function ;

y1= 3(-3³)-1

y1=-82

At ; x2 = 3

y2 can be calculated from the function ;

y2 = 3(3³)-1

y2=80

The rate of change can be calculated thus : (y2 - y1) ÷ (x2 - x1)

[80-(-82)]/[3-(-6])

162/6

27

Learn more about the average rate of change here:

brainly.com/question/18550782

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8 0
1 year ago
4 days ago, Emily blew up a balloon (that is a perfect sphere) to a radius of 5cm. Since then, the balloon has lost air and decr
Elan Coil [88]

Answer:

27/125

Step-by-step explanation:

3 0
3 years ago
Factor the following , it is not prime
MrMuchimi
So 1/9-16z^2 this is a diffirence of two perfect squares thing
so (1/3)^2-(4z)^2
so ((1/3)-4z)((1/3)+4z)

4 0
3 years ago
If <img src="https://tex.z-dn.net/?f=%20300cm%5E%7B2%7D%20" id="TexFormula1" title=" 300cm^{2} " alt=" 300cm^{2} " align="absmid
Artist 52 [7]
Check the picture below.  Recall, is an open-top box, so, the top is not part of the surface area, of the 300 cm².  Also, recall, the base is a square, thus, length = width = x.

\bf \textit{volume of a rectangular prism}\\\\&#10;V=lwh\quad &#10;\begin{cases}&#10;l = length\\&#10;w=width\\&#10;h=height\\&#10;-----\\&#10;w=l=x&#10;\end{cases}\implies V=xxh\implies \boxed{V=x^2h}\\\\&#10;-------------------------------\\\\&#10;\textit{surface area}\\\\&#10;S=4xh+x^2\implies 300=4xh+x^2\implies \cfrac{300-x^2}{4x}=h&#10;\\\\\\&#10;\boxed{\cfrac{75}{x}-\cfrac{x}{4}=h}\\\\&#10;-------------------------------\\\\&#10;V=x^2\left( \cfrac{75}{x}-\cfrac{x}{4} \right)\implies V(x)=75x-\cfrac{1}{4}x^3

so.. that'd be the V(x) for such box, now, where is the maximum point at?

\bf V(x)=75x-\cfrac{1}{4}x^3\implies \cfrac{dV}{dx}=75-\cfrac{3}{4}x^2\implies 0=75-\cfrac{3}{4}x^2&#10;\\\\\\&#10;\cfrac{3}{4}x^2=75\implies 3x^2=300\implies x^2=\cfrac{300}{3}\implies x^2=100&#10;\\\\\\&#10;x=\pm10\impliedby \textit{is a length unit, so we can dismiss -10}\qquad \boxed{x=10}

now, let's check if it's a maximum point at 10, by doing a first-derivative test on it.  Check the second picture below.

so, the volume will then be at   \bf V(10)=75(10)-\cfrac{1}{4}(10)^3\implies V(10)=500 \ cm^3

6 0
3 years ago
Find the ratio in simplest form.<br> 30:6
Lunna [17]

Answer:

5:1

Step-by-step explanation:

30:6 divided by 6 is 5:1

6 0
3 years ago
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