geno3141

The function is:  f(x)  =  (1/24)x⁴ - (1/4)x³ + (11/24)x² - (1/4)x + 1

From this function, you can determine f(5).

Since the central angle of the sector is 30^o,

     the area of the sector of the circle is 30^o / 360^o  = 1/12^th the area of the circle: 

                pi·r²/12  =  pi·6²/12

To find the area of the triangle, use the formula: 

                Area  =  ½·a·b·sin(C)  =  ½·r·r·sin(C)  =  ½·6·6·sin(30^o)

Thus, the answer is:  pi·6²/12  -  ½·6·6·sin(30^o)

If the common ratio is r (assumed to be positive), then  a  = 16·r

     and  18  =  (16·r)·r  =  16·r²      --->     16·r²  =  18     --->     r  =  sqrt(18/16)

then  b  =  18·r  =  18·sqrt(18/16)

The area will be:

    one-half the area of a circle whose radius is 10

        plus one-half the area of a circle whose radius is 5

            plus one-half the area of a circle whose radius is 1.

The total number of degrees in the exterior angles of a polygon (one at each vertex) is 360^o.

If each exteror angle has 18^o, the number of sides is 360^o / 18^o  = ...

19-19-2     18-18-4     17-17-6    ...     11-11-18

One way to find the fraction that equals  0.77666666666...

Let  x  =  0.77666666666...

To handle the 0.77, multiply this equation by 100:  (because there are two places)

--->     100x  =  77.66666666...

To handle the repeating 6s, multiply this equation by 10:  (because there is one place that repeats)

--->    1000x  =  776.666666...

Subtract these equations:  1000x  =  776.6666666...

                                    -        100x  =    77.6666666...

To get:                                   900x  =  699

Solve this for x:                           x  =  699 / 900                (this can be reduced)

To calculate the average, 

first, for each row, multiply the number of families times the number of cars that they own:

   2 · 0  =  0

   8 · 1  =  8

   x · 2  =  2x

   2 · 3  =  6

second:  add the totals from each row:  0 + 8 + 2x + 6  =  2x + 14

third:  find the total number of families:  2 + 8 + x + 2  =  x + 12

fourth:  find the average by dividing the result of the second step by the result of the third step:

                       average  =  (2x + 14) / (x + 12)

fifth:  set this average to the known average:  (2x + 14) / (x + 12)  =  4/3

sixth:  solve this equation for x; this willbe your answer.

The possibilites are:  HHT, HTH, THH, HHH

=  (1/2) x (1/2) x (1/2) = 1/8 for each of the four possibilities.

Adding together these possibilities:  (1/8) + (1/8) + (1/8) + (1/8)  =  ....

If all three letters must be different, 

there are 15 choices for the first letter,

14 choices for the second letter, and

13 choices for the third letter.

So, the total number of choices is:  15 x 14 x 13 = ...