All Answers 359153 Answers

I assume something is missing here ://

Let the original amount=x

.8x remains after 1st 1/5 spent.

.8 x .8x=.36x remains after the 2nd 1/5 spent

.36x=36

x=$100 orignal amount he started with

[(-2)^2]^3  =

[4]^3  =

64

A man spends one fifth of the money in his wallet . He then spends one fifth of what remains in the wallet. He spends $36.00 in all. How much money did he have to begin with?

x = Money to begin

\(\begin{array}{c|l|r} \hline & \text{wallet} &\text{giving dollar} \\ \hline & x & 0 \\ &(x)-\frac15\cdot x & \frac15\cdot x \\ &(x-\frac15\cdot x) -\frac15(x-\frac15\cdot x) & \frac15(x-\frac15\cdot x)\\ \hline \text{sum} && $36\\ \hline \end{array}\)

\(\begin{array}{rcl} \frac15\cdot x + \frac15(x-\frac15\cdot x) &=& $36 \quad & | \qquad \cdot 5 \\ x + x-\frac15\cdot x &=& $180 \\ 2x-\frac15\cdot x &=& $180 \quad & | \qquad \cdot 5 \\ 10x-x &=& $900 \\ 9x &=& $900 \quad & | \qquad :9 \\ \mathbf{ x } & \mathbf{=} & \mathbf{$100} \\ \end{array}\)

To begin he has $100.

\(\begin{array}{c|l|r} \hline & \text{wallet} &\text{giving dollar} \\ \hline & \mathbf{$100} & 0 \\ & $100-$20=$80 & \frac{$100}{5}=$20 \\ & $80-$16=$64 & \frac{$80}{5} =$16\\ \hline \text{sum} && $36\\ \hline \end{array}\)

For normal distribution (or any symmetric distribution) Pr(Z<-N) = Pr(Z>N), so, given that the total area under the curve must be 1 we have:  Pr(Z<N) + Pr(Z>N) = 1

Hence:  Pr(Z<N) = 1 - Pr(Z>N) = 1 - Pr(Z<-N) = 1 - p

So B. is the answer. 

Like what?

Let x  be the amount he started with

So....he first spends  1/5 of this  = (1/5)x

So....what's left  =   (4/5)x

And he spends (1/5)  of this  = (1/5)(4/5)x =  (4/25)x

So  he spends   (1/5)x + (4/25)x   and this = $36.......so we have

(1/5)x + (4/25)x  = 36

(5/25)x + (4/25)x   = 36

(9/25)x   = 36      multiply both sides by  25/9

x =36 (25/9)

x = (36/9) * 25

x = 4 * 25   =   $100       and this is what he started with

Proof......he spends  1/5 of  $100  = $ 20

Then....he spends 1/5 of  what's left = (1/5)($80)  = $16

And $20 + $16   = $36

You just use the 10^x button:

.

Thank you so much! That makes a bit more sense now :)

( 1 / 20)  /  (3 / 4)       invert the second fraction and multiply

(1 / 20)  * (4 / 3)         swap denominators

( 1 / 3 ) * ( 4 / 20)

(1 / 3 ) * ( 1 / 5)  =

1 / 15

b. Show, using index laws, that 3¹⁰=9⁵

\(\begin{array}{lrcll} & 3^{{\color{red}10}} &=& 9^5 \quad & | \qquad {\color{red}10} = 2\cdot 5\\ & 3^{2\cdot 5} &=& 9^5 \\\\ \hline \\ \text{formula: } & \boxed{~ \begin{array}{rcll} (a^b)^c = a^{b\cdot c} = a^{c\cdot b} = (a^c)^b \end{array} ~} \\ \\ \hline \\ & (3^2)^5 &=& 9^5 \quad & | \qquad 3^{2\cdot 5} = (3^2)^5\\ & ({\color{green}3^2})^5 &=& 9^5 \quad & | \qquad {\color{green}3^2} = 3\cdot 3 = 9\\ & 9^5 &=& 9^5 \\ \end{array}\)

Would you mind explaining 'b' in a little bit more detail? as in how you got that answer?

a. Show, by expanding, that 3¹⁰=9⁵

b. Show, using index laws, that 3¹⁰=9⁵

Don't they just mean the same thing?

