CPhill

Nope.....there are some questions on here that throw me.....fortunately....we usually have someone who knows the answer....!!!

I assume the Math Genius was busy.....so....you had to settle for me instead......LOL!!!!

  Assuming that the power is an integer

( 5/6)^3  =   5^3 / 6^3   = 125 / 216

(1/2)^4  =  1^4 / 2^4   =  1 / 16

This last  one is a little confusing......let me show you the  "trick'

(3/4)^ (-2)        "flip" the fraction and make the exponent positive

(4/3)^2  = 4^2 / 3^2  =   16 / 9 

Thanks for those good answers, knownhappyman....!!!

As an aside, NSS.....even if we didn't exactly know the answer to the second one.....note that every day, the amount accumulated is always divisible by 4.....and the only answer that is evenly divisible by 4  is 60.....

[No problem with taking my sunglasses....they're not  "trademarked" anyway....LOL !!!  ]

These all look a little funky

To find the side just take the cube root of the volume

So....

Side  =  ∛ 1833  ≈   12.238 in

[ I suppose  "D" comes closest  ]

10%  of  8999

Note.....  10%  = .10

So.....we just have   

.10  *  8999  =

89.99

5a + 5b       a  = -6     b = -5

5(-6) + 5(-5)  =

-30 - 25  =

-55

-3 (-4y + 3) + 7y         distribute the  -3   over the terms in the parentheses

12y - 9 + 7y              combine like terms

19y - 9

What is the density of a solid piece of lead which has a mass of 144.0 grams and is 2.75 cm long,
1.25 cm wide, and 3.25 cm thick?

The volume is    (2.75 cm) (1.25 cm) ( 3.25 cm)   = 11.171875 cm^3

Density  = Mass /  Volume     

So we have

Density  =  144 grams /  11.171875 cm^3    ≈  12.89 grams / cm^3

156  = cans to be stacked

8 = cans per row

8r = cans already stacked

$23.57   =  amount of money available

$3.69  = price per set

$3.69x = amount spent so far

Note that  minor arcs

AD + AB + BC + CD  = 360°    or....put another way.....

AD + 3BC  = 360  →   AD  = 360 - 3BC   (1)

Also

Angle BEC  = (1/2) ( BC -  AD)      sub (1) into this

40  =  (1/2) [  BC - (360 - 3BC) ]       multiply through by 2  and simplify

80 =  4  BC - 360          add 360 to both sides

440  = 4  BC                divide both sides by 4

110°  =  BC

So, since AB = BC = CD.....then major arc  ACD  = 330°

And arc AD  must = 30°

And since angle ACD  is an inscribed angle intercepting this arc...

Its measure is (1/2) arc AD  = 15°