There are two coats in Xiao Wang's wardrobe, one is red, the other is yellow, and there are three pairs of trousers, which are white, blue and yellow. If you take out a coat and a pair of trousers at will, the probability is () A. 56B. 16C. 13D. 15

It can be seen from the tree diagram that there are 2 × 3 = 6 possibilities, and there is exactly one possibility that all are yellow, so the probability that all are yellow is 16

Use the five numbers 1, 2, 3, 4, 5 to form a two digit number without repetition
1. The probability that the composed two digits are even?
2. The probability that the two digits of the composition are greater than 40?
If there are 9 people in line, among them
How many different arrangements does a have to stand in the middle?
2. How many different arrangements do a and B have to stand first and last?
How many different arrangements do a, B and C have to stand together?
4. If there are 4 people in the front row and 5 people in the back row, then A. B
How many different arrangements do you have to stand in the front row
But I didn't learn to do it myself. Let me compare it

1. 0.4
2. 0.4
1. 40320
2. 10080
3. 30240
4. 60480

There are 52 cards in a deck
What is the probability of drawing at least one red heart
I'm sorry. It's two. There's no king

1-P(A),
A: Twice is not a heart
P(A)=39/52 * 38/51=19/34
So the answer is 15 / 34

Positive and negative number exercises
In 2006, the annual average precipitation decreased by 24 mm compared with the previous year, increased by 8 mm compared with the previous year in 2005, and decreased by 20 mm compared with the previous year in 2004

First year + 24
Year 2 + 16
Year 3 - 4

All calculation formulas related to acceleration

Physical theorem, law, formula table
1、 Motion of particle (1) --- linear motion
1) Uniform linear motion
1. Average velocity v = s / T (definition) 2. Useful inference vt2-vo2 = 2As
3. Velocity at intermediate time VT / 2 = vplat = (VT + VO) / 2 4. Final velocity VT = VO + at
5. Middle position velocity vs / 2 = [(VO2 + vt2) / 2] 1 / 2 6. Displacement S = V flat t = VOT + at2 / 2 = VT / 2T
7. Acceleration a = (VT VO) / T {take VO as positive direction, a and VO in the same direction (acceleration) a > 0; opposite direction, af2)
2. Synthesis of mutual angular forces
When f = (F12 + F22 + 2f1f2cos α) 1 / 2 (cosine theorem) F1 ⊥ F2: F = (F12 + F22) 1 / 2
3. Range of resultant force: | F1-F2 | ≤ f ≤| F1 + F2|
4. The orthogonal components of the force FX = fcos β, FY = fsin β (β is the angle between the resultant force and the x-axis, TG β = FY / FX)
Note:
(1) The composition and decomposition of force (vector) follow parallelogram rule;
(2) The relationship between resultant force and component force is equivalent substitution relationship, which can replace the joint action of component force with resultant force, and vice versa;
(3) In addition to the formula method, it can also be solved by the drawing method. In this case, the scale should be selected and the drawing should be strict;
(4) When the value of F1 and F2 is fixed, the larger the angle (α angle) between F1 and F2 is, the smaller the resultant force is;
(5) The combination of forces on the same straight line can take the positive direction along the straight line, and the direction of force can be represented by sign, which is simplified to algebraic operation
4、 Dynamics (motion and force)
1. Newton's first law of motion (Law of inertia): an object has inertia, and always maintains a state of uniform linear motion or static state until it is forced to change this state by an external force
2. Newton's second law of motion: F = ma or a = f / MA {determined by the combined external force, consistent with the direction of the combined external force}
3. Newton's third law of motion: F = - F & # 180; {negative sign means opposite direction, F, F & # 180; each acting on the other side, the difference between balance force and reaction force, practical application: recoil motion}
4. The equilibrium F of copoint force is equal to 0, and {orthogonal decomposition method, principle of intersection of three forces} is extended
5. Overweight: FN > G, weightlessness: FNR}
3. Forced vibration frequency characteristics: F = f driving force
4. Resonance conditions: F driving force = f solid, a = max, resonance prevention and application [see Volume I P175]
5. Mechanical wave, shear wave and longitudinal wave
6. Wave velocity v = s / T = λ f = λ / T
7. The velocity of sound wave (in air) 0 ℃: 332m / S; 20 ℃: 344M / S; 30 ℃: 349m / S; (sound wave is longitudinal wave)
8. Obvious diffraction of wave (wave continues to propagate around the obstacle or hole) condition: the size of the obstacle or hole is smaller than the wavelength, or the difference is not big
9. Interference condition of wave: the frequency of two waves is the same (the difference is constant, the amplitude is similar, and the vibration direction is the same)
10. Doppler effect: due to the mutual movement between the wave source and the observer, the transmitting frequency and receiving frequency of the wave source are different {close to each other, the receiving frequency increases, otherwise, it decreases}
Note:
(1) The natural frequency of a body is independent of amplitude and driving force frequency, but depends on the vibration system itself;
(2) The strengthening area is where the wave crest meets the wave crest or the wave trough meets the wave trough, while the weakening area is where the wave crest meets the wave trough;
(3) The wave only propagates the vibration, the medium itself does not move with the wave, it is a way of transferring energy;
(4) There are interference and diffraction;
(5) Vibration image and wave image;
(6) Other related contents: ultrasound and its application [see Volume 2 P22] / energy conversion in vibration [see volume 1 p173]
6、 Impulse and momentum
1. Momentum: P = MV {P: momentum (kg / s), M: mass (kg), V: velocity (M / s), same direction as velocity}
3. Impulse: I = ft {I: impulse (n &; s), F: constant force (n), t: acting time of force (s), direction determined by F}
4. Momentum theorem: I = Δ P or ft = MVT – MVO {Δ P: momentum change Δ P = MVT – MVO, is vector}
5. Law of conservation of momentum: P before total = P after total or P = P '&# 180; it can also be m1v1 + m2v2 = m1v1 & # 180; + m2v2 & # 180;
6. Elastic collision: Δ P = 0; Δ EK = 0 {that is, the momentum and kinetic energy of the system are conserved}
7. Inelastic impact Δ P = 0; 0ra [or RX > (rarv) 1 / 2] select circuit condition Rx

