geno3141

XY · XY  =  XA · XB

9 · 9  =  15 · XB

  XB  =  81 / 15  =  5.4

AX =  AB + BX

15  =  AB + 5.4

AB  =  9.6 

r  =  sqrt( x² + y² )         y  =  r·sin(theta)

     r - r·sin(theta)  =  4

sqrt( x² + y² )  - y  =  4

sqrt( x² + y² )        =  y +4

[ sqrt( x² + y² ) ]²  =  [ y + 4 ]²

                x² + y²  =  y² + 8y + 16

                 x² -16  =  8y

                       8y  =  x² -16 

                         y  =  (1/8)·x² - 2

I don't understand what you have written ...

        theta  =  -7·pi / 6

tan(theta)  =  tan( -7·pi / 6 )

tan(theta)  =  - sqrt(3) / 3

     y / x     =  - sqrt(3) / 3

            y  =  (  - sqrt(3) / 3 ) · x

x  =  r·cos(theta)         y  =  r·sin(theta)

(x + 2)² + y²  =  4     --->     ( r·cos(theta)  + 2 )² + ( r·sin(theta) )²  =  4

--->                  r²·cos²(theta) + 4·r·cos(theta) + 4 + r²·sin²(theta)  =  4                               multiply out

--->                        r²·cos²(theta) + 4·r·cos(theta) + r²·sin²(theta)  =  0                               subtract the 4

--->                       r²·cos²(theta) + r²·sin²(theta) + 4·r·cos(theta)   =  0                               rearrange

--->                       r²·( cos²(theta) + sin²(theta) ) + 4·r·cos(theta)   =  0                               factor

--->                                                                   r² + 4·r·cos(theta)   =  0                               sin² + cos² =  1

--->                                                                   r( r + 4·cos(theta) )  =  0                              factor

The front is a triangle:  A  =  ½·6·4

The back is the same as the front.

The base is a rectangle:  A  =  6·7

The right side is a rectangle:  A  =  7·5

The left side is the same as the right side.

Add the five answers together to get the total surface area.

For the first bowl: there are 6 cereal bowls and 8 bowls to choose from:                6/8

For the second bowl: there are 5 cereal bowls remaining and 7 bowls remaining:  5/7

For the third bowl: there are 4 cereal bowls remaining and 6 bowls remaining:       4/6

For the fourth bowl: there are 3 cereal bowls remaining and 5 bowls remaining:    3/5

For the fifth bowl: there are 2 cereal bowls remaining and 4 bowls remaining:        2/4

To find the final probability, multiply these fractions together:  6/8 x 5/7 x 4/6 x 3/5 x 2/4  =     

First problem:  1000 pins were made at a cost of 1.10 each =  1100.

35% were given to charities   --->   65% were sold; 65% of 1000 pins = 650 pins.

60% of these pins were sold at 3.00 each   --->   0.60 x 650 x 3.00  =  1170.

40% of these pins were sold at 5.00 for 2 (which is 2.50 each)   --->   0.40 x 650 x 2.50  =  650.

Total money earned  =  1170 + 650  =  1820.

Profit  =  1820 - 1100  =  720.

Profit as a percentage of cost:  720 / 1100  =  0.6545  =  65.5%

Let's assum that the original price was !00.

With a 20% sale (100 x 0.20  =  20), the sale price is 100 - 20  =  80.

Now, there is a further 25% off (80 x 0.25  =  20), so the final price is 80 - 20  =  60.

The total off is 100 - 60  =  40.

40 off from 100 is a percentage of 40/100  =  0.40  =  40%

The first number chosen is either a 1 or a 3.(with a probability of 1/2 each).

If the first number chosen were a 1, the second number could either be a 1, 2, or 3 (with a probability of 3/9).

If the first number chosen were a 3, the second number would have to be a 1 (with a probability of 1/9).

Total probability is:  (1/2) x (1/3)  +  (1/2) x (1/9)  =   ....   the answer.