BlackjackEd

Well first let us replace "what" with x and make an equation.

\({6x\over4}=12 \)

(please correct me if this is not what you meant, it is a bit hard to understand what you wrote)

Now to solve it:

\({4\cdot6x\over4}=12\cdot4\)

\(6x=48\)

\({6x\over6}={48\over6}\)

\(x=8\)

The answer to your question is 8.

a) Let us first find out the total number of numbers. There are 99 as it is a pattern going up by 1s starting on 1.

To solve this problem, the first thing I did was to separate the 1-digit and 2-digit numbers. We know that the only 1-digit numbers are 1-9, and everything else is 2-digit numbers.

Let us list this information:

1-digit = 9x

2-digit = 90x (99-9)

Now to find the total number of digits, we can multiply the number of x-digit numbers by x.

\(9\cdot1=9\) (1-digit total) 

\(90\cdot2=180\)(2-digit total)

\(9+180=189\)(total)

Sam wrote down 189 digits in total.

b) For this one, to find the probability of getting a 0 out of all digits, we can divide the number of 0s by the total number of digits.

As there are only a few 0s, we can list them out:

10,

20,

30,

40,

50,

60,

70,

80, and 

90.

In total, there are 9 0s.

As we have already evaluated the total number of digits in part a), we can divide 9 by 189.

The probability that Sam chooses a 0 is 9 out of 189. (I think you should be able to do some simplifying yourself???)

c) I am so sorry, I'll come back to this question in about 20 mins, but I don't have time right now to explain it in detail.

However, I can tell you that it has something to do with this:

\(1+99\),

\(2+98\),

\(3+97\)...

\(49+51\),

\(50\)

I hope you will be able to solve it from here, but if not, I'll be back.

Hope this helped,

First, we should find out the formula for the area of an octagon (if you already know this Guest, just scroll down).

This is the formula:

\(A=2(1+\sqrt2)a ^2\)

(where a is the length of a side)

Since we know that the length is 12, we can easily replace the a for 12.

\(A=2(1+\sqrt2)12 ^2\)

If you are lazy like me, you will dutifully plug it into a calculator and achieve the approximate result of 

\(695.29 \) \(cm ^2\)

The value rounded to five decimal places is 

\(695.29351\) \(cm ^2\)

Hope this helped!

Could you please check again for grammatical errors? I'm not sure I understand.

Thanks,

Hmm, well could you check the question again? (just to be sure)

If I am still wrong, my deepest apologies.

We already know that exponents mean you multiply the same number by itself. With fractions, the typical strategy is this:

When the

numerator = n,

denominator = d,

and the 

exponent = x,

\( (n/d) ^x =(n ^x/d ^x)\)

Therefore, if we plug 1 in for n and 4 in for d with 4 as x, the equation becomes

\(1 ^4/4 ^4\)

We know that 1 to any power is itself, so we can simplify to

\(1/4 ^4\)

Now we can easily do 4 to the power of 4 in our heads, or you could plug it in a calculator if you'd like.

\(4*4*4*4=16*4*4=64*4=256\)

Knowing this, the equation becomes

\(1/256\)

To answer the full question (Write −(1/4⋅1/4⋅1/4⋅1/4) using exponents), all we have to do is put 1/256 inside the bracket, as we have evaluated what 1/4 to the power of 4 is, and simply place a negative sign next to it!

\(-1/256\)

Please correct me if I am wrong,

In that case, we can multiply the number of choices for each letter by each other.

We know that the 1st letter has 5 different possible options, A, E, I, O, and U.

For the 2nd, 3rd, and 4th letters, there are 26 different possible options for each letter (as there are 26 letters in the alphabet).

Now, we can multiply these numbers together.

\(5*26*26*26\)

If you are lazy like me, you can plug it into a calculator and achieve the result

87880.

However, if you are a really hardcore mathematician, you can write it out:

\( 5*26*26*26 = 130*26*26 = 3380 * 26 = 87880\)

Hope this helped!

I remain,

The answer is 97.

If you wanted the explanation too, please let me know! (I didn't really want to write down all of my calculations, as I am admittedly a bit lazy :P)

Hope this helped!

How many letter words? It might just be me, but I see your question goes "How many -letter ...".

Do you mean 3-?

Thanks,