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8 /12 =  x /24     cross-multiply

24 * 8   =12 * x

192  =    12 * x

192  /  12  =  x =   16 cups

( 5 + 8 + 10+ 16 + 18 + 28 + 30 + x )  / 8  =  x - 4.5

(115 + x)  =  8 ( x - 4.5)

115 + x  = 8x  - 36

115 + 36   = 8x   - x

151  = 7x

151 / 7 =   x

Factors of 60  = 

1,2,3,4,5,6,10,12,15,20,30,60

P (< 3)  =  2 /12  = 1 / 6

A graph seems the way to  go, here

https://www.desmos.com/calculator/04zmr3pddp

The smallest value occurs when x =  0

And that value =   sqrt (2) + sqrt (8) =  sqrt (2)  ( 1 + 2)  =  3sqrt (2) 

Just 10

Choose  "GE"  and   then any 1 of the remaining 10

assuming that x isnt equal to 1/2 simplify 8x^2 - 4x / 4x - 2  

Wouldn't that just be 2x  

Maybe I'm wrong but I'm visualizing that (2x)(4x – 2) = 8x² – 4x 

Okay, I see what the first guest did. 

I assumed that (8x² – 4x) quantity is the numerator 

and that (4x – 2) quantity is the denominator.  

Hard to tell what the problem is asking for. 

_.

The semicircle below has a diameter of 20, find the area of the blue region  

The area of the blue region is the area of the semicircle minus the area of the big triangle.  

A_semicircle  =  (1/2) • π • r²  =  (1/2) • (3.14) • (100)  =  157    

A_{largetriangle}  =  (1/2) • base • height  =  (1/2) • (20) • (10)  = 100   

A_blueregion  =  157 – 100  =  57 square units   

_.

a/b = ((10^(log(ab)))/2b) + 3

Find a/b if $\displaystyle 2\log{(a - 3b)} = \log a + \log b$

350 * (6% + 1) = 371

From 1 to 100 ==20 
From 101 to 1000 ==280
[20 + 280] * 5 ==1,500 - "9s" between 1 and 5,000.

230 * (1 + 6%) = 243.8

130 * (1 - 20%) = 104

Let say Luther has x books.

=> Jarred had 1 3/5x = 8/5x books.

Luther gives x/2 books to Jarred and he had 35 fewer book

=> x/2 = x - 35

=> x/2 - x = -35

=> x/2 = 35

=> x/2 = 35

=> x = 70 

70 books

The answer is 32.

The answer is 23.

8x^2 - 4x / 4x - 2 = 8x^2 - 1 - 2 = 8x^2 - 3.

There are 5 possible ways.

The remainder is x^2 - 2x + 5.

There are 6 ways.

10x + 25y = 805

35x = 805

x = 23

5 chairs have odd numbers.

(a,b,c) = (6,30,1)