On positive and negative numbers
Scientific experiments show that the charge of the nucleus and the electron in the atom are two opposite charges. Physics stipulates that the charge of the nucleus is a positive charge, and that of the nucleus and the electron in the hydrogen atom each has one charge. The charges they carry are expressed by positive and negative numbers

Hydrogen + 1
Electronic-1

Formula related to acceleration
Find all formulas related to acceleration

Physical theorem, law, formula table
1、 Motion of particle (1) --- linear motion
1) Uniform linear motion
1. Average velocity v = s / T (definition) 2. Useful inference vt2-vo2 = 2As
3. Velocity at intermediate time VT / 2 = vplat = (VT + VO) / 2 4. Final velocity VT = VO + at
5. Middle position velocity vs / 2 = [(VO2 + vt2) / 2] 1 / 2 6. Displacement S = V flat t = VOT + at2 / 2 = VT / 2T
7. Acceleration a = (VT VO) / T {take VO as positive direction, a and VO in the same direction (acceleration) a > 0; opposite direction, af2)
2. Synthesis of mutual angular forces
When f = (F12 + F22 + 2f1f2cos α) 1 / 2 (cosine theorem) F1 ⊥ F2: F = (F12 + F22) 1 / 2
3. Range of resultant force: | F1-F2 | ≤ f ≤| F1 + F2|
4. The orthogonal components of the force FX = fcos β, FY = fsin β (β is the angle between the resultant force and the x-axis, TG β = FY / FX)
Note:
(1) The composition and decomposition of force (vector) follow parallelogram rule;
(2) The relationship between resultant force and component force is equivalent substitution relationship, which can replace the joint action of component force with resultant force, and vice versa;
(3) In addition to the formula method, it can also be solved by the drawing method. In this case, the scale should be selected and the drawing should be strict;
(4) When the value of F1 and F2 is fixed, the larger the angle (α angle) between F1 and F2 is, the smaller the resultant force is;
(5) The combination of forces on the same straight line can take the positive direction along the straight line, and the direction of force can be represented by sign, which is simplified to algebraic operation
4、 Dynamics (motion and force)
1. Newton's first law of motion (Law of inertia): an object has inertia, and always maintains a state of uniform linear motion or static state until it is forced to change this state by an external force
2. Newton's second law of motion: F = ma or a = f / MA {determined by the combined external force, consistent with the direction of the combined external force}
3. Newton's third law of motion: F = - F & acute; {negative sign means opposite direction, F and F & acute; act on each other respectively, the difference between balance force and reaction force, practical application: recoil motion}
4. The equilibrium F of copoint force is equal to 0, and {orthogonal decomposition method, principle of intersection of three forces} is extended
5. Overweight: FN > G, weightlessness: FNR}
3. Forced vibration frequency characteristics: F = f driving force
4. Resonance conditions: F driving force = f solid, a = max, resonance prevention and application [see Volume I P175]
5. Mechanical wave, shear wave and longitudinal wave
6. Wave velocity v = s / T = λ f = λ / T
7. The velocity of sound wave (in air) 0 ℃: 332m / S; 20 ℃: 344M / S; 30 ℃: 349m / S; (sound wave is longitudinal wave)
8. Obvious diffraction of wave (wave continues to propagate around the obstacle or hole) condition: the size of the obstacle or hole is smaller than the wavelength, or the difference is not big
