Which number is the smallest? 4.4 ⋅ 10−5, 3.99 ⋅ 10−6, 2.6 ⋅ 102, 1.85 ⋅ 103

The answer is:  [B]:  " 3.99 * 10⁻⁶ " .

  Note:

We are given the following answer choices, and we are asked which one is the "smallest number" :

  [A]:  4.4 * 10⁻⁵

  [B]:  3.99 ⋅ 10⁻⁶

  [C]:  2.6 ⋅ 10²

  [D]:  1.85 ⋅ 10³

         We can rule out answer choices: [C] and [D]; since these values, essentially "direct us" to move the decimal point FORWARD "2 places" and "3 places", respectively;  whereas choices [A] and [B] essentially "direct us" to move the decimal point BACKWARD "5 places" and "6 places" respectively.  Note that all values given in the answer choices are written in proper "scientific notation" —that is, beginning with a "single integer followed by (a) decimal point(s) and then additional digits (when needed).  So, the answer choice that essentially "directs us" to move the decimal point BACKWARD "6 places" —

             →   Answer choice:  [B]:  " 3.99 * 10⁻⁶ "  ;

                  is the smallest value ; and as such, the correct answer.

                   

Answer choice: B:  " 3.99 * 10⁻⁶

                  Explanation:

  I got it right so don't worry :)

13. $25/month

14. 36 and 37

Step-by-step explanation:

Let a = monthly rate ($/month)

t = time (months)

k = installation cost

The equation for the cost of the internet service C is

C = at + k

Since C = $685. t = 24 months (2 years) and k = $85, we can solve for a:

at = C - k

or

a = (C - k)/t

= ($685 - $85)/(24 months)

= $25/month

14. Let n = the number

n + 1 = the number after n

Since the sum of two consecutive numbers is 73, we can write the equation as

n + (n + 1) = 73

which simplifies to

2n + 1 = 73

2n = 72

Solving for n, we find that

n = 36

so the other number is 36 + 1 = 37.