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The answer is......

A not      a/b = c/d       multiply both sides by d

          d a/b = c           divide both sides a

           d/b = c/a          this is answer  C    so A and C are equiv    similar can be shown for B   but not for D

Answer D

The volume of the stack is the sum of its parts

5 x 4 x 7     +      12 x 14 x 11       +       24 x 18 x24     = 12356 in^3    = 7.15 ft^3

Volume of each pyramid is given by    a^2 h/3     a = 5  h = 7

Volume = 25 * 7/3 = 58 1/3 cm^3    for EACH      total volume would be = 2 x 58.33 = 116 2/3 cm^3

To use as a timer , you would likely only use the  58  1/3 cm^3 volume so the sand could trickle out of one and into the other pyramid.

See Principia Mathematica by Russell and Whitehead !!!.

Let her age 29 years ago =A

A + 29 + 8 = 2A

A =37 - her age 29 years ago

37 + 29 + 8 - 4 =70 years 4 years from now.

2^18    or   7^6*3    3^15*5     10^8*7       from question heading....I guess

2 2/3  x  1 1/8  x  1 1/5   ft^3

8/3  x 9/8  x 6/5   = 432/120 = 18/5 = 3 3/5 ft^3

There are only 7, 14, 21, 28, 35 that are factors of 35!

Thus there are only 5 powers of 7 in 35! and thus it is not divisible by 7⁶*3

This forms an arithmetic series with:
First term =8,002,000
Difference for each term= -(1/2(n^3+n^2) =31,973,323,333/7,998
Number of Terms =4,000
∑[8,002,000*n -(1/2(n^3+n^2)), n, 1, 4000]=32,005,331,333,000

Or, using AP Formula, we get:

4000/2*(8002000*2 + (31973323333/7998*3999))=32,005,331,333,000

\(\text{The sum of all the real coefficients is simply the real part of }\\ \left . (1+ix)^{2009} \right |_{x=1}\)

\((1+i)^{2009} = \sqrt{2}^{2009}e^{i 2009 \left(\frac \pi 4\right)} = \sqrt{2}^{2009}\left(\cos\left(\dfrac \pi 4\right)+i \sin\left(\dfrac \pi 4 \right)\right)\)

\(Re\left[(1+i)^{2009}\right] = \sqrt{2}^{2009} \cdot \dfrac{\sqrt{2}}{2} = 2^{1004}\\ \log_2\left(2^{1004}\right) = 1004\)

I can't express how much I appreciate your help!!! Thank you a million^1000 

In 8 years Mac's grandma will be twice as old as she was 29 years ago. How old will Mac's grandmother be in 4 years

Let her age now = A

29 years ago her age = A - 29

And in 8 years, her age will be A + 8

So...we know that

2 (A - 29) = A + 8         simplify

2A - 58 =  A + 8        add 58 to both sides, subtract A from both sides

A =  66       this is her age now

So....in 4 years, she will be   70

3. Medians DP and EQ of triangle DEF are perpendicular....DP = 18  and  EQ =  24

Let the medians intersect at   M

Then   DM = (2/3)DP =  (2/3)18 =  12

And EM =  (1/3)EQ =  (1/3)(24) = 8

So.....using the Pythagorean Theorem, ......DQ  =   sqrt ( DM^2 + EM^2 )  =  sqrt (12^2 + 8^2)  =  sqrt (144 + 64) =

sqrt ( 208)  =  4sqrt (13)

But  DF = 2DQ =   2 * 4sqrt (13)  =   8sqrt (13)

Exactly in the middle  between the two of them is  1/4.

I think you must mean the value of each trig function of 180°

Note that  at 180°   x = -1, y = 0  and r = 1

So

sin (180)   =  y /r  =  0 /1  =  0

cos(180) = x / r =  -1 /1   = -1

sec (180)  = r /x = 1/-1  = -1

tan (180)  = y /x  =  0/ -1 = 0

Note that the csc and cot  are undefined because they are the reciprocals of sin and tan.....and each of these would result in a division by 0

Tan  = sin / cos    at 180 degrees =  0 /(-1) = 0

1. In the trapezoid shown, the ratio of the area of triangle ABC to the area of triangle ADC is 7:3. If AB+CD=210 cm, how long is segment  AB ? 

Triangles ABC and ADC  are under the same altitudes....so.....their bases are to each other as their areas...

So.....the base length of  ABC   is (7/10)  of  210 cm   =   147 cm  =  AB

Thanks EP :)

Oh okay thank you!!! :):)

Note that second column is in percentage

So....we have 200 riders in total

The relative % of those under 55%  =   [ 2 + 0 + 10 + 24 + 30 +12 + 9 ]   =  87%

So.....100 - 87 =  13%    are older than 55

So.....13% * 200 = .13 * 200 =   26

5 x 10^-4       Move the decimal point 4 places LEFT to get     =  .0005

Realize the table is PERCENTAGES of 200.....you probably found 13%    13% of 200 = 26