geno3141

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

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

If you want to find the horizontal side that you don't know, subtract 10 in from 17 in to get 7 in.

If you want to find the vertical side that you don't know, subtract 11 in from19 in to get 8 in.

You now know all the sides:  add 10 in to 19 in to 17 in to 11 in to 7 in to 8 in to get your answer.

To find out how many cookies (at 35 cents each) must be sold to make more than $15.00,

divide $15.00 by 0.35  --->   42.85... cookies

So she must sell at least 43 cookies.

Checking:  43 x 0.35  =  15.05 ...

Continue line EF to the left so that it intersects line BCD at point X

Since FEX is parallel to AB, angle(CXE)  =  180^o - angle(ABC)  =  180^o - 120^o  =  60^o.

In triangle(CXE), angle(CXE) = 60^o and angle(ECD) = 55^o, so angle(XEC) = 65^o.

This means that angle(CEF) = 115^o.

Let X be the point where the external tangent meets circle A.

Let Y be the point where the external tangent meets circle B.

Because AX is perpendicular to CYX and BY is perpendicular to CYX, triangle(ACX) is similar to triangle(BCY).

Therefore:  CB : CA  =  BY : AX.

Since  CA  =  CB + BA  =  CB + 17  and  BY  =  7  and  AX  =  10:

--->   CB : CB + 17  =  7 : 10

--->  10 · CB  =  7 · (CB + 17)

Can you finish it from here?

Provided that you have to choose 1 of each and since all these choices are independent from each other, multiply them together:

    answer  =  11 x 4 x 9 x 4 x 2 x 7

Do you have to choose one of each? If not, we will get a different answer.