CPhill

x + 13 > 5x - 3     add 3 to both sides

x + 16 > 5x           subtract x from both sides

16 > 4x                 divide both sides by 4

4 > x           which means the same thing as

x < 4

Let's see.....

Oh, yeah.......people who use the singular verb "is" when they should be using the plural verb "are."  Of, course, then we would also have to change your "stupidest' to "stupid."

If we drew a Venn diagram of this inclusive set....you would lie in the "shaded" area.....

The tangent is given by the ratio..... (opposite / adjacent)

So we have 

tangent(θ) = 4/13    where θ is the angle we're looking for

To find this, use the tangent inverse denoted by atan (or tan^-1)

atan (4/13) = θ

atan(4/13) = about 17.1°

940/960 = 94/96 = 47/48 = .9792 or about 98%

Hyperbola

16x^2 - y^2 +32x  +2y - 1 = 0    Add 1 to both sides

16x^2 - y^2 +32x  +2y  = 1        Complete the square on x and y

16(x^2 + 2x + 1) - (y^2 - 2y +1) = 1 + 16 -1

16(x + 1)^2 - (y -1)^2 = 16         divide both sides by 16

(x+1)^2 - (y-1)^2 / 16  = 1

The center is (-1, 1)

The vertices are (-1± a, 1) = (-2,1) and (0,1)

The equations of the asymptotes are y =±b/a = ±4x

4x^2 + 9y^2 -64x + 72y + 364 = 0   Subtract 364 from both sides

4x^2 + 9y^2 -64x + 72y = -364        Complete the square on x and y

4(x^2 - 16x + 64) +9(y^2 + 8y + 16) = -364 + 256 + 144

4(x - 8)^2 + 9(y + 4)^2 = 36                divide both sides by 36

(x-8)^2 / 9  +  (y+4)^2 / 4   = 1

The center is (8, -4)

The length of the major axis = 2(3) = 6

The length of the minor axis = 2(2) = 4

[1 + cos(2x)] / [cscx sin(2x)] = cosx

[1 + (cosx)^2 - (sinx)^2] / (1/sinx)*2sinxcosx]  = cosx

[1 - (sinx)^2 + (cosx)^2] / (1/sinx)*2sinxcosx]  = cosx

[2(cosx)^2] / [2cosx]   = cosx

cosx          =    cosx  

P(nickel, dime quarter) = (3/10)(2/10)(5/10) = 30/1000 =  3/100 = .03

P(3 dimes) = (2/10)(2/10)(2/10) = 8/1000 = ..008

So we have

(1/2)x*10sin(30) = 20

5xsin(30) = 20         divide both sides by 5x

sin(30) = 4/x            sin(30) = !/2

1/2 = 4/x 

x = 8   

50000(1+.03)^(3)

$${\mathtt{50\,000}}{\mathtt{\,\times\,}}{\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.03}}\right)}^{\left({\mathtt{3}}\right)} = {\mathtt{54\,636.35}}$$

And that's in dollars, of course