9. Interference condition of wave: the frequency of two waves is the same (the difference is constant, the amplitude is similar, and the vibration direction is the same)
10. Doppler effect: due to the mutual movement between the wave source and the observer, the transmitting frequency and receiving frequency of the wave source are different {close to each other, the receiving frequency increases, otherwise, it decreases}
Note:
(1) The natural frequency of a body is independent of amplitude and driving force frequency, but depends on the vibration system itself;
(2) The strengthening area is where the wave crest meets the wave crest or the wave trough meets the wave trough, while the weakening area is where the wave crest meets the wave trough;
(3) The wave only propagates the vibration, the medium itself does not move with the wave, it is a way of transferring energy;
(4) There are interference and diffraction;
(5) Vibration image and wave image;
(6) Other related contents: ultrasound and its application [see Volume 2 P22] / energy conversion in vibration [see volume 1 p173]
6、 Impulse and momentum
1. Momentum: P = MV {P: momentum (kg / s), M: mass (kg), V: velocity (M / s), same direction as velocity}
3. Impulse: I = ft {I: impulse (n &; s), F: constant force (n), t: acting time of force (s), direction determined by F}
4. Momentum theorem: I = Δ P or ft = MVT – MVO {Δ P: momentum change Δ P = MVT – MVO, is vector}
5. Law of conservation of momentum: P before total = P after total or P = P '& acute; it can also be m1v1 + m2v2 = m1v1 & acute; + m2v2 & acute;
6. Elastic collision: Δ P = 0; Δ EK = 0 {that is, the momentum and kinetic energy of the system are conserved}
7. Inelastic impact Δ P = 0; 0ra [or RX > (rarv) 1 / 2] select circuit condition Rx

Exercises of positive and negative numbers
The diameter dimension of a part is 30 + / - 0.03-0.02 (unit: mm) on the drawing, which means that the standard dimension of the part is 30mm, and the maximum dimension required for machining is ()
A.0.03 B.0.02 C.30.03 D.29.98

C, of course
30 is standard, - 0.03 those are errors

All the formulas for acceleration?

1. Average velocity v = s / T (definition) 2. Useful inference vt2-vo2 = 2As
3. Velocity at intermediate time VT / 2 = vplat = (VT + VO) / 2 4. Final velocity VT = VO + at
5. Middle position velocity vs / 2 = [(VO2 + vt2) / 2] 1 / 2 6. Displacement S = V flat t = VOT + at2 / 2 = VT / 2T
7. Acceleration a = (VT VO) / T {with VO as the positive direction, a and VO are in the same direction (acceleration) a > 0; if a is in the opposite direction, a

I have a question like this: positive + negative = positive, positive negative = positive; negative positive = negative, negative positive = negative. Is this correct? Please correct it. For example, if - 7 + 4 = - 11, can you think like this: - 7 + 4 = - 11, is its inverse operation subtraction or addition? If this number 4 becomes x, how can you think about finding x, Can you explain it in the most understandable way? In addition, there are many examples. Can you give some examples? Thank you

If you don't listen well in class, positive number (x) + negative number (y) = x - | y |, for example: 4 + (- 7) = 4 - | - 7 | = - 3
Positive number (x) - negative number (y) = x + | y |, for example: 4 - (- 7) = 4 + | - 7 | = 11
Negative (y) - positive (x) = - (| y | + x), for example: - 7-4 = - (| 7)

There are two coats in Xiao Wang's wardrobe, one is red, the other is yellow, and there are three pairs of trousers, which are white, blue and yellow. If you take out a coat and a pair of trousers at will, the probability is () A. 56B. 16C. 13D. 15