In an opaque pocket, there are 12 yellow balls and several red balls. These balls have no other difference except color. After many touching tests, Xiao Li found that if the frequency value of randomly picking out a red ball is stable at 25%, the number of red balls in the bag may be 25%______ One

Suppose there are x red balls in the bag. From the meaning of the question, we get xx + 12 × 100% = 25%, and we get x = 4

There are four identical balls in a pocket. Take them labeled as 1, 2, 3 and 4, randomly select a small ball and put it back. After randomly selecting a small ball, calculate the probability of the following events
1. The size of the ball is the same twice
2. The sum of labels extracted twice is 4

1. The size of the ball is the same twice
There are 16 cases when a small ball is randomly selected: (1,1), (1,2), (1,3), (1,4), (2,1),..., (4.4)
There are four kinds of cases in which the two labels are the same: (1,1), (2,2), (3,3), (4,4)
So, P (the same label twice) = 4 / 16 = 1 / 4
2. The sum of labels extracted twice is 4
There are four cases when the sum of labels is 4: (1,3), (2,2), (3,1)
The calculated probability is 3 / 16

1. There are six balls numbered one to six in a pocket. First, take one ball out of the bag, put it back into the bag, and then touch it again. What is the probability that the balls touched twice are the same? 2. The password of a password lock consists of four numbers, each of which is one of the 10 numbers from 0 to 9, Careless Xiao Ming forgets the two numbers in the middle. What's the probability that he can unlock the lock at one time?

Question 1: 1 / 6 * 1 / 6 = 1 / 36
Question 2: 1 out of 99

How to deal with probability in ninth grade mathematics of people's Education Press

Probability is not particularly difficult, can be in the total review of the time to seriously learn again, practice some questions, it should be ok
Note the format of the answers

When to use Lorentz positive transformation and when to use inverse transformation?

According to the principle of relativity, inertial frame s and s' frame are equivalent. When you look at s' frame in s' frame, it is far away from you at the speed of - V. whether to use positive transformation or inverse transformation depends on which frame is used as observation frame and the relative speed between them. Generally, if the ground is used as reference frame, the events occurring on the moving s' frame are positive transformation, and the moving s' frame is used as reference frame, In fact, there is no big difference between using positive transformation and inverse transformation, as long as the relative velocity between the reference system and the observed system (there are positive and negative points, which can be seen from the specific analysis) is clear, and then the Lorentz transformation can be used to solve the problem

In order to improve his mental arithmetic ability, Xiao Dong does five more mental arithmetic every day than before. Now it only takes eight days to do the original 10 day problem, and now he does several mental arithmetic problems every day on average
Do it with equations

Let's do X questions every day
8x=10(x-5)
8x=10x-50
10x-8x=50
x=25

A small problem on the derivation of Lorentz transformation
"Suppose that a beam of light in the positive direction along the x-axis is emitted from the coincident origin o (o '). Let the wavefront coordinates of the beam be (x, y, Z, t), (x', y ', Z', t '). According to the constant speed of light, x = CT (6) x' = CT '(7)"
The seventh equation x '= CT' is why it requires the speed of light to be divided by the displacement of light motion. Why is x 'the displacement of light motion here? Isn't X' the distance from the origin of the reference frame s' when the event occurs? With s' as the reference frame, the place where the event occurs is not close to the origin of s', so how can the displacement of light motion be x '?

X 'is the displacement measured in the moving reference frame, which is equal to the time in that reference frame multiplied by the speed of light. In s reference frame, the displacement x = CT, which has nothing to do with the existence of X' reference frame. Similarly, in X 'reference frame, the light starts from o', the time is t ', and the displacement X' = CT ', which has nothing to do with the existence of X reference frame

Xiaohua can do 12 mental arithmetic problems per minute, which is two-thirds of Xiaojun's speed. How many mental arithmetic problems can Xiaojun do per minute?

12 divided by two thirds 18

There are many books about the derivation of Lorentz transformation, which is almost the same as that of Baidu Encyclopedia. Please see the expressions (6) and (7) given by Baidu Encyclopedia, that is, x = CT, X '= CT'. This is a special condition, which only holds for luminous events. The formula based on special cases naturally needs to be extended to general cases, But I can't find the generalization process. The rigorous derivation process of Lorentz transformation is given

I think so, too. Most books have additional assumptions about the derivation of Lorentz transformation
Finally, I wrote in a Book special relativity（ ISBN:9787030226150 ）The strict derivation is found in the appendix of, which was given by Weyl, but I still don't understand it. It's too complicated
If you are interested, you can go and see it. It's sold on Dangdang excellence

Ming Ming did 60 mental arithmetic problems in a fifth of an hour. At this speed, how many mental arithmetic problems did he do in an hour? How many minutes did he take to do one problem?

(1) A: he does 300 mental arithmetic in an hour
(2) Answer: it takes 0.2 minutes to do a question

In an opaque pocket, there are 12 yellow balls and several red balls. These balls have no other difference except color. After many touching tests, Xiao Li found that if the frequency value of randomly picking out a red ball is stable at 25%, the number of red balls in the bag may be 25%______ One