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thank you very much 

Using the equation  1 GB  =  1000 MB ,  we get.....

1 GB  =  1000 MB

                                     Multiply both sides of the equation by  6.8

6.8 GB  =  6800 MB

How many  1.43  MB  fit into  6800 MB  ?

6800 MB / 1.43 MB  ≈  4755.245

He won't be able to fit  4756  books on the tablet.

He can fit  4755  books on the tablet at most.

35/128

Can you post the question again? The title is too long...

A 10-inches pizza has a 5-inches radius.

A 12-inches pizza has a 6-inches radius.

The area of (Pizza 1) is 5^2pi=25pi and the area of (Pizza 2) is 6^2pi=36pi

The percent of the increase is \(\frac{36-25}{25}*100=\boxed{44}\% \)

sorry its GB

"Joost still has 6.8 memory on his tablet"

6.8 what? 6.8 GB? 6.8 MB?

do you know how to take partial derivatives?

I can understand being confused by the Curl, but Divergence is so straightforward I just don't

see how you can be confused by it.

To find the Divergence of a vector field take

the partial with repect to x of the x coordinate

the partial with repect to y of the y coordinate

the partial with repect to z of the z coordinate

and add them.  That's all there is to it.

See if you can do that and then we'll talk about the Curl.

\(\frac{w^6}{z^8} \Rightarrow \frac{w*w*w*w*w*w}{z*z*z*z*z*z*z*z}\)

Then you make a fraction with w/z. \(\frac{w^6}{z^6}\), and also multiply it by 1/z^2

So you have a new expression of \(\frac{w^6}{z^6}*\frac{1}{z^2}\)

I don't know if that is what you are looking for...

\(\text{stellation $n$ has an $n \times n$ square of dots, and 4 identical triangular regions containing}\\ \dfrac{n(n-1)}{2} \text{ dots each}\\ dots_n = n^2 + 4\dfrac{n(n-1)}{2} = 3n^2 - 2n\\ \text{I leave you to plug 20 in}\)

Is  00001  a  "5-digit number" ?

Is  1  a  "5-digit number" ?

If we're meant to include the numbers 0-9999 in the list of "5-digit numbers" then the question may have said

"How many nonnegative numbers less than 100000 are there which are multiples of 5 and. . ."

3)

2)
\(f(x) = \left\{ \begin{array}{cl} -2x & \text{if } x < 0, \\ \frac{x}{2} & \text{if } x \ge 0. \end{array} \right.\)

Let  y  =  f(x)  so we can say that...

The range includes the smallest possible y value to the biggest possible y value.
 

A graph might help:

The smallest possible y value is  0

There isn't a biggest possible y value because we can always find a bigger one, so we say it's  ∞

So the range is  [0, ∞)

1)

\(f(x) = \left\{ \begin{array}{cl} 3x & \text{if } x < 3, \\ 3^x & \text{if } x \ge 3. \end{array} \right.\)

Let's find  f(2)

2  <  3     so  we use   f(x)  =  3x

f(2)  =  3(2)

f(2)  =  6

Let's find  f(3)

3  ≥  3     so we use   f(x)  =  3^x

f(3)  =  3³

f(3)  =  27

Let's find  f(4)

4  ≥  3  so we use   f(x)  =  3^x

f(4)  =  . . .?  Can you figure this one out?

Hint: Try to figure out a pattern with the tessellations!

Thanks!

A man drags a 10.0 kg bag of mulch at a constant speed, applying a 22.5 N force at 32.0. What is the friction force acting on the bag?

\(\frac{x}{3}+\frac{4}{5} < \frac{5}{3}\)

                                      Subtract  \(\frac45\)  from both sides of the inequality.

\(\frac{x}{3}+\frac{4}{5}{\color{blue}-\frac45} < \frac{5}{3}{\color{blue}-\frac45}\)

\(\frac{x}{3} < \frac{5}{3}-\frac45\)

                                      Get a common denominator on the right side.

\(\frac{x}{3} < \frac{5}{3}\cdot\frac55-\frac45\cdot\frac33\)

\(\frac{x}{3} < \frac{25}{15}-\frac{12}{15}\)

                                      Combine the fractions on the right side.

\(\frac{x}{3} < \frac{13}{15}\)

                                      Multiply both sides by  3 , a positive number.

\(\frac{x}{3}{\color{blue}\cdot3} < \frac{13}{15}{\color{blue}\cdot3}\)

\(x < \frac{39}{15}\)

                                      And  \(\frac{39}{15}\)  =  2.6

\(x <2.6\)

What is the largest integer  x  such that  x < 2.6   ?

What is the largest integer less than  2.6 ?

The largest integer less than  2.6  is  2 , so

x  =  2

Find the semi-major axis.

Mmm I do not think that  a number starting with 0 is really a number. I mean it is not presented as a counting number.

Perhaps a zip code should be thought of as a string of digits rather than a number.  Afterall, it would make no sense to add or subrtract them. etc

But I do get your point. This is why maths questions needs to be worded very precisely.

Yes my answer does includes duplicate digits, the question did not say that the digits cold not be duplicates.

It said that the numbers must all different and they are.

5554 is a  different  number from  4555 is it not?

I will admit though that the question is poorly worded.

"How many 5-digit numbers are there which are multiples of 5 and are ALL different and that the 2nd digit from the left is odd? "

Hi Melody: Your count includes many duplicate numbers such as:1 1 4 5 0. Notice the duplicate "1". This number is allowed only if it is: 1 3 4 5 0. All 5 numbers must be different and the 2nd digit from the left must be odd. You start with 9 digits from the left. But one of them, 3, cannot be included because you will have 2 "3s", which is not allowed. That leaves 8 digits. But the first digit cannot be "4" or "5" because you will have duplicates. That leaves only 6 numbers: 1, 2, 6, 7, 8, 9. And so on. In the above computer code, I have included all these exceptions in and have a full list of all allowable numbers. They total =2,856 such numbers.

Hi Melody.....   I looked this up to be sure.....

As above.....there ARE zip codes that begin with zero.....so I think the answer is 10,000

There ARE ZIP codes that begin with 0    so I would modify your answer to

  10  x 5  x 10 x 10 x 2 = 10, 000