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We want the biggest numbers, and we can get a 9 from \(6\times 3\) which is \(9\times 2\) .

Therefore, now we have the biggest digit as 9 with 2, 2, 4, 5, and 7 left over.

The next largest digit is probably 8 as \(2\times 4=8\) , leaving us with 2, 5, and 7.

So far we have 98___ and we can see that \(2\times 5=10, 2\times 7=14, 5\times7=35\)and the tens digits are all less than 7 so now we go decreasing order and get

98752.

You are very welcome!

:P

Yes, sorry. I knew that but I chose the wrong answer xD

*facepalm* I know, I just mixed them up... thanks for noticing.

We had a robot check that.....he/she found no problem.....apparently, robots aren't expert with the finer details of the English language.....

[ We should have one of Ginger Ale's chimps check this.....they rarely miss anything....particularly after a few stiff drinks... ]

The correct answer was choice 4. Thanks for your help anyway.

Nope...it has been pointed out before....

Let r be the radius of the  tank

The volume of the tank is

6000pi = pi * r^2 * h

Solving for h, we have that

h = 6000/r^2

So....the surface area cost is given by

Sa cost  =   ($1)pi*r^2 + ($2)pi *r^2 + ($4)2pi * r * 6000/r^2

Sa cost  =  3pi*r^2 + 8pi* 6000r^(-1)

Take the derivative of this to find the radius that minimizes the cost

Sa ' =   6pir - 48000pi / r^2

Set this to 0  and solve for r

pi ( 6r - 48000/r^2)  = 0

6r -  48000/^2  = 0

6 ( r - 8000/^2) = 0

r - 8000/r^2 = 0

r^3 - 8000  = 0

r^3 = 8000

r = 20 ft

So....the minimum cost is 

3pi*(20)^2 + 8pi* 6000/20 =

pi [ 1200 + 2400]  =   $ 3600pi    ≈  $11309.73

Thanks, Heureka!

Note: 275/12221 can be simplified to 25/1111.

( f + g) (x)  = 

 f(x) + g(x) =

[ x^3 - x ] + [ x^3 + 2x^2 - 10 ]  =

2x^3 + 2x^2 - x - 10

( f - g) (x) =

f(x) - g(x)   =

[ x^3 - 2x^2  + 12x - 6 ] - [ 4x^2 - 6x + 4 ]  =

x^3 - 6x^2 + 18x - 10

( f * g)(x)  =

f(x) * g(x) =

[x^2 + 2x - 6 ] * [ x^4  + 3 ]   =     

x^6 + 2x^5  - 6x^4 + 3x^2 + 6x - 18  

No prob.....!!!

Thanks, I really appreciate you helping me.

The relative max of -3 occurs at about x = 1.5

The relative min of -14 occurs at about x = 4.5

Thus....#4  is the correct choice....

Rate of change from 7 - 9 =    [5760 - 1920 ] / [9 - 7] = 1920

Rate of change from 4- 6 =   [945 - 105] / [ 6 - 4 ] = 420

1920 / 420    ≈   4.57 times as great

Note that we can write this as

1 x 3/3 x 5/5 x 7/7 x.......x 1/99 =

1/99

If one integer is 48, the other must be 24, 72, 120, etc. because if the numbers are 48, 96, 144, etc. then the GCD would be 48. Also, the other integer must be less than 240 because... it can't be over.

Listing the integers,

24, 72, 120, 168, 216

We see that 24 definitely doesn't work, and neither does 168 or 216 because they are strange numbers. 72 and 120 are our choices, and after testing only 120 works. Therefore, the other integer is 120.

You are very welcome!

:P

98752 still works but is greater than 87653

Well, we only want the x values of 1 to 5.

We can easily see that the Relative Maximum is around -3 at around x=1.5 because it has the greatest y-value in our interval. The Relative Minimum is around -15 at around x=4.5 because it has the least y-value in our interval. Therefore the answer is #4.

You are very welcome!

:P 

Big question there... it turns into \(\frac{255861111}{5966911}\) simplified, around \(42.87999452\)in decimal form, and \(42 \frac{5250849}{5966911}\) as a mixed number.

You are very welcome!

:P

There are  24 * 60 =  1440 minutes in a 24-hr period

The LCM of 2 and 5  = 10

So....they back up at the same time every 10 minutes

So

1440 / 10   =     144 times

...or just enter it into the Web2.0 calc as you entered it in your Q

2.5*10^3*3.5*10^-7 = 0.000875

2.5 x 10^3 = 2500

3.5 x 10^-7 = .000 000 35

2500 X .000 000 35 = 2500*.00000035 = 0.000875

See the answer here:  https://web2.0calc.com/questions/need-the-help-i-can-get

Just re-arrange your 7 numbers slightly by multiplying 2 x 4 = 8 and put them in order from the biggest to the smallest and you get this: 87,653.

Don't know that this is the correct answer, JGA....but here's my best attempt :

If we have 10 ditinct positive integers....the median is the average of the 5th and 6th data values [ assuming the we have ordered the values in increasing order from left to right ]

It's obvious that the first four integers will be 1, 2, 3 , 4

To have the smallest overall average, we need to have the 5th and 6th values as close to 10 as possible such that their average is 10.....these are 9 and 11

And the remaining integers are 12, 13, 14 and 15

So....the data set is

1,2, 3, 4, 9, 11, 12, 13, 14, 15

The median  = 10

The average = 8.4