Is Nora or Sofia correct? Explain your reasoning.

  Nora is correct

Step-by-step explanation:

Sophia used an appropriate method for computing the value of the repeating decimal fraction ...

  0.1212_12

Close examination of the given decimal fraction shows that it is non-repeating, so is an irrational number. It cannot be represented by the ratio of integers.

Nora is correct in saying Sophia made a mistake.

___

Sophia depended on 100x -x cancelling some part of the fraction, so the result was a finite decimal. For repeating 2-digit fractions, this works well:

However, the decimal does not repeat, so this does not work:

  100x = 12.1121112

  100x -x = 12.1121112 -0.121121112 = 11.99099009900099... non-repeating

That is, the decimal part is not cancelled by Sophia's work, as we said above.

$75.00

step-by-step explanation:

i = prt

i = 1,5000 * 0.025 * 2

i = 75

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)