\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\)
\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
\(A=1-\dfrac{1}{100}\)
\(A=\dfrac{99}{100}\)

A = \(\dfrac{1}{1.2}\) +  \(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + ... + \(\dfrac{1}{99.100}\)

A = 1 - \(\dfrac{1}{2}\) +  \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) +  \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + ... + \(\dfrac{1}{99}\) - \(\dfrac{1}{100}\)

A = 1 -\(\dfrac{1}{100}\)

A = \(\dfrac{99}{100}\)

Convert: 1 foot = 12 inches, 12 feet by 13 feet = 144 inches by 156 inches.

The total area of 10 tiles (bought in 1 box) is: \(\left(6.6\right).10=360\left(cubic-inches\right)\)

The area of the floor is: \(144.156=22464\left(cubic-inches\right)\)

The box that must bought is: \(22464:360=62,4\left(box\right)\)

So the minimum number of boxes must be purchased is: \(63boxes\)

Digits thousands have 2 choices are 1 or 2

Digits hundreds have 2 choices are 1 or 2 too.

Digits tens and Digits units have 2 choices too.

So The numbers of four digits containing two digits 1 and 2 are:

2.2.2.2 = 16 

The thousands digit and the unit digit of the palindrome are the same. So are its hundreds digit and its tens digit. Hence, there are 2 satisfied palindromes : 1221 ; 2112

The new base of the triangle is :

 \(100\%+10\%=110\%=\dfrac{11}{10}\) of the original base

The new height of the triangle is :

\(100\%-10\%=90\%=\dfrac{9}{10}\) of the original height

The answer is : \(\dfrac{11}{10}\times\dfrac{9}{10}=\dfrac{99}{100}=99\%\)

Let's take the frist 20 positive intergers 1 to 20.

The number of odd prime numbers : 3;5;7;11;13;17;19.

The probability is : \(\dfrac{7}{20}\cdot100\%=35\%\)

The length of this rectange is:

\(\left(\dfrac{62}{2}\right)\div\left(1+4\right)\cdot4=24,8\left(m\right)\)

The width of this rectange is:

24,8 : 4 = 6,2 [m]

So the area of this rectange is:

24,8 . 6,2 = 153,76 [m²]

Answer: 153,76m²

The length of this rectange is:

The width of this rectange is:

24,8 : 4 = 6,2 [m]

So the area of this rectange is:

24,8 . 6,2 = 153,76 [m2]

Answer: 153,76m

The length of this rectange is:

(622)÷(1+4)⋅4=24,8(m)

The width of this rectange is:

24,8 : 4 = 6,2 [m]

So the area of this rectange is:

24,8 . 6,2 = 153,76 [m2]

Answer: 153,76m2