All Answers 358367 Answers

I have added this thread to our reference material thread.  :)

I think that is standard deviation of a sample

For standard deviation of a population I think that you use n instead of n-1    

For all his reputation, Isaac Newton was a bit of a fruitcake.

Sitting under an apple tree when the apples are falling doesn't seem sensible, did he have some sort of death wish ?

 He apparently fancied himself as a bit of an alchemist and spent a fair bit of time trying to find out how to turn lead into gold. He, when investigating the properties of light, was apt to push needles into his eye to change the shape of his eyeball.

He also, reputedly, invented the catflap. He cut a hole in a outhouse door so that his cat could get in and out, and then when the cat had kittens, he cut out a smaller hole for them alongside the first one. 

It's fortunate that he produced some decent results, otherwise history would see him in a different light.

$$\\9-\frac{7}{8}\\\\
=8+1-\frac{7}{8}\\\\
=8\frac{1}{8}\\\\$$

A shipping company makes a display to show how many cubes can fit into a large box. Each cube has a side of 2 inches. The large box has sides of 10 inches.

Question 1:

Use exponents to express the volume of each cube and the large box.

Volume of the cube = 2*2*2 inches cubed 

Volume of the large box =10*10*10 inches cubed

Question 2:

Find out how many cubes will fit in the box.    Divide

Question 3:

Suppose the shipping company were packing b***s with the diameter of 2 inches instead of cubes. Would the large box hold more b***s or fewer b***s than the cubes. Explain your answer.   

Well it would not hold fewer.

Question 4:

Suppose the size of each cube is doubled and the size of the large box is doubled. How many of these new cubes will fit into that new large box? Explain how you found your answer.

Anonymous   

0 Answer

186,453,000 people

190,000,000 people

$$1.9\times 10^8$$

x must be between 1 and 10

$$1\le X <10$$

$$\\15000=10000(1+r)^4\\\\
3=2(1+r)^4\\\\
1.5=(1+r)^4\\\\
1.5^{0.25}=1+r\\\\
r=1.5^{0.25}-1\\\\$$

$${{\mathtt{1.5}}}^{\left\{{\mathtt{0.25}}\right\}}{\mathtt{\,-\,}}{\mathtt{1}} = {\mathtt{0.106\: \!681\: \!919\: \!700\: \!321\: \!6}}$$

So the interest rate is approximately  10.67%

Beats me 

I suppose it could swim upstream just as good as it could swim downstream 

So what do you want to know?

Chris has used this fact - Thanks Chris.  

For any solid where one is the enlargement of the other. (They are similar figures)

if the lengths are in the ratio   $$a:b$$

then the surface area will be in the ratio    $$a^2:b^2$$

and the volumes will be in the ratio      $$a^3:b^3$$

----------------------------------

In any 2 dimensional shape

if the lengths are in the ratio   $$a:b$$

then the  area will be in the ratio    $$a^2:b^2$$

 ------------------------------------

IT IS REALLY HANDY TO KNOW THIS!

integrate \sqrt{1+(-1.97+0.6156x+0.0438x^2)^2} x=1.2 to 8.7

$$\\\int_{1.2}^{8.2}\; \sqrt{1+(-1.97+0.6156x+0.0438x^2)^2} \;\;dx\\\\
\int_{1.2}^{8.2}\; [1+(-1.97+0.6156x+0.0438x^2)^2]^{0.5} \;\;dx\\\\$$

Beats me.    

how do you simplify 6 times the cubed root of 250 y to the 7th

is this your intended question?

$$\\6*\sqrt[3]{250}*y^7\\\\
=6*\sqrt[3]{125*2}*y^7\\\\
=6*5\sqrt[3]{2}*y^7\\\\
=30y^7\sqrt[3]{2}\\\\$$

1 pile of leaves :3

$${\frac{{\mathtt{3}}}{{\mathtt{4}}}}{\mathtt{\,\small\textbf+\,}}\left({\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{5}}}{{\mathtt{12}}}}\right) = {\frac{{\mathtt{19}}}{{\mathtt{6}}}} = {\mathtt{3.166\: \!666\: \!666\: \!666\: \!666\: \!7}}$$

Look at the sticky notes on the right

Did you mean off or of?

0.62

$${\mathtt{0.62}} = {\frac{{\mathtt{31}}}{{\mathtt{50}}}}$$

I just entered 0.62 straight in.   

What do you mean by solution.  there are 2 unknowns  Do you want the integer solutions?

I'll try to make x the subject

$$\begin{array}{rll}
\sqrt{a-\sqrt{a-x}}&=&x\\\\
a-\sqrt{a-x}&=&x^2\\\\
-\sqrt{a-x}&=&x^2-a\\\\
a-x&=&(x^2-a)^2\\\\
a-x&=&x^4-2ax^2+a^2\\\\
a-a^2-x+2ax^2-x^4&=&0\\\\
-((a-x-x^2)(-1+a+x-x^2))&=&0\\\\
(a-x-x^2)(-1+a+x-x^2)&=&0\\\\
(a-x-x^2)(-1+a+x-x^2)&=&0\\\\
\end{array}
so \\
a-x-x^2=0\qquad or \qquad -1+a+x-x^2=0\\\\
x^2+x-a=0\qquad or \qquad x^2-x+(1-a)=0\\\\$$

You can now solve these seperately using the quadratic formula and you will end up with 4 solutions where x is the subject.

the numeric value of x will depend on your value of a.

here is a graph

Er....one pile....???

HAHAHAHA!!!....that's great Anonymous.....!!!!

ROFLMAO....!!!!!

well then the 120 of them had better get a wriggle on then.  :))

Well...that depends on how big the hole is.......maybe they're digging to China...LOL!!!

Very nice, Anonymous.....

25sinxcosx-5sinx+20cosx= 4

Following your lead....

25sinxcosx + 20cosx = 4 + 5sinx

5cosx(5sinx + 4) = (5six + 4)

5cosx = 1

cosx =1/5  at 78.46°

And the other value where sin x = (-4/5) is  about 233°

So...that's all our angles on [0,360]

I always find these questions super tricky.

I am going to do it without algebra. :)

2 people   take   5hours

If you have more people, it would take less time - that makes sense doesn't it?

so

2*5people  take  5 ÷ 5 hours

10 people    take    1 hour

now 5 minutes is 5/60=1/12 of an hour

10*12 people would take  1/12 hours

120 people will take  5 minutes

Of course they would all get in each others way so I do not think it would really work that way.   LOL