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Volume of a sphere: (4/3)*π*r^3
Volumen of a hemisphere: ((4/3)*π*r^3)/2
The volume of the bowl = ((4/3)*π*5^3)/2 = 261.799 m^3

So x can be any number, 4 =< x < 5

If we mutiply by 4. 

4 =< x < 5

16 =< x < 20

=^._.^=

8000 * .40   = 3200 were originally men

So

8000   - 3200     =   4800 were women

When 50 women left there  were  4750

Let  x  be  the  number of men who left

And we  ,now  that

3200 -  x              3

________  =      ___            cross-multiply

4750                  5

5 (3200 - x)  =  3(4750)

16000 -  5x  =  14250

16000 - 14250  =  5x

1750  = 5x

1750 /  5   =    350  men left

So   50  + 350  = 400 left

A number will not be possible if the denominator is 0, since you can't divide a number by 0. 

We have 4 denominators, x-64, x^2-64, x^3-64, x^4-64. 

Figure out the number of x where at least one of them equals to 0.

=^._.^=

4000 miles x  5280   =  21120000 ft

We have a right  triangle  with  one leg  =  21120000 ft   and  a hypotenuse  of  21120000 +  6684   = 21126684 ft

And  the other leg is  the  distance from the montain top to the horizon  = 

sqrt  [ 21126684^2  - 21120000^2 )   =  531391.4 ft  =  [531391    / 5280  ]  ≈  101 miles  

Very good.  Don't forget that square roots are dual polarity, for example, sqrt(4) is +4 ... both +4 and –4 

The surface area is 4*r^2*pi. 

Find r, then plug it into the volume equation, 4/3*r^3*pi.

=^._.^=

hm, idk wht 9yd represents. 

The volume of a sphere is 4/3*r^3*pi. 

If r = 9, the volume is 972pi

=^._.^=

The surface area of this sphere is 6 cubic centimeters What is the volume of this sphere? Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.  

the area is in cubic cm?  did you mean square cm?  

Area  =   pi ( radius)^2  *   (78  / 360)   = 

pi  ( 2.9)^2  (78 /360)   ≈  5.7 sq  meters

That is another way to do it, but for me it was definitely easier to solve through the whole problem instead of going through each and every way to get a coefficient of three. It's just my opinion, though.

Come on, you can work this out!

1000=3^x

3,9,27,81,243,729, too big

6

I am going to mathematically show you how to solve these problems:

1. \(\sqrt{\frac{25}{144}}=\frac{\sqrt{25}}{\sqrt{144}}=\frac{5}{12}\) = 5/12

2. \(\sqrt{\frac{1}{9}}=\frac{\sqrt{1}}{\sqrt{9}}=\frac{1}{3}\) = 1/3

3. \(\sqrt{\frac{25}{49}}=\frac{\sqrt{25}}{\sqrt{49}}=\frac{5}{7}\) = 5/7

Hope this helps :)

The multiplication of a monomial with a monomial will always result in a monomial. Here is my reasoning:

The definition of a binomial (in my own words) is an algebraic expression consisting of more than one terms. Now, a term is a product of multiplication of numbers and variables. Because of this, no matter what monomials you take, a binomial will always have a plus or minus sign between two terms. So, if you multiply two monomials, no matter what, it will be impossible to get a plus or minus sign. Let me show you some examples:

(4a) * (2a) = 8a

(3z) * (3w) = 3z3w

(2x^3) * (4z^2) = 2x^3 * 4z^2

And these are all monomials. A monomial cannot have a plus/minus sign, or else it would be a binomial, and so if you multiply two monomials, it will result in:

a) a monomial

thanks for help 

The easiest divisibility rule to work with (at least for me) is the divisibility rule of 2^n, where n is some positive integer. That rule says that if the last n digits of any number is divisible by 2^n, then the whole number is. 

Since we need to find a number bigger than 100, n must be at least 7, since 2^7 = 128 > 100.

The smallest 7 digit multiple of 128 with no digits equal to zero is 1111168 because 1111111 is the smallest 7 digit number with no digits equal to zero, and \(\lfloor{\frac{1111111}{128}}\rfloor\cdot128=1111168\)

The rest of the 93 digits have to sum up to 128-1-1-1-1-1-6-8=109. Obviously, there is a lot of ways to make 93 one-digit numbers sum to 109, but the problem only asks for 1 example, so you could just use ninety 1's, two 5's, and one 9, for the rest of the digits of the number. 

The full number would look like this: \(\boxed{1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111115591111168}\)

(you could check in WA or some other calculator to see if it's correct)

In this question, it is probably possible to represent it as an algebraic equation, but I think it would be easier to look at it from a different perspective. Because the Goofy Gardener (weird name, by the way) found that the pigeon plant was 1 foot high and the monster fern was 7 feet high, we can represent the height with a table.

We can stop at day 5, because on this day, the monster fern is three times as big as the pigeon plant. So, you have your answer:

The monster fern will be three times as big as the pigeon plant in 5 days.

the total number of numbers is 9*9!

The total number starting with an even and having each consecutive pair adding to an odd is  4*4!*5!

The total number starting with an odd and having each consecutive pair adding to an odd is  5!*5!

\(Prob=\frac{4*4!*5!+5!*5!}{9*9!}\\ Prob=\frac{5!4!(4+5)}{9*9!}\\ Prob=\frac{5!4!}{9!}\\ Prob=\frac{2*3*4}{6*7*8*9}\\ Prob=\frac{1}{6*7*3}\\ Prob=\frac{1}{126}\\\)

Hi Jenny,

Q1

Start with sin(3x)=sin(2x+x)

Do the expansion and just keep expanding what you get until it all falls out.

Give it a go and come back with what you have done.

You cannot find the square root of a negative number 

So x is a positive square number.

and     \(0\le 63-3\sqrt{x} \le63\)

Now just test integer square values of x starting with x=0, then 1,4,9 etc

As follows:

I think you have made this much more difficult and longer than necessary NotGuest.

You only need x^3 terms

These are the only terms that are relevant.      

\(6x^3*4=24x^3\\ 4x^2*-3x=-12x^3\\ 7x*3x^2=21x^3\\ -5*6x^3=-30x^3\\\)