CPhill

6(x-3)=2x+38   distribute the 6 over the terms in the parentheses on the left

6x - 18 = 2x + 38   add 18 to both sides and subtract 2x from both sides

4x = 56        divide both sides by 4

x = 14

The total cost was 4 x $2.99 = $11.96......so the $2.00 coupon made Sandar's cost just $9.96

I know zippo about biology, but it's enzyme "x.'   Note that it's active in colder temps, but the activity starts slowing at temps above about 30 degrees, or so.  Enzyme "y' is active all temps > 0 , but particularly in "hotter" temps !!!

Arithmetic...we're just subtracting 5 from the previous term to get the next term !!!

It would have 12......to see why....note that there are 10 multiples of 5 in 50! that could be paired with 10 even numbers in the product of 50! to produce a "0"  with each pairing. But 25 and 50 each have an additional factor of  "5" that could be paired with two other even numbers in the product of 50! ......so that gives us 12 trailing zeroes.

Note that there are 25 pairs of even numbers in the product of 50!, so we will be guaranteed to be able to pair twelve "5's with any twelve of them to produce 12 trailing zeroes.....!!!!

Here's the proceedure for finding the answer

• Take the number that you've been given the factorial of.
• Divide by 5; if you get a decimal, truncate to a whole number.
• Divide by 5² = 25; if you get a decimal, truncate to a whole number.
• Divide by 5³ = 125; if you get a decimal, truncate to a whole number.
• Continue with ever-higher powers of 5, until your division results in a number less than 1. Once the division is less than 1, stop.
• Sum all the whole numbers you got in your divisions. This is the number of trailing zeroes.

So we have

2014 / 5 = 402.8 = 402

2014 / 5² = 80.56 = 80

2014 / 5³ =  16.112 = 16

2014 / 5⁴ = 3.2224 = 3

2014 / 5⁵ =  .644   and we can stop

So...summing   402 + 80 + 16 + 3   we have   501 trailing zeroes

The max depth of the water is 24.5 ft.

HAHAHA!!!!!......1 hour ago......the only "Lays" I was familiar with comes in a bag and is consumed while watching football on TV !!!!!!!

DS.......Here are two definitions of that word...I'm unsure of the origin(s)

1. A narrative poem, such as one sung by medieval minstrels; a ballad.
2. A song; a tune.

We have.......

Rate*Time = Distance  ......  so let Jack's time be "T' ....and we have 6T = D

And since Sarah ran 1 hour more, we have...... R(T + 1) = D  →  4(T + 1) = D

And since the distances are the same, we have

6T = 4(T + 1)     ....simplify

6T = 4T + 4    ...... subtract 4T from both sides

2T = 4    ....... divide by 2 on both sides

T = 2 hrs = Jack's time  ...  and  Sarah's time was 1 hour more = 3 hrs.

So, the race was 6mph*(2hrs) = 4mph*(2 + 1)hrs = 4mph(3 hrs) = 12 miles  !!!