CPhill

I think you are computing this based on 2.7% interest being compounded quarterly for 17 years....the "formula" should be :

14900(1+0.027/4)^(4*17)  =     

14900 (1 + .00675)^(68)  = about   $23542.78

pH  = - log 0.723

Just take the log of 0.723  = -0.140862  and then take the negative of it = .140862

(A) looks good

This question makes no sense.......

NO!!!!!

(18+35)*4=  (53)*4   = 212       but

18+35*4   =  18 + 140  = 158

In the first example....we're actually "distributing" the "4" over both terms in the parentheses. In the second example, we're only distributing it over the "35"

Hayley is correct.....here's the graph of both y= l x l  and y = l x + 5 l

https://www.desmos.com/calculator/erxstf20t3

Good work, Hayley....

And if we just wanted "z" we could take the square root  of  19.62198225  ≈ 4.42967

tan (30)    =  1/sqrt(3)

So

15 tan(30)   = 15 * 1/sqrt(3)  =  15/sqrt(3) = 15sqrt(3)/3  = 5sqrt(3)  = about 8.66

Oh....I see what you mean.....!!!

Here are the 1st 100 digits of pi :

3.[141592653589793238462643383279502884197169399]37510582097494459

23078164062862089986280348253421170679

Here is the result of your expression as given by WolframAlpha :

3.[141592653589793238462643383279502884197169399]2820711147894514138

916383017070856233260338755405432911712444501586...

So...it looks as though your expression is accurate  up to 45 decimal digits  [if i counted correctly.....!!!]

Thanks, Yura_chan.....here's another method that doesn't involve common denominators at all  !!!

7 / 10        9 /14      

Cross-multiply the 14 and 7 and put the result  on the left......then......do the same with the 10 and 9 and put the result on the right......so we have

14*7        10*9

98            90

Since the number on the left is larger than the number on the right......the original fraction on the left [7/10]  is larger than the origiinal fraction on the right [ 9/14]  !!!

The equation for direct variation is :

y = kx      where k is a constant      ......dividing both sides by x, we have

y/x  = k      so....let x double and we have

y/ [2x]  = k    but......k is assumed to be a constant and this "k"  is 1/2 of our original "k"  !!!

Thus......if x doubles, y must double as well to keep k constant.....