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Good Job EP, I got the answer of 90 (92.5-2.5) as well!

I'm pretty sure that this is correct, Nice Try!

14.88  +.06(3)   +  .06x    =   15.38 - .12 x      solve for 'x' the number of hours until they are equal

15.06 + .06x   = 15.38-.12x

.18x = .32

x = 1.77 hr        ~ 1 hr  47 min

Circumference of circle of which arc is a part is    pi x d  = 80 pi

fraction of the circumference   18/360

18/360 x 80 pi = .......

Nice work Gino.

I would have to some work before I found the 1/3 part. 

But the rest all seems reasonable ... I think.

Get a common denominator for the second expression, so the addition can be done above a single denominator. 

                                                                          ( 2x² + 3 )( 2x + 1)  =  4x³ + 2x² + 6x + 3 

so the second expression can be rewritten as    4x³ + 2x² + 6x + 3          4    

                                                                           ————————  +  ———   

                                                                                  2x + 1                   2x + 1   

when you add those together, it is      4x³ + 2x² + 6x + 3 + 4                                                      4x³ + 2x² + 6x + 7

                                                           ——————————  and adding the 3 + 4 we obtain   ———————— 

                                                                        2x + 1                                                                          2x + 1  

This is the same as the first expression, so the two are equivalent for every

value (not just 10) except x = –1/2 because when x = –1/2 the denominator 

becomes zero and Rule No. 1 is "Thou shall not divide by zero."   

 _.

The minimum perimeter will occur if the rectangle is a square.

The area of a square is:  x²  =  200

                                          x  =  sqrt(200)

                                          x  =  10sqrt(2)

Perimeter  =  4 · 10sqrt(2)  =  40sqrt(2)

Part c:  rewrite the second expression using the common denominator of 2x + 1

              2x² · [ (2x +1) / (2x + 1) ]  + 3· [ (2x +1) / (2x + 1) ]   + (4 )/ (2x + 1) 

=            (4x³ + 2x² ) / (2x + 1)       +  (6x + 3) / (2x + 1)          +  (4) / (2x + 1)

=            [ (4x³ + 2x² )  +  (6x + 3)  +  (4) ] / (2x + 1)

=            ( 4x³ + 2x² + 6x + 7 ) / (2x + 1)

       4 of them in each of the 6 columns =  24 

and 4 of them in each of the 6 rows       =  24 

add them together for a total of                  48 

The diameter of the sphere will be 1.

The inscribed cube will have a distance from one vertex to its opposite vertex the same as the diameter of the sphere,

so this distance is also 1.

If the inner cube has each dimenstion called 'x', the distance from one vertex to its opposite vertex can be found

by using this equation:  d²  =  l² + w² + h²     or     d²  =  x² + x² + x² 

Since  d = 1                                                             1²  =  3x²

                                                                                  1  =  3x²

                                                                                 x²  =  1/3

                                                                                   x  =  sqrt(1/3)   or   sqrt(3) / 3

[5! / 3!.2!] = 10 x 6C1 x 5C1 =10 x 6 x 5=300 / 6^5 =25 / 648 =3.858%

Thank you

- 7 pi / 4   takes us to the same place as  pi / 4

-3   takes us into the opposite direction

choice a

Let  n  be the number of pieces.    He sold  n - 2  pieces

Let  p  be the original price.           His selling price  =  p + 4

Then  n · p  =  70.00

And   (n - 2) · (p + 4)  =  88.00     --->   np + 4n - 2p - 8  =  88.00

                                                     --->        np + 4n - 2p  =  96.00 

                                                     --->   70.00 + 4n - 2p  =  96.00

                                                                           4n - 2p  =  26.00

                                                                             2n - p  =  13.00

Trying some possibilities (7 & 1), (8 & 3), (9 & 5), and (10 & 7), finally gets us to the answer:  n  =  10   and  p  =  7.00.

How did I not see that ?? I really need to get better at thinking outside the box.

(x,y)=(-8,1)

m=-1/8

y-y₁=m(x-x₁)

y-1=(-1/8)(x-(-8))

y-1=(-1/8)(x+8)

Since each of the points P_i is the centroid of the triangle that includes it, it is found one-third from the distance from the base to the vertext of this triangle.

Therefore, the height of the inner tetrahedron is 1/3rd the height of the outer tetrahedron. 

Since these shapes are similar, the volume of the inner tetrahedron is (1/3)³, or one-twenty-seventh the volume of the outer tetrahedron.

This makes the volume of the outer tetrahedron 27 times the volume of the inner tetrahedron.

 e

Tulip petals:  10% of 50 doyles  =    5 doyles   --   at $4.00 per doyle  =  $20.00

Tea:               30% of 50 doyles  =  15 doyles   --   at $2.00 per doyle  =  $30.00

Cardboard:   60% of 50 doyles  =   30 doyles   --   at $1.50 per doyle  =  $45.00

Adding these together:  $95.00

Well then guest, look through the answer carefully and find it!

The answer is 7/72, use casework.

That answer was incorrect. I think there was a mistake somewhere.

Since each of the points P_i is the centroid of the triangle that includes it, it is found one-third from the distance from the base to the vertext of this triangle.

Therefore, the height of the inner tetrahedron is 1/3^rd the height of the outer tetrahedron. 

Since these shapes are similar, the volume of the inner tetrahedron is (1/3)³, or one-twenty-seventh the volume of the outer tetrahedron.

This makes the volume of the outer tetrahedron 27 times the volume of the inner tetrahedron.

Use the formula:   A  =  P(1 + r)^y

                             A  =  1500(1 + 0.09)²

                             A  =  1500(1.09)²

Now, finish the calculation.

Since this is a test, maybe I shouldn't answer at all; but, I will give you some hints.

Take out a sheet of graph paper. Using a ruler, carefully reproduce this on the graph paper, counting the blocks carefully so that you end with an accurage drawing.

Using your ruler, divide the picture into rectangles and triangles and find the area of each rectangle and triangle.

Find the sum of all the individual areas.

Using this sum, find the cost for each of the options.

The volume of a pyramid is  (1/3)·(area of the base)·(height).

The base is triangle(AEH)

-- the area of this triangle is one-half the area of rectangle(ADHE)

-- the area of rectangle(ADHE)  =  6·5  =  30

-- so the aea of triangle(AEH)  =  15

The height is FE  =  4

So, the volume of he pyramid  =  (1/3)·(15)·(4)  =  20

Just wait a bit and it'll go through moderation, I'm fairly sure