Oh, I was wrong! Thanks Dao Trong Luan and Kaya Renger :) 

I'd add the answer more from Dao Trong Luan's answer:

Because 30 is Tuesday (1) => The month has 31 days. (2)

From (1) and (2) => The last day of the month is Wednesday.

We have: abc + bb = cba.

=> b = 9, a > 5 and c - a = 1 (the only situation satisfy)

So the numbers abc are: 596;697;798

P/s: with \(a\ne b\ne c\) and no proving.

Because a,b are positive numbers and a + b = 1

=> a = b = 0 or a = 1; b = 0 or a = 0;b = 1.

If a = b = 0 then \(\dfrac{1}{ab}=\dfrac{1}{0}\) (unsatisfy)

If a or b = 0 or 1, then \(\dfrac{1}{ab}=\dfrac{1}{0}\) (unsatisfy)

So there is no \(a,b\) satisfy.

Multiple of 91 <=> Divisible by 91.

We have: \(abc⋮d\) => \(abcabc⋮d\)

=> \(5ab⋮91\) => \(546⋮91\)

So the number is: 546

The distance of /4 - 1 (out of 4 and minus 1) of each number is: 1 (4.1-1), 2 ( 4.2-1), 3(4.3-1).

The least possible score of the distance is: 1.6 = 6

The biggest possible score of the distance is: 3.6 = 18

Therefore, there are: \(18-6+1=13\left(different-scores\right)\)

ANSWER: 13 different scores.

Call the number: abcd.

We have: 

+ \(a=1;2;3;4;5;6\)  

+ \(b=2;3;4;5;6;7\)

+ \(c=3;4;5;6;7;8\)

+\(d=4;5;6;7;8;9\)

So then there are: \(6.6.6.6=1296\left(numbers\right)\)

ANSWER: 1296 numbers

Four husband-and-wife = 8 people.

The number of people that are not chosen after the first choose is: \(8-1=7\left(people\right)\)

So the probability that the two are selected as a married couple is: \(\dfrac{1}{7-1}=\dfrac{1}{6}\)

So the answer is: \(\dfrac{1}{6}\)

Mình đồng ý với VTK-VangTrangKhuyet.

Sorry, the answer is: \(4^3-\left(0-1^2-2^2-3^2\right)=50cubes\)

Formula: \(a^3-\left[0^2-1^2-...-\left(a-1\right)^2\right]\)

We see: 

- At the first pattern, there is: \(1^3-\left(0\right)=1cube\)

- At the second pattern, there are: \(2^3-\left(0+1\right)=7cubes\)

- At the third pattern, there are: \(3^3-\left(0+1+2\right)=24cubes\)

So at the fourth pattern, there are: \(4^3-\left(0+1+2+3\right)=58cubes\)

ANSWER: 58 cubes

P/s: Formula: \(a^3-\left(0+1+...+a-1\right)\) and a is the number of 1 side of the cube.

There are no numbers satisfy the question from 0-9 or number 100

There are 5 numbers a tenth-row (10s ; 20s ; ... ; 90s)  numbers satisfy the question from 10-99. Because there are 9 tenth-row from 10-99 and there are no numbers from 0-9 or 100 => There are: \(9\cdot5=45\left(numbers\right)\) satisfy the question.

ANSWER: 45 numbers

The thickness of 1 paper is: \(14:\left(10\cdot20\right)=0,07\left(mm\right)\)

The thickness of 1 cover (front or back) is: \(\left[17-\left(11\cdot20\cdot0,07\right)\right]:2=0,8\left(mm\right)\)

The thickness of the first book total is: \(14+1,6=15,6\left(mm\right)\)

The total thickness when two books are stacked cover to cover is: \(15,6+17=32,6\left(mm\right)\)

ANSWER: 32,6 mm

Sorry for my error answer. You only need to answer the question.

Two numbers, x and y, each between 0 and 1, are multiplied. If the tenths digit of x is 1 and the tenths digit of y is 2, what is the greatest possible value of the hundredths digit of the product?

Because \(5x^2-4x=5x^2-4x\) and \(2>-3\) => a > b 

You are right (True).

But the questions is only to be Math in English, so I will only increase a little-bit the question you order.

Thank you for your comment. I will fix it.

Because a = 80 ; b = 10 and c = 30

=> a : b : c = 80 : 10 : 30 = 8 : 30 = \(\dfrac{4}{15}\)

We know this from a long time ago. Thank you very much.