geno3141

You can use this identity:  a³ - b³  =  (a - b)(a² + a·b + b²)

In this case:  a = cubr(3)  and  b = cubr(2)

So:  multiply the numerator and denominator by:  cubr(3²) + cubr(3·2) + cubr(2²}  =  cubr(9) + cubr(6) + cubr(4)

The numerator becomes:  cubr(9) + cubr(6) + cubr(4)

while the denominator becomes 3 - 2  =  1

A + B + C + D  =  cubr(9) + cubr(6) + cubr(4) + 1

Since the ratio is 3:4:5, this means that the ratio is in the form of  3 parts : 4 parts : 5 parts.

Adding 3 parts to 4 parts to 5 parts, we get 12 parts.

Now, let's figure what each part is worth:  Divide $24,000.00 into 12 parts, you get $2000.00 per part.

Ahmed, with his 3 parts get 3 x $2000.00  =  $6000.00.

Brian, with his 4 parts get 4 x $2000.00  =  $8000.00.

Charles, with his 5 parts get 5 x $2000.00  =  $10,000.00.

The formula for the mean of a binomial distribution is:  sqrt( n · p · q )

For this problem:     n  =  18          p  =  0.70          q  =  1.00 - 0.70  =  0.30

Stamdard Deviation  =  sqrt( 18 · 0.70 · 0.30 )  =                         (calculator time)

An even number must end with an even digit (2 or 4); however, all the other digits can be either even or odd.

5 choices for the first digit

5 choices for the second digit

5 choices for the third digit

5 choices for the fourth digit

2 choices for the last digit

answer  -  5 x 5 x 5 x 5 x 2  =                 

Let  T  =  price of one ticket

Let  S  =  price of one souvenir

Smith:       2T + 1S  =  17.25   --->   multiply by -2   --->   -4T - 2S  =  -34.50

Lockhart:  5T + 2S  =  42.00                                              5T + 2S  =  42.00

(adding down the columns)                                                 T           =    7.50

die + card = sum

1 + 6  =  7

1 + 7  =  8

2 + 6  =

2 + 7  =

3 + 6  =

3 + 7  =

4 + 6  =

4 + 7  =

5 + 6  =

5 + 7  =

6 + 6  =

6 + 7  =

You'll need to finish ...

The formula for the volume of a cylinder is:  V  =  pi·r²·h.

                                                                      V  =  pi·7²·12  cu. in.

                                                                      V  =  1847.26  cu. in.

The formula or the volume of a sphere is:  V  =  (4/3)·pi·r³.

(diameter = 1.75 -> radius = 0.875)            V  =  (4/3)·pi·(0.875)³  cu. in.                      

                                                                    V  =  2.806  cu. in.

23 scoops  =  23 x 2.806  cu. in.  =  64.54 cu. in.

1847.26  cu.in.  -  64.54  cu. in.  =  1782.72  cu. in,

1  cu. ft  =  (12 in)³  =  1728  cu. in

1782.72  cu. in.  /  1728  cu. in. (per cu. ft.)  =  1.03  cu. ft. remaining

I got the same answer that guest got, 108, but not in so nearly elegant way.

I placed the diagram on a coordinate axis, with P(0,0), C(4,0), and B(-14,0).

Since PA = 13, it is on a circle with center P and radius 13:  x² + y²  =  13

-- I called the x-value of this point 'a', so the y-value became  sqrt(169 - a²).

I used the theorem that the center of a circle is on the perpendicular bisectors of the chords.

Since one chord is BP, its midpoint has x-value -7 and its y-value is on the line x = -7.

Since another chord is PC, its midpoint has x-value 2 and its y-value is on the line x = 2.

Another chord is AP: using its endpoints, I found its midpoint and its slope.

From these values, I could find the equation of its perpendicular bisector (not a lot of fun, for it had a lot of a-terms and square roots).

Then, I found the intersection of this perpendicular biscector with the line x = -7 and the intersection of this perpendicular bisector with the line x = 2 (there were still a lot of a-terms and square roots).

With these two points (the centers of the circumcircles), I could find the distance from one center to point P and the distance from the other center to point P (By this time, I was on a firt-name basis with the a-terms and square roots).

Since these are equal, by solving this equation, I could find the value of a, which was -5.

This is the x-value of point A, allowing me to find the y-value of point A, 12, which is the height of triangle ABC.

With the height 8 and the base 18, the area is 108.

Rock-n-Bowl:  Let R represent the number of games bowled; then the cost will be 2.00 + 3.50R

Strikz:             Let S represent the number of games bowled; then the cost will be 4.50 + 3.00S

If the same amount of money is spent:  2.00 + 3.50R  =  4.50 + 3.00S

Rearranging:                                          3.50R - 3.00S  =  2.50

At 50 cents more per game bowled (3.50 - 3.00), there would have to be 5 games bowled to make the 2.50 difference.

The radius of the outer ring is 5' + 8' + 6'  =  19'.

The circumference of the outer ring is:  C  =  2·pi·r  =  2·pi·19  =  119.38'.