geno3141

3 - +2 means to subtract a positive 2 from a positive 3 (positive numbers don't need a positive sign in front of them, so 3 = + 3 and +2 = 2):

=  3 - 2

=  1

To reduce by 80% means to save 20%:

20% of 1/1000  =  0.0002  =  2/10 000  =  1/5000

Student's t cumulative distribution function:  this evaluates to 0.887

(using a TI-83+ calculator).

2(5 - 2m)  =  -6(3m - 2)

Multiply out by using the distributive property:

10 - 4m  =  -18m + 12

Add  18m  to both sides:

10 + 14m  =  12

Subtract  10  from both sides:

14m  =  2

Divide both sides by  14:

m  =  1/7

First, divide by 2:  72 = 2 x 36

Since 36 is even, divide again by 2:  72 = 2 x 2 x 18

Since 18 is even, divide agian by 2:  72 = 2 x 2 x 2 x 9

Since 9 = 3 x 3, finish:  72 = 2 x 2 x 2 x 3 x 3

So, the prime factors are 2 and 3; three 2s and two 3s.

You can google that for descriptions, from (relatively) easy to (relatively) complete.

-2(1 + p) + p(p - 1)

=  -2 - 2p + p² - p

=  -2 - 3p + p²

or:  p² - 3p - 2

Because 0.9999 ... (repeating forever) 

IS  1.0000 ... (repeating forever)

First:  factor out the common factor of x² - 2x + 1:

y²(x² - 2x + 1) + 11y(x² - 2x + 1) + 30(x² - 2x + 1)

=  (x² - 2x + 1)[ y² + 11y + 30 ]

Factor  x² - 2x + 1  to get  (x - 1)(x - 1)  or  (x - 1)²

and factor  y² + 11y + 30  to get  (y + 6)(y + 5)

Substitute these into the expression above to get:

=  (x - 1)²(Y + 6)(y + 5y)

(20%) of (500)  =  (0.20) x (500)  =  100