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What is the least four-digit positive integer, with all different digits, that is divisible by each of its digits?

1236 / 1 =1236

1236 / 2 =618

1236 / 3 =412

1236 / 6 =206

Find the remainder when $1^3 + 2^3 + 3^3 + \dots + 100^3$ is divided by 6.

(1/4 n^2 (n+1)^2) mod 6 = 4

How do you simplify 2log4 9 - log3 ​3?

(log(9/2)) / (log(2))

What is the remainder when $13^{51}$ is divided by 5?

13^51 mod 5 =2 Remainder.

$2^{2005}$ is divided by 7?

2^2005 mod 7 =2 Remainder.

64,708,952

-0.19634322978 

1)  Using a 3 x 3 ft square to estimate a crowd in a 100 x 150 ft field. What would the equation/formula be?

          Since a 3 ft x 3 ft square contains 9 square feet and a 100 ft x 150 ft field contains 15,000 square feet:

          let  x  be the number of persons in a 3 ft x 3 ft square and  y  be the number of persons in a 100 ft x 150 ft field

          --->   y  =  (15 000 / 9) · x

2)  Using a 10 x 10 ft square to estimate a crowd in a 250 x 250 ft field. What would the equation/formula be?

         Since a 10 ft x 10 ft square contains 100 square feet and a 250 ft x 250 ft field contains 62,500 square feet:

          let  x  be the number of persons in a 10 ft x 10 ft square and  y  be the number of persons in a 250 ft x 250 ft field

          --->   y  =  (62 500 / 100) · x                      --->   y  =  625x

Solve:     (3x + 2)⁴  =  232

First:  find the fourth root of both sides:     3x + 2  =  232^1/4                            3x + 2  =  3.90276 ...

Second:  subtract 2 from both sides:               3x  =  232^1/4 - 2                      3x  =  1.90276 ...

Third:  divide both sides by 3:                            x  =  (232^1/4 - 2) / 3                x  =  0.63425,,,

This is an arithetic sequence because the difference between each two consecutive numbers is 4.

The formula for any term in an arithmetic sequence is:  t_n  =  t₁ + (n - 1)d

t_n  =  t₃₅   (the 35^th term)                     t₁  =  3   (the first term)                    n = 35   (the 35^th term)

d  =  4   (the common difference)

t_n  =  t₁ + (n - 1)d     --->     t₃₅  =  3 + (35 - 1)·4     --->     t₃₅  =  139

20 

it is 2.333. Since 1/3 is .3, just add it to the 2. Also if you see a number like that occurring, put a bar on the top of the first three. We call that type of decimals repeating decimals.

1)  For the first 7 minutes, 50 x 7  =  350 persons walked by you.

2)  Since the rate decreased by 20%, only 80% as many persons walked passed (per minute) the next 3 minutes.

     0.80 x 50  =  40 persons per minute

     40 x 3  =  120 persons.

3)  Now, does the phrase "this rate" refer to the rate of part #1, or the rate of part #2?

     If it refers to part #1, 50% of 50 is 25 persons per minute.

     25 x 2  =  50 persons for a total of 350 + 120 + 50  =  520 persons.

     If it refers to part #2, 50% of 40 is 20 persons per minute.

     20 x 2  =  40 persons for a total of 350 + 120 + 40  =  510 persons.

1)  A 9 foot by 9 foot square contains  9 x 9  =  81 square feet

     If 50 persons squeeze into this area, the average number of square feet per person is  

          81 / 50  =  1.62  square feet per person.

2)  A hallway that measures  16 feet  x  75 feet  =  1200 square feet.

    At  1.62  square feet per person:  1200 / 1.62  =  740,74  persons.

    In this case, round down to get 740 persons. 

2,000 persons at an average of 3.5 square feet per person requires:  2000 x 3.5  =  7,000 square feet.

If you draw a diamond, the cards are worth: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 20, 20

If you draw a heart, the cards are worth:  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 20, 20

If you draw a club, the cards are worth:  2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 40, 40, 40

If you draw a spade, the cards are worth: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 60, 60, 60

Adding these together, you get:  115 + 115 + 230 + 345

The total of all the card are 595.

Since there are 52 cards, the average value is  595 / 52  or  11.44230...  or 11 23/52

which is the fair price.

Rounded to the nearest penny:  11.44  (which actually gives the player a slight advantage).

3e0 is 3     if you enter '3' then '='   that is what you will get....make sure you actually hit the sqrt key

[(32−3)÷2−50]*2=[29/2-100/2]*2

=[-71/2]*2

=-71

If it's [(32−3)÷2−50]²:

[(32−3)÷2−50]²=(29/2-50)²

=(-71/2)²

=5401/4

157+129-526+649=286+123=409

what is the square root of 463652

\(\sqrt(463652)=\sqrt(4*115913)=2*\sqrt(115913)\)

115913 has all prime factors, no squares

Find x. 

Subtract eight from both sides. 

2x=2

Divide 2 from both sides.

x=1

How would you say 0.4 in mathematical terms? It would be four tenths. So, you can do 4/10

Using the property that  (a)^-n = (1/a)ⁿ

(1/3)^-4 = 

[ 1 / (1/3) ] ⁴

[ 3 ] ⁴  = 

81