CPhill

 I think you might just be having trouble lining up the decimals...

Just do this

          4.59

+      65.98

+  1000.50

+      60.00

--------------

Now....just add down the columns as you normally would....!!!

The area of the two bases = 2(3.1 inches)(20.8 inches)

And the area of the sides is 2* [ (3.1 inches)(6.2 inches) + (20.8 inches)(6.2 inches) ]

I'll let you finish this one....

I think we have

sin (2 arcsin (4/5) )

Let arcsin (4/5) = Θ ... and this is an angle whose sin = 4/5 ...  so the cosΘ = ±3/5

So we have

sin (2Θ) = 2sinΘcosΘ = 2(4/5)(±3/5) = ±24/25

Let me add something to Alan's answer.....

Note that  -1/24000 is very close to 0

And e^0  = 1

So

e^(-1/24000)  should be close to 1  ..   !!!   (and, as Alan showed...it is  !!!)

15 / 17 = 0.8823529411764706

This isn't as dark and deep as you might think....!!!

6 mod 3   just means ... "What is the remainder when we divide 6 by 3??"

The answer   ..    0   !!!

See???.... not too mysterious, is it???

Here's another approach....find the circle's center as Alan did  = (5,11)

And the distance from a line to a point not on that line is given by

d = abs ( Ax + By + C) / √(A² + B²)       where (x,y) is the given point and Ax + By + C = 0 is the equation of the line.....so we have....

d = abs (12(5) + 5(11) + 54 ) / √(12² + 5²) = abs(169) / 13 = 13

Here's the graph ...

Very nice, Alan....!!!

I really like that one....a definite "Daily Wrap" candidate

Let N be the number of weeks that she will need to save

125 + 15N = 245    subtract 125 from both sides

15N  = 120      divide both sides by 15

N = 8 weeks

Let N be the number of passes....so we have

7 + 1.50N = 29.50    subtract 7  from both sides

1.50N = 22.50         divide both sides by 1.50

N = 15 passes