I assume

a.

\(\begin{array}{rcll} 3^{10} &=& 9^5 \\ 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3 &=& 9\cdot 9\cdot 9\cdot 9\cdot 9 \\ 59049 &=& 59049 \end{array}\)

b.

\(\begin{array}{rcll} 3^{10} &=& 9^5 \\ 3^{2\cdot 5} &=& 9^5 \\ (3^2)^5 &=& 9^5 \\ 9^5 &=& 9^5 \\ \end{array}\)

Thanks Heureka, you got the same answer as me.  That must have been a dash and not a minus sign at all :))

The windows of a downtown office building are arranged so that each floor has six fewer windows than the floor below it. If the ground floor has 52 windows, how many total windows are on the first eight floors?

arithmetic series:

 \( a_1 = 52,~d = +6\)

formular:

\(a_n = a_1+(n-1)\cdot d\)

\(\begin{array}{rcll} a_n~?\\ a_n &=& 52+(n-1)\cdot 6 \\ a_n &=& 52+6n-6 \\ \mathbf{a_n} & \mathbf{=} & \mathbf{46+6n} \end{array}\)

sum:

\(\begin{array}{rcll} s_n~? \\ s_n &=& \left( \frac{a_1+a_n}{2} \right) \cdot n \\ s_n &=& \left( \frac{ 52+(46+6n) }{2} \right)\cdot n \\ \mathbf{s_n} & \mathbf{=} & \mathbf{\left( \frac{ 98+6n }{2}\right)\cdot n} \end{array}\)

total windows on the first eight floors?

n=8

\(\begin{array}{rcll} s_8~? \\ s_8 & = & \left( \frac{ 98+6\cdot8 }{2}\right)\cdot 8 \\ s_8 & = & \left( \frac{ 98+48 }{2}\right)\cdot 8 \\ s_8 & = & \left( \frac{ 146 }{2}\right)\cdot 8 \\ s_8 & = & 146 \cdot 4 \\ \mathbf{s_8} & \mathbf{=} & \mathbf{584} \\ \end{array}\)

On the first eight floors are total 584 windows.

When you have a quadratic equation in the form:  \(ax^2+bx+c=0\)

the two solutions are given by:  \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

In your case:

A)   a = 5,  b = 7 and c = 2   (because it can be rewritten as 5x² + 7x + 2 = 0

B)  a = 12, b = -28 and c = 15

Plug these values into the formula above.

.

The sinh function is on many calculators including the one on the home page here.

It is defined as:  (e^x - e^-x)/2  where e is Euler's number 2.71828...

Use the calculator on the home page here.

nvm, guys :D I figures it out XD

Solve using the quadratic formula:

A) 5x^2+7x=-2                              B) 12x^2-28x+15=0

Here is your quadratic equation factored:

Factor the following:
2 x^2+9 x-5

Factor the quadratic 2 x^2+9 x-5. The coefficient of x^2 is 2 and the constant term is -5. The product of 2 and -5 is -10. The factors of -10 which sum to 9 are -1 and 10. So 2 x^2+9 x-5  =  2 x^2+10 x-x-5  =  5 (2 x-1)+x (2 x-1):
5 (2 x-1)+x (2 x-1)

Factor 2 x-1 from 5 (2 x-1)+x (2 x-1):
Answer: |  (2 x-1) (x+5)

Now, to graph it, go to this link and learn how to use the graphing calculator there:https://www.desmos.com/calculator.

Good luck to you.

Complementary angle:either of two angles whose sum is 90°.

If one angle =x, then the other is:

2x + 5, but we have:

x + 2x + 5 =90

3x=85 divide both sides by 3

x=85/3

x=28 1/3 degrees-one of the angles.

(2 x 28 1/3) + 5

=61 2/3 degrees-the 2nd angle.

$4,200 / .12 =$35,000 her salary this year.

$35,000 - $3,000=$32,000 Her salary last year.

An equation representing this would look  something like this:

S=(C/I) - R, where, S=her salary last year, C=amount of her savings, I= rate of her savings, R=salary increase.

5/5 ÷ 1/2=

1 / (1/2) =

1 x (2/1)=2. This is your answer.