geno3141

To find the distance from one vertex to the opposite vertex, use the three-dimensional distance formula:

     distance  =  sqrt( height² + width² + length² )

Any question about how to use this formula?

The possibilities that contain at least one blue ball are:

blue - blue - blue     (3/7) x (2/6) x (1/5)  =  1/35

blue - blue - red      (3/7) x (2/6) x (4/5)  =  4/35

blue - red - blue      (3/7) x (4/6) x (2/5)  =  4/35

red - blue - blue      (4/7) x (3/6) x (2/5)  =  4/35

blue - red - red       (3/7) x (4/6) x (3/5)  =  6/35 

red - blue - red       (4/7) x (3/6) x (3/5)  =  6/35

red - red - blue       (4/7) x (3/6) x (3/5)  =  6/35

1)  The sum of all the probabilities that have exactely two blue balls is:  12/35.

2)  The sum of all the probabilities that have at least one blue ball is:     31/35.

Dividing the result of 1) by the result of 2) gives:  (12/35) / (31/35)  =  12/31.

Just to expand upon EP's answer

Let x represent the number of liter of water to be added.:

The percentage of bleach solution in pure water is 0.00.

The final percent must be between the percentages of the parts.

The final amount is found by adding the amounts of the parts together.

(percent · amount)  +  (percent · amount)  =  (final percent · final amount)

               0.00 · x     +     0.14 · 18              =  0.10 · (x + 18)

Then finish, as EP states.

The degree of the dividing polynomial is 5; the remainder can have any degree smaller than that:  4, 3, 2, 1, 0.

[The remainder can be an x⁴, x³, x², x, polynomial, or a constant (degree = 0).]

1)  42  =  2b - 14      --->     solve for b

2)  b  =  3 + 4g         --->     solve for g

3)  x + y  =  84

     x  =  12 + y          --->     solve for x and y

4)  x + x + 1  =  37   --->     solve for x and x + 1

5)  x  =  10 + y

     2y + 3x  =  55     --->     solve for x and y

6)  x + 2x + (2x - 5)  =  80     

7)  one person paints a wall in 23 minutes; so, how long will it take 9 persons to paint 9 walls?

8)  P  =  2l + 2w

     l  =  3w              --->     solve for l and w

     P  =  104

The probability that a cube is drawn from Bin A is 6/8.

Now, there are 4 cubes and 4 tetrahedrons in Bin B.

The pobability that a cube is drawn from Bin B is 4/8.

The final probability is  (6/8) x (4/8)  =  your answer

You start with 15 cc cookies and 33 total cookies.

The probability that the first cookie is cc is 15/33.

Now, there are 14 cc cookies and 32 total cookies.

The probability that the second cookie is cc is 14/32.

Continue this pattern and multiply all the individual probabilities together:

 (15/33) x (14/32) x (13/31) x (12/30) x ... x (2/20) x (1/19)  =  your answer

or:  15! / ( 33! / 18! )

I'm not sure that this is correct, but:

There are 16 cards, 4 aces and 12 non-aces.

The first player must get 1 ace out of 4 and 3 non-aces out of 12:  ₄C₁ · ₁₂C₃  =  880.

This is out of a total of choosing 4 cards out of 16 cards:  ₁₆C₄  =  1820.

The probability that this occurs is:  880/1620.

There are now 12 cards, 3 aces and 9 non-aces.

The second player must get 1 ace out of 3 and 3 non-aces out of 9:  ₃C₁ · ₉C₃  =  252

This is out of a total of choosing 4 cards out of 12 cards:  ₉C₄  =  .495

The probability that this occurs is:  252/495.

There are now 8 cards, 2 aces and 6 non-aces.

The second player must get 1 ace out of 2 and 3 non-aces out of 6:  ₂C₁ · ₆C₃  =  40

This is out of a total of choosing 4 cards out of 8 cards:  ₈C₄  =  .70

The probability that this occurs is:  40/70.

There are now 4 cards, 1 ace and 3 non-aces.

The second player must get 1 ace out of 1 and 3 non-aces out of 3:  ₁C₁ · ₃C₃  =  1

This is out of a total of choosing 4 cards out of 4 cards:  ₄C₄  =  .1

The probability that this occurs is:  1/1

Now, we need to multiply these together:  (880/1620) x (252/495) x (40/70) x (1/1)  =  8 870 400 / 56 133 000.

If        r(x)  =  1 + 3x,

then   r(a)  =  1 + 3a

and  3r(a)  =  3(1 + 3a)  =  3 + 9a

To find the probability of the three white balls:

You have to select all of the winning balls; in other words, you have to select three winning balls from three winning balls, and this can be done in ₃C₃ ways (which is just 1 way).

You also have to select none of the losing balls, in other words, you have to select zero losing balls from seven losing balls, and this can be done in ₇C₀ ways (which, also, is just 1 way).

Then, you have to divide this result from the total number of ways that 3 balls can be drawn from 10 balls, and this can be done in ₁₀C₃ ways (which is 120 ways).

Summarizing:     [ ₃C₃ · ₇C₀ ] / ₁₀C₃   =  1 · 1 / 120  =  1/120.

You also have to select the SuperBall. Since there are 10 possibilities and you must select the 1 that is the winner, your probability of selecting the SuperBall is  1/10.

Your probability of selecting all three white balls and the SuperBall is:  (1/120) · (1/10)  =  1/1200.