CPhill

8in  = 2/3 ft

Lateral surface area  = 

2 * pi * r * h  =

2 * pi * (2/3) * 24  =

32pi  ft^2  ≈  100.5 ft^2

(1/3)^(-2)  =  27^x

Get the bases equal......

(3^(-1))^(-2)  = ( 3^3 )^x

3^2  = 3^(3x)

We have the bases equal...solve for the exponents....

2 = 3x

x =2/3

No need to guess and check....we can solve directly

Let the boxes of thank you cards  = x

Let the boxes of get well cards  = 8 - x

So  we can solve this

4x + 6 ( 8 - x)  = 36     simplify

4x + 48 - 6x  = 36

-2x + 48  =  36        subtract 48 from both sides

-2x = -12      divide both sides by -2

x =6 =  boxes of thank you cars

8 - 6 = 2 boxes of get well cards

Assuming that the other adjacent side to the 40° angle is the hypotenuse (it looks to be the greatest side )

The angle opposite the side of 128 '  =  50°

We can use the Law of Sines to find d

d/ sin 40  = 128 / sin 50

d  = 128 * sin 40 / sin 50  ≈  107.4 '

Second one....a little difficult

Circle : Stall = 2 : 5

If the Circle   seats 528 people, the Stall will seat  5/2 times this  = 528 (5/2)  = 1320

But only (2/3)  of these were occupied  = 1320 (2/3)  = 880 seats

So....the percentage of total occupancy  =

[ 880 + 528 ]            1408

___________  =     ______  ≈  76%

[ 1320 + 528]           1848 

First one

480  sandwiches

3/8 are tuna  = (3/8) ( 480)  =  180  are tuna

35%  are beef  = .35 (480)  = 168 are beef

So  480 - (180 + 168)  = 132  are  either  ham or cheese

Ham : Cheese  = 5 : 6

So   (5/11)  of the remaining sandwiches are ham  = (5/11) * (132)  = 60 

LOL!!!!...you guys are tough to keep up with   !!!!

4.every point on a particular line is shifted 2 units down. the resulting line has equaiton y=3x-5. what is the equation of the original line?

The equation of the original  line  must have been :

y =  3x - 5 + 2    =   3x - 3

3. Write down the equation of a line parallel to the y axis that passes through(-7,4)

The equation is

x   = -7

2. Write down the equation of the line that is perpendicular to the y axis and passes through (-5,1)

The  equation  is

y  = 1