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Let the number of gallon of 50% antifrreeze =G

0.50G + 0.30*60 =0.42 *[G + 60]

0.50G +  18 =0.42G + 25.2

0.50G - 0.42G =25.2 - 18

0.08G = 7.2

G = 7.2 / 0.08

G = 90 - gallons of 50% antifreeze must be mixed with 60 gallons of 30% antifreeze to make [90 + 60]=150 gallons of 0.42% of antifreeze.

We can form a "proportion" with information. First, let's find out a general "formula":

a%         b%           c%

----   +    ----   =    ---------

 x            y             x+y

Multiplying the percentages with the corresponding gallon, we see:    ax + by = c(x+y)

From here, we can plug in numbers:

0.5x + 0.3(60) = (0.42)(x + 60)

=> 0.5x + 18 = 0.42x + 25.2

=> 0.5x = 0.42x + 7.2

=> 0.08x = 7.2

=> x = 90

Therefore, we must add 90 gallons.

Edit: Thanks to guest's answer, I corrected my numbers (but my answer remains the same...)

:)

Um that answer is wrong and how did you get 85?

Using only 2,4,6,8 and +,-,×, divide to get the answer 125 think of 5 solutions  

The problem does not specify whether all of the digits must be used or if just some of them can. 

The problem does not specify whether each digit can be used only once of if it can be repeated. 

You have to think of ways to get a 5. 

There are (10 divided by 2), (20 divided by 4), (40 divided by 8) and many other ways.

      (6 x 8) – 8 

      —————      This equals 5.  Just multiply it by itself 3 times and you get 125. 

             8   

                     (8 + 8 + 8 + 8 + 8)                (4 x 8) + 8                 (8 + 2)

       ditto       ————————     and     —————     and     ——–—        

                                  8                                    8                             2    

Those are four ways to get 5, and then just multiply it by itself 3 times, or mix 'em up.  You take it from here. 

_.

Could I have some more help? I do not know the process, and I do not understand your process.

A library has six identical copies of a certain book. At any given time, some of these copies are at the library and some are checked out. How many different ways are there for some of the books to be in the library and the rest to be checked out if at least one book is in the library and at least one is checked out? (The books should be considered indistinguishable.)  

                       5    

One book must be in and one book out, leaving the four others to contend with. 

Counting the one in and one out, looks like there can be 5 different arrangements: 

                    In  Out    

                    5     1   

                    4     2   

                    3     3   

                    2     4   

                    1     5    

Yeah, thanks to all who actually helped!

Sorry, there was a copying error in answer #2;

(x - 5) + (3x + 2) =(6x - 23), solve for x
x + 3x - 6x =- 23 - 2 + 5
- 2x = - 20
x = - 20 / -2
x = 10
NP =3x + 2 =3*10 + 2 =30 + 2 =32

(x - 9) + (3x + 2) =(6x - 23), solve for x
x + 3x - 6x =- 23 - 2 + 9
- 2x = - 16
x = - 16 / -2
x = 8
NP =3x + 2 =3*8 + 2 =24 + 2 =26

Note: In future, don't say: "Find NP.  I need the answer". Always be polite, and say something like: "Please, help me find the answer to this question", or something like that. OK? Good luck!

The number you are looking for is: 428,571. So that:

4 * 428,571 = 3 * 571,428

1,714,284 =1,714,284

Note:The above number is an abbreviated version of this "Special Number":

142,857 * 2 =285,714 - Same digits in different order.

142,857 * 3 =428,571 - Same digits in different order.

142,857 * 4 =571,428 - Same digits in different order.

142,857 * 5 =714,285 - Same digits in different order.

142,857 * 6 =857,142 - Same digits in different order.

142,857 * 7 =999,999  !!!

I don't understand piecewise functions.  Please explain.

a. Solve this system of equations using Gaussian elimination.

10^7 = 10000000     (seven zeros)

b=85+​(15+7​)w 

210 = 85 + (22)*w

210 - 85 = 22w

125 = 22w

w = 125 / 22

w = 5.68 weeks to have $210 in the bank.

Line BC may or may not be parallel to line AO. 

If BC = DC then    y = 1/2 (180 - 82)

In 1856, Andrew Waugh announced Mount Everest to be 8840 m high, after several years of calculations based on observations by the Great Trigonometric Survey. More recent surveys confirm the height as 8848 m. Calculate the percentage error made in the earlier survey. Round answers to 3 s.f.

Im Jahr 1856 kündigte Andrew Waugh nach mehrjährigen Berechnungen auf der Grundlage von Beobachtungen des Great Trigonometric Survey an, dass der Mount Everest 8840 m hoch sei. Neuere Erhebungen bestätigen die Höhe mit 8848 m. Berechnen Sie den prozentualen Fehler, der in der früheren Umfrage gemacht wurde.

Hello Rizos!

\(8848m \widehat{=}100\%\\ 8848m-8840m=8m \widehat{=}x\)

\(8848m:100\%=8m:x\\ x\cdot 8848m=8m\cdot 100\%\\ x=\frac{8m\cdot 100\%}{8848m}=0.090416\%\)

\(x=0.09\%\)

The percentage error made in the earlier survey is 0.09%.

  !

Old Mc Donald raises ducks and cows. The animals have a total of 100 heads and 354 feet. How many ducks and how many cows does Old Mc Donald have?

Hello Guest!

\(x+y=100\\ y=100-x\\ 2x+4y=354\\ 2x+4(100-x)=354\\ 2x+400-4x=354\)

\(-2x=354-400\\ -2x=-46\)

\(x=23\)

\(y=100-x\\ y=100-23 \)

\(y=77\)

Old Mac Donald has 77 cows and 23 ducks.

  !

It's good that you want an explanation instead of just an answer/wrong answer! ilorty also explained it well! Do you get the question now?

10 weeks

From x + 3y = -5, y = -x/3 - 5, so the slope of the line is -1/3. The slope of the new line is also -1/3, so y = -x/3 + B.  Pugging in x = 2 and y = -7, we get -7 = -2/3 + B, so B = -19/3.

Then the line is y = -x/3 - 19/3.  Then 3y = -x - 19, so 3y + x = -19.  We want the right-hand side to be 3, so we mutiply both sides by -3/19: -9/19*y - 3/19*x = 3.  Therefore, B - A = -19/3 - 3 = -28/3.

A/[XYZ] = 5/9.