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We have 10 ways to choose the first number, 9 ways to choose the second and 8 ways to choose the third

So

10 * 9 * 8   =    720  possible combinations

We can solve with a proportion

12.1 / 607   =  x / 1220        cross-multiply

1220 * 12.1  =  607 * x        simplify

14762  =  607 * x        divide both sides by  607

 About   24.32   gallons   =  x

I'm assuming that you might want to solve this :

x^2 - 3x - 18 = 0      factor

(x - 6)  ( x + 3)  = 0

Setting both factors 0  and solving for x.......

x = 6       or   x  = -3

The two most identifiable points  are   ( 1, 30)  and ( 7, 55 )

Slope  =  

[ subtract the y coordinates in some order ] / [ subtract the x coordinates in the same order ]

[ 55 - 30 ]  / [ 7 - 1 ]   =

25 / 6   ≈  4.2

Maria's calculation of the final price

Discounted price      +  10%  of discounted price

[26.50 - .25(26.50)] + .10 [26.50 - .25(26.50)]    ≈ $21.87

Edwin's calculation of the final price

75% of price * 110%

[26.50 (75)] (1.10 ) ≈  $21.87

Both methods result in the exact same amount  !!!! 

2^(-3)

\(2^{-3}=\frac{ 1*2^{-3}}{\color{green}{1}}=\frac{ 1}{\color{green}{1*2^3}}=\frac{1}{8}\)

Whatever is raised to a negative power gets swapped to the other side of the fraction line and the negative power becomes a positive power.

Your question does not make sense!

\(4^3=64\)

or maybe you mean 

\(4^{1/3}=\sqrt[3]{4}\)

4^(1/3)  approx = 1.5874010519681994

This graph should help you to be confident!

.

hi Asad,

If some one else has you password then the obvious thing to do is change your password!

Thanks for the diagram, hectictar....!!!!  That really helps.....

To be honest....it was a little bit of a head-scratcher for me, too......I first tried to "over-complicate" things.....then, as usual......the "easy way" just kind of  "fell out ".....LOL!!!!

Ohhh !!!    I was stumped on this one...!

Here is how I saw it from your answer:

Let the center of the circle be O

And we can construct  right triangle OQP  with angle OQP  being = 90° 

Let the hypotenuse of this triangle  be OP  =  the radius, R

Let  one of the legs of this triangle  = PQ  = (R - 27)

And let  the other leg = OQ  = (R - 6)

And by the Pythagorean Theorem, we have that

PQ^2  +  OQ^2   =  OP^2

(R - 27)^2  + (R - 6)^2  = R^2   simplify

R^2 - 54R + 729  + R^2  - 12R + 36  = R^2

2R^2  -  66R + 765  = R^2

R^2 - 66R  +  765  = 0

This can be factored as

(R - 15) (R - 51)  = 0

Setting each factor to  0  we have that R = 15 or R  = 51

We must reject R = 15  because one of the legs, PQ, would have a negative length

So the radius  =  51

area = (1/2) * base * height

Let's call the base   10 km .

Here, I just rotated it so that the base is at the bottom and added the pink line for the height.

sin θ  =  opposite / hypotenuse

sin 37º  =  height / 7                          Multiply both sides of this equation by  7  .

7 sin 37º  =  height

area  =  (1/2) * base * height

area  =  (1/2) * (10) * (7 sin 37º)

area  =  35 sin 37º                           Put this into a calculator to get that...

area  ≈  21.064   square km

10^(10^(10^3*1000(10*100)

\( \Large 10^{(10^{(10^{3}\cdot 1000\cdot(10\cdot100)}}\)

Where should the braces close?

  ?

23,90*15/16

\({\color{red}23.90\cdot\frac{15}{16}}=\frac{239}{10}\cdot\frac{15}{16}=\frac{239\cdot3\cdot5}{5\cdot32}\\ \color{blue}=\frac{717}{32}=22\frac{13}{32}=22.40625\)

  !

The word geometry has eight letters. Three letters are chosen at random. What is the probability that two consonants and one vowel are chosen?

answer choices:

0.536
0.268
0.179
0.089

geometry 

5 consonants, 3 vowels

\(\frac{5}{8}\times\frac{4}{7}\times\frac{3}{6} =\frac{60}{336}\color{blue}=0.179\)

The probability for the above event is 0.179.
With 28 games, it will arrive on average 5 times.

  !

First, you have to find the Future Value of all her father's deposits for 17 years. Since it is not specified whether the deposits are made at the beginning or the end of the year, will assume for the purpose of this calculation, that the deposits are made at the beginning of year 1 for 17 years @ 8% comp. annually.

For that purpose, will use the following formula:

FV=P{[1 + R]^N - 1/ R} x [1 + R]

FV = 5,000 x {[1.08]^17 - 1 / (0.08)} x 1.08

FV = 5,000 x         33.750225.......        x 1.08

FV = $ 182,251.22 - This is the Future Value of the 17 deposits of $5,000 each.

The second part consists of finding out the annual payment that she can withdraw at the beginning of year 18 through year 22 for a total of 4 payments. To that end, will use this formula:

PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1} / [1 + R]

PMT = 182,251.22 x 0.08 {[1.08^4] / [1.08]^4 - 1} / 1.08

PMT = 14,580.10 x                           3.77401....            /  1.08

PMT = $50,949.48 - This is the amount that she will able to withdraw for each of the 4 years.

8[7 - (6x - 6)] + 6x  =  0          Distribute the   -1   to each term in   (6x - 6)  .

8[7 - 6x + 6] + 6x  =  0           Distribute the   8     to each term in   [7 - 6x + 6]  .

56 - 48x + 48 + 6x  =  0         Combine like terms.

104 - 42x  =  0                       Subtract   104  from both sides of the equation.

- 42x  =  - 104                        Divide both sides of the equation by   -42  .

x  =  52 / 21

x  ≈  2.476

\(0.1\,*\,50\,=\,\frac1{10}\,*\,50\,=\,\frac1{10}\,*\,\frac{50}1\,=\,\frac{1\,*\,50}{10\,*\,1}\,=\,\frac{50}{10}\,=\,\frac51\,=\,5\)

Here, the height of the tree is labeled  " t " .

Since the tree makes a  90º  angle with the ground, we can say...

tan 58º  =  t / 20                                 Multiply both sides of the equation by  20  .

20 tan 58º  =  t                                   Put this into a calculator to get that...

32.007  m  ≈  t

It is easier to multiply fractions.

For example:

\(\frac34\div\frac57=\frac34\,*\,\frac75\)

Then, just multiply straight across.

\(=\frac{3*7}{4*5}=\frac{21}{20}\)

It  is  true that

\(\frac34\div\frac57=\frac{3\div5}{4\div7}=\frac{21}{20}\)

But how are you going to evaluate   3 / 5    and   4 / 7    without using a calculator or long division?

And...to see why inverting and multiplying is the same as dividing, take a simple example:

\(10\div2=10\,*\,\frac12=\frac{10}{1}\,*\,\frac12=\frac{10}{2}\)