El número 18 tiene la siguiente propiedad: al sumar sus dígitos da como resultado1+8=9, y 18 se puede dividir por 9 (el valor de la suma). No todos los números tienen esa curiosa propiedad. Por ejemplo, para el número 28 se tiene 2 + 8 = 10, pero 28 no se puede dividir de manera exacta por 10.El caracol Jacinto dice que el número de dos dígitos más grande que tiene la propiedad de dividirse por la suma de sus dígitos es el 60. Tú sabes que el caracol Jacinto está equivocado. El problema consiste en explicarle al caracol jacinto porqué está equivocado (para lo cual deberás escribir tu explicación). Además, debes encontrar el número de dos dígitos más grande que pueda dividirse por la suma de sus dígitos y dar un argumento que convenza al caracol (que es conocido por ser muy porfiado) de que el número que tú descubriste efectivamente es el más grande.

Step-by-step explanation:

First of all, we can easily find that, for example, 63, has that particular property, therefore Jacinto is wrong.

Now we proceed to show that every (two digit) number is divisible by 3 if and only if it's sum of digits is.

Let n be a natural two digits number, and let a and b be the digits of said number, with

We can write n as

Let's call r1 the remainder of 10a/3, with, of course,

(for example, if a=1 then r1=1, because 10=3*3+1)

Now, each power of 10 leaves a remainder of 1 when divided by 3, thus r1 is equal to the remainder of a/3.

As an example, if a=3, then r1=0, because 30=3*10.

And let's call r2 the remainder of b/3.

In order for n to be divisible by 3, r1+r2 must be equal to a multiple of 3 (otherwise the division would leave a remainder).

Now, a can be written as

And similarly, b can be written as

Therefore, a+b is equal to (a multiple of 3)+r1+r2.

But since we already showed that r1+r2 needs to be equal to a multiple of 3, we have that 3 divides n if and only if the sum of its digits is a multiple of 3.

With a similar reasoning we can find that the same holds for 9.

The largest two digits multiple of 9 is 99, but it doesn't work, because 9+9=18, and 99 is odd.

Next up we have 90, which is of course good, since 90/9=10.

It is the largest two digits integer to have this property, since it's easily checked that others do not work

the results from a pre-test for students for the year 2000 and the year 2010 are illustrated in the box plot. what do these results tell us about how students performed on the 29 question pre-test for the two years?

if we compare only the lowest and highest scores between the two years, we might conclude that the students in 2010 did better than the students in 2010. this conclusion seems to follow since the lowest score of 8 in 2010 is greater in value than the lowest score of 6 in 2000. also, the highest score of 28 in 2010 is greater in value than the highest score of 27 in 2000.

but the box portion of the illustration gives us more detailed information. the middle bar in each box shows us that the median score of 20 in 2000 is greater in value than the median score of 17 in 2010. further, we note that the box and whiskers divide the illustration into four pieces. each of these four pieces represents the same portion of students. so, the upper half of the students in 2000 scored in the same score range as the upper one-fourth of the students in 2010, see the illustration at a score of 20.

by considering the upper one-fourth, upper half, and upper three-fourths instead of just the lowest and highest scores, we would conclude that the students as a whole did much better in 2000 than in 2010. we would conclude that as a whole the students in 2010 are less prepared than the students in 2000.

in this section, we discuss box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. the key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.

step-by-step explanation: