geno3141

The only two distinct digits that, when multiplied, have a product that ends in 1 is 3 and 7.

So, it will be either 23 x 37 or 27 x 73.

One of these is correct, the other isn't.

In the second-to-the-last line, shouldn't the times sign be a minus sign?

That is:  12x  =  ln(y + 1)  -  ln(y - 1)

                x  =  [ ln(y + 1)  -  ln(y - 1) ] / 12

An example of conjugates is:  a + bi  and  a - bi

Multiply them as you would any two binomials, using First, Outside, Inside, Last:

(a + bi)(a - bi)  =  a·a + a(-bi) + (bi)a - (bi)(bi)

                       =  a² - abi + abi - b²i²

Since i² = -1:    =  a² - (b²)(-1)

                       =  a² + b²

This gives you a formula:  (a + bi)(a - bi)  =  a² + b²

Example:  (3 + 4i)(3 - 4i)  =  3² + 4²  =  9 + 16  =  25

Example:  (3x + 4yi)(3x - 4yi)  =  (3x)² + (4y)²  =  9x² + 16y²

You will need to multiply the number of crates times the number of cans in each crate:  

125 x 48  =          <--- the answer  

Percent of interest is the amount of interest divided by the original amount (and then multiplied by 100).

($622.50 ÷ $12,450) x 100  =  5.00%

2000 copies at $14.95 each is  2000 x $14.95  =  $29.900.00

8% of $29.900.00  is 0.08 x $29.900.00  =  $2392.00

4 + 3·5 - 6⁴/(4 + 2)³·2

First, do what is inside parentheses first:

=  4 + 3·5 - 6⁴/(6)³·2

=  4 + 3·5 - 6⁴/6³·2

Next, do exponents:  6⁴  =  1296  and  6³  =  216

=  4 + 3·5 - 1296/216·2

Next, do multiplications and divisions from left to right:

=  4 + 15 - 1296/216·2

=  4 + 15 - 6·2

=  4 + 15 - 12

Finally, do additions and subtractions from left to right:

=  19 - 12

=  7

Since each person plays every other person once, each girl will play four games against boys.

The total number of games that all girls play agains boys is 5 x 4 = 20 games.

Parallel lines have the same slope, so let's find the slope of the line 3x + 4y  = 0:

     3x + 4y  =  0    --->     4y  =  -3x     --->     y  =  (-3/4)x

The slope is  -3/4.

The equation of any line with a slope of  -3/4  is  y - k  =  (-3/4)(x - h)  where (h, k) is some point.

Now, let's find the point of intersection:

     x - 2y  =  a     --->     x  =  2y + a

     x + 3y  =  2a  --->     x  =  -3y + 2a

Combining these equations:  2y + a  =  -3y + 2a     --->     5y  =  a     --->     y  =  (1/5)a

Since  x - 2y  =  a, substituting:  x -2(1/5)a  =  a     --->     x  =  (7/5)a

So, an equation is:  y - (1/5)a  =  (-3/4)[x - (7/5)a]

Some algebra will make the equation look prettier!

There is a total of 25 trophies.

The probability of randomly pulling a basketball trophy is 5 divided by the numbef of trophies remaining.

The probability of randomly pulling a baseball trophy is 12 divided by the number of trophies remaining.

The probability of randomly pulling a second baseball trophy is 11 divided by the number of trophies remaining.

The probability of the trophies randomly chosen in the order  basketball - baseball - baseball is:

     5/25 x 12/24 x 11/23  =  0.0478 (approximately)

The probability of the trophies randomly chosen in the order  baseball - basketball - baseball is:

     12/25 x5/24 x 11/23  =  0.0478 (approximately)

The probability of the trophies randomly chosen in the order  baseball - baseball - basketball is:

     12/25 x 11/24 x 5/23  =  0.0478 (approximately)

Since all are possible and independent of each other, add those probabilities together to get:  0.143