ElectricPavlov

Cold rate =  1tub/30 min

Hot rate   =  1tub/60 min

x min ( 1tub/30min + 1tub/60min) = 1tub

x(1/30 + 1/60) = 1

x(2/60+1/60) = 1

3/60 * x = 1

x = 60/3 = 20 minutes to fill tub when both are turned on

The numbers will be  5   5  10  15  20

5 numbers mean = 11      5 x11= 55

there are  1+1+2+3+4 = 11 parts    each part = 5

the largest number has 4 parts of the 55       55/11 x 4 = 20 = biggest number

.....hmmmm     the question asks for mode = 6    not mode = 8

If the base is a square or rectangle , yes  , volume =  1/3 (base area * height)

Nope....building + tower will be 101.86 ft tall    ....assuming tower is on top of the building.

Tan 56 = (h+40)/d         h = height of building    d = distance from point to base of building

Tan 42 = h/d  

         d = h/tan42 = 1.1106 h    substitute this into the first equation

Tan 56 = 1.4826    SUbstitute this into the first equation too:

1.4826 = (h+40)/1.1106h

1.6465 h = h+40

,6465h = 40

h = height of building = 61.868 ft        add to this the tower height of 40 ft results in 101.86 ft tall ....too tall.

The volume of a triangular pyramid can be found using the formula V = 1/3AH where A = area of the triangle base, and H = height of the pyramid or the distance from the pyramid's base to the apex.

a   13 = x^2-23

    36 = x^2

     x = +6 and -6

b "Even Function. A function with a graph that is symmetric with respect to the y-axis. A function is even if and only if f(–x) = f(x)"

        Let's try   6  and -6   (which we already found  both equate to 13....so it is even)

c  -b/2a  is the x value of the vertex point    0/-2 = 0   

       to find y   sub x=0 into the equation  = -23                        Vertex = (0,-23)

d  Domain is all  x       (-inf , + inf)

          range is    all y >= -23              [-23, +inf)

Maybe     3,  6,  6,  6,  9 ?

Yah...a toughie!