From the four numbers of 2345, put them back three times, take any number each time, and find the probability that the product of the three numbers obtained can be divided by 10

If it can be divided by 10, there must be 5 and even number, that is, at least one of 2 or 4
Classification discussion. There is a case of 5, an even number. 523534
One 5, two even numbers, 524.522544
Two 5S, one even, 552554
Because you can change the order
Each of the above 523, 534, 524 has a (3,3) = 6 cases
So there are 6 * 3 + 4 * 3 = 30
A total of 4 * 4 * 4 = 64, probability = 30 / 64
Does it feel a bit troublesome, but other methods may easily lead to repetition, so although it seems troublesome, as long as it is organized, not heavy and not missed, there is no difficulty in thinking about the process

If 1-2000 is not divisible by 6 or 8, then the probability of 1-2000 is high

The number divisible by 6 is 2000 / 6 = 333
The number divided by 8 is 2000 / 8 = 250
Divided by the least common multiple 24 of 6 and 8, there are 2000 / 24 = 83
So the number that can be divided by 6 and 8 is 333 + 250-83 = 500
There are 500 numbers that cannot be divided by these two numbers
The probability is one in two

Matlab, in the 1-2000 integers randomly take a number, ask the integer can not be divided by 6, and can not be divided by 8, what is the probability? Find the program process

I don't know whether you need to solve this problem by experiment or by mathematics
Easy mathematical solution: find all the numbers that can be divided into 6 or 8: 2000 / 6 + 2000 / 8-2000 / (the least common multiple of 6 and 8) = 333 + 250-83 = 500 (all values are rounded down)
So the probability is: (2000-500) / 2000 = 0.75
If using MATLAB experiment solution, the following procedure
M = 2000;% total
N = 0;% counter
K = 100000;% matlab calculation times
for i=1:k
Rou = ceil (rand * m);% randomly generate an integer from 1 to M
if mod(rou,6)~=0 & mod(rou,8)~=0
%Round if not divisible by 6 and not divisible by 8
n=n+1;
end
end
n/k
The result of this program is different every time, because it is a random experiment, the size of K can be adjusted to consider the number of experiments, and the result is basically about 0.75

If x + y = - Z, then the value of (x ^ 2-y ^ 2) + (XZ YZ) is?

(x^2-y^2)+(xz-yz)
=(x-y)(X+Y+Z)
x+y=-z,X+Y+Z=0
Then (x ^ 2-y ^ 2) + (XZ YZ) = 0

X + y = - Z, then the value of (x ^ 2-y ^ 2) + (XZ YZ) is

The original formula can be written as (x + y) * (X-Y) + Z (X-Y)
You can get it by substituting x + y = - Z
-Z(X-Y)+Z(X-Y)
The final result is 0

Given x ^ 2 + y ^ 2 + Z ^ 2-xy-yz-xz = 0, find the size relation of X, y, Z
Tonight

x^2+y^2+z^2-xy-yz-xz=0
(1/2)*2(x^2+y^2+z^2-xy-yz-xz)=0
(1/2)*(x^2+y^2-2xy+z^2+y^2-2zy+x^2+z^2-2xz)=0
(x-y)^2+(y-z)^2+(z-x)^2=0
x-y=y-z=z-x=0
x=y=z

Characteristics of numbers divisible by 11.12

1、 Let me introduce a method to divide a number divisible by 11. The absolute value of the difference between the sum of the even digits and the sum of the odd digits must be divisible by 11. For example, 619319362376... 2. The number divisible by 12 must be divisible by 3 and 4 at the same time. For example, 6127524,... 1

What are the characteristics of divisible by 11

For example, in 792 (7 + 2) - 9 = 0, then 792 is a multiple of 11 (0 is a multiple of 11). In 7183 (7 + 8) - (1 + 3) = 11, then 7183 is a multiple of 11. In 7183 = 11 * 653.7138 (7 + 3) - (1

Characteristics of numbers divisible by seven

If the number of one digit of an integer is truncated, and then two times of the number of one digit is subtracted from the remaining number, if the difference is a multiple of 7, then the original number can be divided by 7. If the difference is too large or it is difficult to see whether it is a multiple of 7 by mental arithmetic, we need to continue the above process of "truncation, multiplication, subtraction and difference checking" until we can make a clear judgment. For example, the process of judging whether 133 is a multiple of 7 is as follows: 13-3 × 2 = 7, So 133 is a multiple of 7; for example, the process of judging whether 6139 is a multiple of 7 is as follows: 613-9 × 2 = 595, 59-5 × 2 = 49, so 6139 is a multiple of 7, and so on

What are the numbers divisible by 4, 7, 8, 11 and 13?
You'd better help me with the characteristics

There are many, such as 8008, as long as it is the common multiple of 7, 8, 11 and 13

From the four numbers of 2345, put them back three times, take any number each time, and find the probability that the product of the three numbers obtained can be divided by 10