All Answers 359395 Answers

you can build this up from the left

one such number is

123654321

$${\frac{{\mathtt{123\,654\,321}}}{{\mathtt{9}}}} = {\mathtt{13\,739\,369}}$$

$${\frac{{\mathtt{12\,365\,432}}}{{\mathtt{8}}}} = {\mathtt{1\,545\,679}}$$

$${\frac{{\mathtt{1\,236\,543}}}{{\mathtt{7}}}} = {\mathtt{176\,649}}$$

$${\frac{{\mathtt{123\,654}}}{{\mathtt{6}}}} = {\mathtt{20\,609}}$$

$${\frac{{\mathtt{12\,365}}}{{\mathtt{5}}}} = {\mathtt{2\,473}}$$

$${\frac{{\mathtt{1\,236}}}{{\mathtt{4}}}} = {\mathtt{309}}$$

$${\frac{{\mathtt{123}}}{{\mathtt{3}}}} = {\mathtt{41}}$$

$${\frac{{\mathtt{12}}}{{\mathtt{2}}}} = {\mathtt{6}}$$

$${\frac{{\mathtt{1}}}{{\mathtt{1}}}} = {\mathtt{1}}$$

if you just work this backwards you can see how it's constructed.  Just make sure your condition is met each time you add a new digit.

based on the observation so far the probabilty of getting a white ball is

$${\frac{{\mathtt{7}}}{{\mathtt{14}}}} = {\mathtt{0.5}}$$

so you'd expect that of then next 18 b***s

$${\mathtt{18}}{\mathtt{\,\times\,}}{\mathtt{0.5}} = {\mathtt{9}}$$

b***s would be white

you do it much like long division of two numbers

       x + 6

       ---------------

x-1 |x^2 + 5x - 1

        x^2 -    x

      ----------------

                   6x - 1

                   6x - 6

                   -------

                           5

so (x^2+5x-1) = (x-1)(x+6)+5

Deleted Deleted

I'm not sure what "conservative" means but 

the 99% confidence margin of error is 

$$1.29\sqrt n$$

and the 95% confidence margin of error is 

$$0.98 \sqrt n$$

with n=450 these numbers are

$${\mathtt{1.29}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{450}}}} = {\mathtt{27.365\: \!032\: \!431\: \!919\: \!389\: \!2}}$$

$${\mathtt{0.98}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{450}}}} = {\mathtt{20.788\: \!939\: \!366\: \!884\: \!497\: \!2}}$$

Which of the following is equivalent to sintheta csc(–theta) wherever sintheta csc(–theta) is defined? F. –1 G. 1 H. –tan theta J. tan theta K. –sin2 theta

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Note csc(-θ ) = -csc(θ)

So we have

sin(θ) [-csc(θ)] =

-sin(θ) [csc(θ)] =

- sin(θ) [1/ sin(θ)] =  -1

The base of a 50 foot ladder rests 33.6 feet from the side of the house. How far up the side of a house does the top of the ladder reach?

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This just a right triangle problem that we can solve with the Pytagorean Theorem..

The hypoteneuse is 50 and one of the legs is 33.6. So, to find the other leg, we have...

SQRT (50² - 33.6²) ≈ 37.03 ft up the side of the house

This is a right triangle with hypotenuse equal to the length of the ladder, 50 feet, and one leg equal to 33.6 feet.

By the Pythagorean theorem we have

$$50^2=(33.6)^2+h^2$$

$${{\mathtt{50}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\left({\mathtt{33.6}}\right)}^{{\mathtt{2}}} = {\mathtt{1\,371.04}}$$

$${\mathtt{h}} = {\sqrt{{\mathtt{1\,371.04}}}} = {\mathtt{h}} = {\mathtt{37.027\: \!557\: \!305\: \!336\: \!791\: \!6}}$$

so about 37.03 feet up the side of the house.

$$80=2 \sqrt{5s}$$

$$40=\sqrt{5s}$$

$$1600=5s$$

$$s=320$$

Sorry...didn't see the (-)....!!!

Yes that is right

Here is the graph. 

https://www.desmos.com/calculator/0fime4jc06

The last step is (it is needed)

x < 4

You mean that all x-values have a y-coordinate of -3, right?

It can never be equal -1/12, because all the terms you are adding up are positive.  Moreover, the sum of the series is divergent, so it cannot converge to a number.

to find the slope of something you do rise over run 

Especially for Chris - and anyone else that would like to learn Latex.  

2/3[(5+3)^2-31]

in latex I would write this as

\frac{2}{3}((5+3)^2-31)

and this would be the output

$$\frac{2}{3}((5+3)^2-31)$$

Thanks Fiyero and welcome to web2.0calc forum 

5w^2(3w^8-w^6)

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OK......this isn't too hard...we just have to remember a property of exponents.....aⁿ * a^m = a ^n+m

Notice what we have is really   5w²*3w⁸ - 5w²w⁶   = 5*3*w²*w⁸ - 5*w^2*w⁶ 

So this is just

15w¹⁰ - 5w⁸

And that's it !!

Maybe not so brilliant. But Hi.

When I used to tutor, this is a question I always pondered, too, .......then I figured it out.......everyone has different abilities.

Foe instance, if you asked me to draw a picture, forget it!!! I have no talent in that direction.

Here's what I would tell you....practice!!.....most people aren't born "knowing" how to do math,  anymore than they're born knowing how to play a piano!!

Coming to the forum to ask questions isn't a bad idea, either. We might not have any Sir Isaac Newtons on here (but then again, I can't be sure), but we have a lot of people who are pretty knowledgeable!!

Hang in there....."math" isn't the "only" thing in life......

Sorry......you mean everyone doesn't understand the language as I do ??     (LOL!!!)

Actually...I translated it using a Croatian-to-English app.

But if you tell me it's Slovak....I couldn't call you on it!!!

What is y=-3 graphed?

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It's just a line parallel to the x-axis that passes through the y-intercept of 3 -  the point (0,3).

All points on its graph have a y coordinate =3, no matter what their x coordinates. Also, this line has a slope = 0.

Thanks Alan,

or you could just do it on the site calc

you use the divide by sign as a fraction line.

$$\left({\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2}}}{{\mathtt{5}}}}\right){\mathtt{\,\small\textbf+\,}}\left({\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right) = {\mathtt{4.65}}$$

I did this using the "Math (Input=Result)" button on the ribbon.

If you do it on the actual calculator and hit the = sign again it will give it to you as an improper fraction.

Unfortunately you have to do more work to turn it into a mixed numeral.

I believe you made a small mistake Alan.  It is 3+a

$$x^3y^3x^4y^a=x^7\\

x^7y^{3+a}=x^7\\

y^{3+a}=1\\

y^{3+a}=y^0\\

3+a=0\\

a=\: -3\\$$

Thanks Kitty