From the question => The lowest \(\left|x+1\right|\) is \(3\) and the biggest is \(108\).

So there are: \(\left(108-3+1\right).2=212\left(integers\right)\) \(x\) satisfy this question.

There are: \(100-\left(12+25\right)=63\%\) people have black hair.

There are: \(\left(600:100\right).63=378\left(people\right)\) have black hair.

So the answer is \(378\) people have black hair.

The volume of the cube is:

\(15.15.15=3375\left(cm^3\right)\)

\(\dfrac{3^5.5^6}{9^2.25^4}-\dfrac{7^3.8^4}{21.7^2.16^2}\)

\(=\dfrac{3^5.5^6}{3^4.5^8}-\dfrac{7^3.8^4}{\left(7.3\right).7^2.\left(8.2\right)^2}\)

\(=\dfrac{3}{5^2}-\dfrac{7^3.8^4}{7^3.3.8^2.2^2}\)

\(=\dfrac{3}{25}-\dfrac{8^2}{3.2^2}\)

\(=\dfrac{3}{25}-\dfrac{64}{12}\)

\(=\dfrac{3}{25}-\dfrac{16}{3}\)

\(=\dfrac{-391}{75}\)

Sorry, Phan Thanh Tinh made the right comment.

The value of y must be \(y\le3\) because if \(y\ge4\) then \(5^{y+1}>1000\).

If \(y=0;1;3\) then it is not possible for \(x\) to have the result \(2^{x+1}.5^{y+1}=1000\).

So \(y\) must be \(2\). 

When \(y=2\), then \(5^{y+1}=5^{2+1}=5^3=125\).

Then \(2^{x+1}=1000:125=8\).

=> \(x=2\).

So \(x=2\) and \(y=2\)

Arrcoding to the question, we have:

\(N:7\left(r=3\right)\)  <1>

 \(N:5\left(r=4\right)\) <2>

From <1> we have: \(3;10;17;24;31...;7k+3\)

From <2> we have: \(4;9;14;19;24;...;5k+4\)

We have number \(24\) satisfy the question.

So the answer is \(24\).

There is total: \(\left(100-1\right)+1=100\left(numbers\right)\)

The sum of all numbers is: \(\left(1+100\right).100:2=5050\)

The average of all numbers is: \(5050:100=50,5\)

So the answer is: \(50,5\)

We have: \(1cm=10mm\)

=> \(20cm=200mm\)

So the answer is \(200mm\) (200 millimeter).

We have:

\(\dfrac{x+1}{2}+3< \dfrac{9}{2}\)

<=> \(\dfrac{x+1}{2}+\dfrac{6}{2}< \dfrac{9}{2}\)

<=> \(\dfrac{x+1}{2}< \dfrac{9}{2}-\dfrac{6}{2}\)

<=> \(\dfrac{x+1}{2}< \dfrac{3}{2}\)

=> \(x+1< 3\)

=> \(x< 2\)

So \(x< 2\) satisfy \(\dfrac{x+1}{2}+3< \dfrac{9}{2}\)

The answer is D.

The graph A is not correct at the number of dollars, the graph B and C is not correct at the number of laps.

So the answer is A: \(7^{15}\)

\(7^5.7^{10}=7^{5+10}=7^{15}\)

The answer is A, B,C,D,G,I.

The perimeter of the rectangular playground is:

\(\left(7y-4\right).2+\left(2y+9\right).2=14y-8+4y+18=18y+\left(-8+18\right)=18y+10\)

So the answer is A: \(18y+10\)

We call d = \(D\left(21n+4;14n+3\right)\)

We have:

\(\dfrac{21n+4:d}{14n+3:d}\)

=> \(\dfrac{2\left(21n+4\right):d}{3\left(14n+3\right):d}\)

=> \(\dfrac{42n+8:d}{42n+9:d}\)

=> \(\left(42n+9\right)-\left(42n+8\right):d\)

=> \(1:d\)

So \(\dfrac{21n+4}{14n+3}\) is irreducible for all \(n\in N\)

Into the figure, this shape is made of 8 small cubes.

The surface of the small cube = \(3.3.6=54\left(cm^2\right)\)

The surface of the big cube = \(54.8:2=216\left(cm^2\right)\)

So the answer is \(216cm^2\)

P/s: The surface of the big cube is used by \(\dfrac{1}{2}\) surface of 8 small cubes

The least possible number is: \(1000\)

The biggest possible number is: \(9998\)

There are: \(\left(9998-1000\right):2+1=4500\left(numbers\right)\)

So there are \(4500\)  4-digit-even numbers.

We call the natural numbers: \(x\)

From the context, we have: \(x< 2017\)

The least possible number is: \(0\)

The largest possible number is: \(2016\)

So there are: \(\left(2016-0\right)+1=2017\left(numbers\right)\)

So there are \(2017\) numbers are not greater than 2017.

Sum of their digits equal to 9 <=> The numbers must be divisible by 9.

The least possible number is: \(18\).

The biggest possible number is: \(90\) (99 is not possible because \(9+9\ne9\) ).

So there are: \(\left(90-18\right):9+1=9\left(numbers\right)\)

So there are \(9\) numbers from 10 to 99 have sum of their digits equal to 9.