geno3141

I believe that there is another possibility:  (0, -2).

The volume of a foonie will be the area of its face times its thickness:  5 cm² x 0.5 cm  =  2.5 cm³.

To find the number of foonies in a stack of volume 50 cm³, we can divide the volume of the stack

by the volume of each foonie:  50 cm³ / 2.5 cm³  =  20 foonies

With your problem, the factoring can result in more than one correct answer, but the process shown is good.

The "Newton-Raphson iteration method" has nothing to do with this problem.

a)  Since the deck contains 8 cards labeled "3" and 2 cards labeled "9",

     the total value of the cards is:  8 · 3 + 2 · 9  =  24 + 18  =  42.

     The expected value of one randomly drawn card is  42 / 10  =  4.2.

b)  An additional "9" is added to the deck: the total value is now:  8 · 3 + 3 · 9  =  24 + 27  =  51.

      The expected value is now  51 / 11  =  4.64    (approximately)

c)  Two additional "9"s are addeded to the deck.

      Are these two addition cards added immediately after step a or after step b?

      If they are added after step b, the totall value is now:   8 · 3 + 5 · 9  =  24 + 45  =  69.

      The expected value is now:  69 / 13  =  5.31

d)  This question is incomplete.

The possible is the area of the triangle bounded by the x-axis, the y-axis, and the line y = -x + 6.

The endpoints of this triangle are (0,0), (6,0), and (0,6)  [Sorry; it isn't 81.]

The success is the area of the triangle bounded by the x-axis, the line y = -x + 6 and the line

y = -4x + 6.

The endpoints of this triangle are (1.5,0), (6,0) and (0,6).

Dividing the success by the possible will give you the probability.

My guess is 15.

Since  x + y  =  3     --->     y  =  3 - x

Since  xy  =  3     --->     y  =  3/x

Combining these equations:  3/x  =  3 - x     --->     3  =  3x - x²     --->     x² - 3x + 3  =  0

Use the quadratic formula to get:  x  =  ( 3 + i·sqrt(3) ) / 2  and  x  =  ( 3 - i·sqrt(3) ) / 2

[If x is one of the answers, then y is the other.]

Now, cube the answers to get the final answer ...  (it's an interesting answer) ...

The area of the circle is pi·radius²  =  100 pi

If you were to connect the center of the circle to each of the vertices of the interior hexagon, you would

get 6 congruent equilateral triangle and each of these triangles would be congruent to the six 

equilateral triangles "at the points".

A radius to one of the points on the circle = 10, so the height of each of the equilateral triangles is 5.

This means that the base of the triangle is ( 5 / sqrt(3) ) · 2  =  10/sqrt(3)

The area of each triangle is  ½ · ( 10/sqrt(3) ) · 5  =  25 / sqrt(3).

Since there are 12 congruent triangles, the total area is 300/sqrt(3)  =  100·sqrt(3)

The area inside the circle but outside the hexagram =  100 pi - 100·sqrt(3)

Of this area, one-third is shaded  =  ( 100 pi - 100 sqrt(3) ) / 3  

When you are finding the fourth root of ( 4 / 20.25 ) --

the fourth root is the square root of the square root , so:

  fourth root of ( 4 / 20.25 )  =  sqrt( sqrt( 4/20.25) ) =  sqrt( 4/9 )  =  2/3

     because the sqrt( 4/20.25 )  =  2/4.5  or  4/9

No problems with the rest of the problem ...

I believe that they can be seated as:

M-F-M-F-M-F-M-F

M-F-M-F-M-F-F-M

M-F-M-F-F-M-F-M

M-F-F-M-F-M-F-M

F-M-F-M-F-M-F-M

In each case there will be 4 x 4 x 3 x 3 x 2 x 1 x 1 = 576 was.

5 x 576 = 2880 ways