geno3141

Hint:  100 - 98  =  2

            96 - 94  =  2

            92 - 90  =  2

                      ...

               8 -  6  =  2

               4 -  2  =  2

How many 2s do you need to add together?

When subtracting two different numbers from that set, you can get every positive answer from 1 through 15.

Solve:     (2/3)·(a - 4)  =  -3(a - 3)

Multiply both sides by 3:            3·[ (2/3)·(a - 4) ]  =  3·[ -3·(a - 3) ]

                                                               2·(a - 4)  =  -9·(a - 3)

Distribute:                                                   2a - 8  =  -9a + 27

Add  9a  to both sides;                              11a - 8  =  27

Add  8 to both sides:                                      11a  =  35

Divide both sides by 11:                                   a  =  35/11

To get one and only one of the two counters to be white, you can either

1)  get a white counter followed by a non-white counter:  (6/10)·(4/9)  =  24/90

2)  or get a non-white counter followed by a white counter:  (4/10)·(6/9)  =  24/90

To find the final probability, add those two probabilities together and reduce your answer.

94%  =  94 / 100  =  47 / 50

So, for the winning percentage to be exactly 94%, Teddy must have played at least 50 games.

If cos(a) = 12/13, then the adjacent side is 12 and the hypotenuse is 13 (or a multiple of these).

If the adjacent side is 12 and the hypotenuse is 13, the opposite side is 5 (Pythagorean Theorem).

However, since the angle is in the 4^th quadrant, we'll have to make the opposite side = -5.

sin(2a)  =  2·sin(a)·cos(a)  =  2·(-5/13)·(12/13)  =  .......

cot(2a)  =  1 / tan(2a)  =  1 / (-5/12)  =  ........

The independent variable is the number of boxes of plums sold (because this can vary).

The dependent variable is the revenue because this depends upon the number of boxes sold.

Angle(AOB)  =  360^o - 215^o =  145^o.  

The radius of the circle appears to be slightly larger than 3, so the area of the whole circle is

slightly larger than  pi·3²  or a little more than 9 pi.

Since the central angle is 145^o, the area that we want is slightly more than

                  145/360·9pi  =  11.4 square units.

The closest answer seems to be 11 square units.

This expression will be undefined only when the denominator is zero

--->     a² - 4  =  0     --->     (a - 2)(a + 2)  =  0

So, the two times that the expression is undefined occurs when  a = 2  or  a = -2.

1 / |m|  >=  1 / 8

Multiply both sides by 8 and by |8|:

8  >=  |m|     --->     |m|  <=  8     --->     -8  <=  m  <=  8