(2a+1)³

We could first look to combine like terms to simplify this but there are none we could combine.

Then we could look at order of operations, also known as precedence. There are a number of mneumonics to help us remember the order to do things, PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction), BIDMAS (Brackets, Indecies, Division, Multiplication, Addition, Subtraction) and a few more depending on where you have been taught, but thankfully they all basically mean the same thing.

This means we should do any work we can within the brackets/parenthesis first (following the order of the mneumonic) followed by any exponents/indecies (including roots), followed by multiplication/division (these can be either way around as long as they follow brackets/parenthesis and exponents/indicies) followed by addition/subtraction (these can be either way around as long as they are the last to be completed).

In this case we can't calculate the contents of the brackets/parenthesis as it contains numbers and an algebraic term. Therefor we go straight to applying the exponent/indicies which in this case is "³", meaning cubed or to the power of 3. Put simply this is equivelant to (2a+1)*(2a+1)*(2a+1) though we don't need the * (multiplication) symbol inbetween the brackets as we know that back to back brackets automatically have their contents multiplied, so would be written;

= (2a+1)(2a+1)(2a+1)

We could then multiply the contents of the first two brackets/parenthesis against each other. I use the FOIL method. First from each bracket, Outside from each bracket, Inside from each bracket, Last from each bracket. It ensures that each term from one bracket is multiplied by each term from the other bracket. The order is not important but ensuring all are completed is;

= ((2a*2a)+(2a*1)+(1*2a)+(1*1))(2a+1)

= (4a²+2a+2a+1)(2a+1)

To simplify this we could combine like terms within the brackets/parenthesis;

= (4a²+4a+1)(2a+1)

= We could now multiply the contents of the two remaining brackets/parenthesis though this time we can't use the FOIL method as we have three terms inside the first bracket/parenthesis, another methodical approach will have to be used to ensure all terms from the first bracket/parenthesis are multiplied by all terms in the second bracket/parenthesis;

= (4a²*2a)+(4a²*1)+(4a*2a)+(4a*1)+(1*2a)+(1*1)

= 8a³+4a²+8a²+4a+2a+1

We could then combine like terms leaving us with;

= 8a³+12a²+6a+1

Sorry if this is a bit long winded but I've tried to cover everything for you here. Please bear in mind I am just a newbie so there may be more elegant solutions to this and I may be wrong, though I believe I have it correct.

I think that this  is the meaning Tetration :)

$$\\\frac{2}{11}\times 3\frac{7}{15}\\\\
=\frac{2}{11}\times \frac{3*15+7}{15}\\\\
=\frac{2}{11}\times \frac{52}{15}\\\\
=\frac{104}{165}\\\\$$

$$\\V \alpha\; T\\
V=kT\\
$When V=250 $\quad T =300\quad find\;\;k \\
250=k*300\\
k=250/300=5/6\\
V=\frac{5T}{6}\\\\\\
(B)\\
When T=240\\
V=\frac{5*240}{6}=200ml$$

$$\\h^2=2^2+2^2\\
h^2=4+4\\
h^2=8\\
h=\sqrt{8}\\
h=\sqrt{4*2}\\
h=2\sqrt{2}\\$$

Can't you just change it yourself?  Do you need the calc to do it?

I am not familiar with the calc - I am just asking.    

It is a typo (perhaps they meant to ask for the increase in weight)

You answer is perfect   

Try asking on Quora.

Thanks Heureka    

My answer is wrong - the error was right near the beginning.    

I am sure that Heureka's answer is perfect.

I think that you mean 5.07% and      $12,000

Tax = 5.07/100*12000     dollars

now use the calc on the home page. 

C+A=509  (1)

C=A+59    (2)

find A

Sub 2 inot 1 and solve.    

Can you write the question that you are talking about or upload a picture of something because I don't know what you mean.   

sometimes you have to choose the angle yourself.   

The SAT mathematics scores (1,664,479 students) in 2012 are approxiimately normally distributed with a mean of 514 and a standard deviation of 117.

$$\\\mu=514 \qquad \sigma=117$$

a. bob achieved a score of 700 on the test. How many standard deviations away from the mean is his score of 700?

$$\\z=\frac{700-514}{117}\\\\
z=\frac{186}{117}\\\\$$

$${\frac{{\mathtt{186}}}{{\mathtt{117}}}} = {\frac{{\mathtt{62}}}{{\mathtt{39}}}} = {\mathtt{1.589\: \!743\: \!589\: \!743\: \!589\: \!7}}$$

His score is 1.59 standard deviations above the mean. 

b. What percentage of those who took the test scored higher than Bob?

There is only one ghost of web2 but he actually has the username 'Ghost'

Therefore I think you have been answered by an anony-mouse in a mask.  HaHaHa  

"Anony-mouse"   I like that.  Thanks anon     

John computes the sum of the elements of each of the 21 two-element subsets of {1,2,3,4,5,6,7}.

What is the sum of these 21 sums ?

$$\small{\text{
$
sum = \frac{3}{2} * \left(\ 1*2+2*3+3*4+4*5+5*6+6*7\ \right) =
\frac{3}{2} * \left(\ 2+6+12+20+30+42\ \right)
$
}}$\\$
\small{\text{
$
= \frac{3}{2}*112=168
$
}}$\\\\$
\small{\text{
for n:
$
sum = \frac{3}{2} * \left(\ 1*2+2*3+3*4+4*5+5*6+6*7+\dots + (n-1)*n\ \right) = 3*\left( \begin{array}{c} n+1\\3 \end{array} \right)
$
}}$\\\\$
\small{\text{
$
= \dfrac{(n-1)n(n+1)}{2}
$
}}$\\\\$
\small{\text{
for n=7:
$
sum = 3*\left( \begin{array}{c} 8\\3 \end{array} \right)
=3*\frac{6*7*8}{2*3}=21*8=168
$
}}$$

$${\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{2}}}} = {\mathtt{2.828\: \!427\: \!124\: \!746\: \!190\: \!1}}$$

i think she's on extended vacation.....

-6(4-t) = 12t

⇔  -24+6t = 12t

⇔  -6t = 24

⇔  t = -4 

🗽 

All the anony-mouses here can share your thanks, since we don't know which particular one helped you.   🎭

1/h^5=h^n  ...  notice that 1/h^5 can be written as h^(-5)  ...  so we have

h^(-5)  = h^n     and it's obvious that n = -5

The sum of a series is given by

S = (n/2)[a₁ + a₁ + d(n - 1)]   where n is the number of terms, a₁ is the first term,      a₁ + d(n - 1) is the last term, and d is the common difference between terms .... so we have

S = (n/2)[ 7 +  7 + 5(n-1) ] > 5000

(n/2) [ 9 + 5n ]  > 5000

n[ 9 + 5n  ] > 10000

5n^2 + 9n - 10000 > 0   and solving this ...  n > 43 → n = 44

So...the last number said is

a₄₄ = [ 7 +5(44 - 1) ] =  [ 7 +5(43) ]  = 222

So...we need to find "d"

The sum of the first n terms of an arithmetic series is given by:

S = (n/2)[a₁ + a₁ + d(n-1) ]   .... so we have

(8/2)[a₁ + a₁ +d(8 - 1)]  = 3* (4/2) [ a₁ + a₁ + d(4 - 1) ]

4 [2a₁ + d(7)] = 6 [ 2a₁ + d(3) ]

8a₁ + 28d = 12a₁ + 18d

10d = 4a₁

d = (4/10)a₁ = (2/5)a₁

I'm not overly sure about this one....but I'll submit it for review/criticism....!!!