geno3141

Volume(cylinder)  =  pi · radius² · height  =  pi · radius² · height  =  pi · x² · y

Volume(cone)  =  (1/3) · pi · radius² · height  =  (1/3) · pi · (3x)² · h  =  3 · pi · x² · h

Volume(cylinder)  =  Volume(cone)     --->     pi · x²​ · y  =  3 · pi · x² · h     --->     h  =  (1/3) · y  

If  cos(B) = 6/10, then  AB = 6.

Using the Pythagorean Theorem,  AC = 8.

Then, tan(C) = opposite / adjacent  =  6/8  =  3/4

Using 6, you get:  (3x + 2)(12x - 6)  =  36x² - 6x - 12  which is not a binomial.

If you use 8, you get:  (3x + 2)(12x - 8)  =  36x² -16  which is a binomial.

Note that the ratio:  3/2  =  12/8.

The number of ways to choose 0 girls from a group of 7 girls is:  ₇C₀

The number of ways to choose 2 boys from a group of 6 boys is:  ₆C₂

The number of ways to choose 2 students from a group of 13 students is:  ₁₃C₂ 

So, the probability is:  ₇C₀  x  ₆C₂  / ₁₃C₂ 

31753  =  113 x 281

Since you want one odd number and four even numbers, there are five possibilities:

     OEEEE  +  EOEEE  +  EEOEE  +  EEEOE  +  EEEEO

The probability of getting an odd number is 3/6.

The probability of getting an even number is 3/6.

Therefore, the probability of OEEEE is  (3/6) x (3/6) X (3/6) x (3/6) x (3/6). = 1/32

This is also the probability of each ot the other possibilities.

Adding these together:  (1/32)  +  (1/32)  + (1/32)  +  (1/32)  +  (1/32)  =  5/32

The total of the three is  $46.00.

Since the video game costs  $29.00,  there will be  $46.00 - $29 .00  =  $17.00 remaining.

Since the puzzle costs $16.00 less than the video game, the video game costs  $16.50

                                                                                            and the puzzle costs  $   0.50

The first digit can be any of the ten digits:                              10 / 10

The second digit can be any digit except of the first number:  9 / 10

The third digit can be any digit except either of the first two:    8 / 10

The fourth digit can be any digit not previously chosen:           7 / 10

The last digit can be any digit except those already chosen:    6 / 10

The final probability is the result of multiplying these probabilities: 

                       (10 / 10)  x  (9 / 10)  x  (8 / 10)  x  (7 / 10)  x  (6 / 10)  =  

g(x)  =  2x + 1     --->     g (g(x) )  =  2( 2x + 1 ) + 1  =  4x + 2 + 1     --->     4x + 3

g( g(x) ) - g(x)  =  [ 4x + 3 ] - [2x + 1 ]  =  4x + 3 - 2x - 1  =  2x + 2

f(3)  =  2(3) + 2  =  6 + 2  =  8

I used the first 6 values (n = 2, ... n = 7) to find the values for a, ... f in the equation:

     y  =  ax5 + bx4 + cx3 + dx2 + ex + f

to get these values:

    a  = -7.192460317 x 10-4

    b  =  0.01875

    c  =  -0.1948164682

    d  =  1.01875

    e  =  -2.750892857

    f  =  3.375

If these are correct, they do show that 8/63 is not correct for n = 8.