geno3141

If 30 students had an average of 72, then their total points were 30 x 72  =  2160.

If 6 students had an average of 78, then their total points were 6 x 78  =  468.

Adding the points of both groups:  2160 + 468  =  2628 points

2628 divided by 36 gives an average of 73.

As an percentage, it is 73%.

If you let  x₁ = 0   x₂ = 2pi/3   x₃ = -2pi/3  x₄ = 4pi/3  x₅ = -4pi/3  x₆ = 2pi  x₇ = 8pi/3  x₈ = -8pi/3  x₉ = 4pi

the the sum of cos(3x_i) becomes 9.

f(x)  =  x³(7 - 2x⁹)

If  x³  =  0,  then  x  =  0.

If  7 - 2x⁹  =  0,  then  2x⁹  =  7  --->   x⁹  =  7/3   --->   x  =  (7/3)^(1/9)     (the ninth root of 7/3)

Total number  =  x

White             =  (3/8)x

Red               =  (5/12)x

There are 24 more red than white:  Red  =  White + 24

                                                    (5/12)x  =  (3/8)x  +  24

multiply by 24:                                   10x  =  9x + 576

                                                             x  =  576

What does the expression "E^c" mean?

If you have the diagram drawn, both the regular octagon and the extensions of HA and DC so that they intersect at point P, then also extend side AB so that it intersects DCP at point Q.

Ths will create right triangle AQP (the angle at Q is a right angle because sides AB and DC are perpendicular).

Using this formula     degrees = (n - 2)(180^o)/n      we can find the number of degree in each interior angle.

    degrees  =  (8 - 2)(180^o)/8  =  135^o

Angle BAH is an exterior angle to angle BAP, so angle BAP  =  45^o.

Therefore  the angle at P contains  180^o - 90^o - 45^o  =  45^o.

Let  x  represent the number of $8.00 tickets sold

       y  represent the number of $10.00 tickets sold

       z  represent the number of $12.00 tickets sold

Since the combined number of $8.00 tickets and $10.00 tickets sold was 5 times the number of $12.00 tickets sold:

      x + y  =  5z   --->     z  =  (x + y)/5

Value of the tickets sold:  8x + 10y + 12(x + y)/5  =  3900

(multiply by 5)                  40x + 50y + 12x + 12y  =  19 500

                                                            52x + 62y  =  19 500

Number of tickets sold:  x + y + (x + y)/5  =  420

(multiply by 5)                 5x + 5y + x + y  =  2100

                                                    6x + 6y  =  2100

(divide by 6)                                     x + y  =  350

Combining the two equations:  52x + 62y  =  19500

                                                     x +     y  =  350

(multiplying the bottom equation by  -52:

                                     52x + 62y  =   19500  

                                   -52x -  52y  =   -18200

(adding down)                       10y  =  1300

                                                 y  =  130

x + y   = 350   --->   x + 130  =  350   --->   x  =  220

z  =  (x + y)/5   --->   z  =  (220 + 130) / 5   --->   z  =  70

I'm not the best at this, but this is my attempt:

150  =  2 x 3 x 5 x 5  --  so every multiply must have at least 1 two, 1 three, and 2 fives.

So, from the 2¹⁰ (which consists of 10 twos),

you can select either 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10 twos  -- 10 different selections.

From 3¹⁴ (which consists of 14 threes), 

you can select either 1, 2, 3, ... 14 threes  --  14 different selections.

From 5⁸, you must select at least 2 fives, but it could also be 3, 4, 5, 6, 7, or 8 fives

  --  7 different selections.

Multiplying 10 x 14 x 7, I get 980 different ways.

30 set of parents

9 sets of both cool dads and cool moms

12 have cool dads

     --  subtract out the 9 that also have cool moms and you get 3 cool dads that aren't married to cool

            moms

15 have cool moms

     -- subtract out the 9 that also have cool dads and you get 6 cool moms that aren't married to cool dads

9 have both cool dads and cool moms

3 have cool dads but uncool moms

6 have cool moms but uncool dads

This leaves 30 - 9 - 3 - 6  =  12 that have both uncool moms and uncool dads

The formula for the area of a circle is  A  =  pi · r²   

10-inch pizza:  A  =  pi · 10²  =  100pi  =  314.159  (approximately)

12-inch pizza:  A  =  pi · 12²  =  144pi

Increase in size:  144pi - 100pi  =  44pi  =  138.230  (approximately)

Percent increase:  amount of increase divided by original amount (the 10-inch pizza) times 100

     =     138.230 / 314.159 x 100  =  44%