Fill in the blanks: 1. The area of two rectangles is equal. It is known that the ratio of the length of the two rectangles is 8:5, and the ratio of their width is () 2. Add 6 grams of salt and 14 grams of water to the salt water with 30% salt content, then the salt content in the new salt water is () 3. For a commodity, the price has been reduced by 10% for two consecutive times, and the current price is equal to () of the original price 4. When preparing peracetic acid disinfectant, it should be prepared according to the mass ratio of 1:200. Now the personnel have put 0.3KG peracetic acid into 50kg water. If the disinfectant meets the requirements, it should be () Practical questions: 1. A basket of fruit weighs 50 kg in total. After selling 50% of the fruit, the basket weighs 27 kg in total. How many kg does the fruit weigh? 2. If a commodity is reduced by 10% of its current price, it will still make a profit of 200 yuan; if it is reduced by 20%, it will lose 220 yuan. What is the current price of this commodity? 3. A 60 kilometer long highway is divided into three sections: uphill, flat and downhill. The length ratio of each section is 1:2:3. Uncle Zhang's riding time is 3:4:5. It is known that his riding speed on flat road is 25 kilometers per hour. How long does it take him to complete the whole journey? 4. Zhongshang supermarket is engaged in promotion activities. For those who purchase goods with a value of more than 200 yuan, they can draw a lottery ticket with a total of 2000 tickets until they are finished. There are 20 mid-term first prizes with a value of 800 yuan, 30 second prizes with a value of 500 yuan, and 100 third prizes with a value of 100 yuan. What is the winning rate of this promotion? If all the lottery tickets are drawn, how many yuan of goods have been sold at least, What is the maximum percentage of sales? All practical problems need to be solved by formulas!

1.5 to 82.30% 3.81% 4. Add water 10 kg 1. (50-27) / 50% = 46 kg2. (220 + 200) / (1-10%) - (1-20%) = 4200 yuan, the current price is 4200 yuan 3. Uphill road length is 60 * 1 / (1 + 2 + 3) = 10km, level road length is 60 * 2 / (1 + 2 + 3) = 20km, downhill road length is 60 * 3 / (1 + 2 + 3) = 30km, level road time dimension: 20

Xiaoqiao's father is a pastry maker, and her mother is a cook. & nbsp; & nbsp; & nbsp; & nbsp; (1) on January 3, both father and mother have a rest, so which day is the same rest day for father and mother in January? (2) What are the rest days for mom and dad in February?

The least common multiple of 4 and 3 is 12, so: 3 + 12 = 15, 15 + 12 = 27, so January 15 and January 27 rest at the same time; January 27 + 12 = February 8, 8 + 12 = 20, February 20, so February, February 8 and February 20 rest at the same time

1. Party A and Party B make the same parts. If Party A makes the same parts for one day and Party B starts to make them, they will make the same number of parts after five days. If Party A makes 30 parts first and Party B starts to make them again, Party B will make 10 more parts than Party A after four days. How many parts do Party A and Party B make each day?
2. The distance between a and B is 30 kilometers, and there are two places C and D in the middle (D is close to a). A, B and C go from a to B at the same time. B takes a by bike, and C walks. After a and B arrive at C, B walks forward. A turns back to meet C, and they meet at D. as a result, the three people arrive at B at the same time
3. The distance between a and B is 80 km. Generally, the ship starts from a and travels along the water for 4 hours to reach B, while the ship starts from B and travels against the water for 5 hours to reach a
4. A ship sails between a and B docks. It takes 40 minutes to reach downstream, and 4 kilometers to reach. It takes 1 / 3 of an hour to reach upstream. The known speed of upstream is 12 kilometers per hour. The speed of the ship in still water can be calculated
5. It is known that the length of the upper bottom of the trapezoid is (4h + 3M) cm, the length of the lower bottom is (2m + 5N) cm, and its height is (M + 2n) cm

Let a make X and B make y
So x + 5x = 5Y
30+4X+10=4Y
The solution is x = 50, y = 60
A: a 50, B 60
Let ad = x, CD = y, CB = Z
Because the bicycle distance from a to C is CD + DB = 2Y + Z, and B is Z
Because the time is the same, 2Y + Z = 3Z
That is y = Z
Similarly, according to the speed, AC + CD = 3aD
That is, x + 2Y = 3x
So x = y
So x = y = z = 10km
A: AC is 20km away
Let X be the speed of the ship and y be the speed of the water
From the title: 4 (x + y) = 5 (X-Y)
So x = 9y
And because 4 (x + y) = 80
So 4 (y + 9y) = 80
So y = 2, x = 18
A: ship speed is 18, water speed is 2
(4) Let the flow velocity be x, the static velocity be 12 + X, and the downstream velocity be 12 + 2x
From question: (2 / 3) * (12 + 2x) + 4 = (4 / 3) 12
So x = 3
Still water = 12 + 3 = 15
A: hydrostatic speed is 15km / h
(5) I wonder if the God in the title is 4N + 3M, otherwise it's not easy to solve

Please help me answer a question about inequality
Let a > 0, b > 0, then the following inequality is not always true:
A. (a + b) (1 / A + 1 / b) > = (greater than or equal to)
B.a3+b3>=2a+2b
C.a2+b2+2>=2a+2b
D. A-B | > = a-b
A.(a+b)(1/a+1/b)>=4

A: I don't know what you mean. B: a = b = 1 doesn't work (if your A3 is the three sides of a). C: divide 2 into two 1's and add them together. A square plus one is greater than or equal to 2A. Similarly, b square plus one is greater than or equal to 2B. That's the result. D: both sides are square at the same time to get the result

The distance between a and B is 360 km. The passenger cars and freight cars are facing each other at the same time. They meet three hours later. The passenger cars travel 6 km more per hour than the freight cars, and there are more cars per hour
Less kilometers? (equation)

There are freight cars traveling x km per hour and passenger cars traveling x + 6 km per hour
(x+x+6)*3=360
2x+6=120
2x=114
x=57
Bus 57 + 6 = 62 km

Projective definition

Projection is orthographic projection
Among them, the perpendicular foot of the vertical line from a point to a line is called the orthographic projection of this point on this line. The line segment between the orthographic projections of two ends of a line segment on a line is called the orthographic projection of this line segment on this line
From the similar properties of triangles, it can be concluded that:
Theorem in a right triangle, the height of the hypotenuse is the middle of the proportion of the projection of two right angles on the hypotenuse. Each right angle is the middle of the proportion of the projection of the right angle on the hypotenuse

To build a section of highway, it takes 100 days for Party A to build it alone, and 120 days for Party B to build it alone. If Party B builds it 40 days first, the rest will be built by both teams, and the cost will be reduced
We should also use the formula

If the total amount of highway is 1, then Party A will build 1 / 100 and Party B will build 1 / 120 every day,
If B repairs 40 days in advance, the remaining amount is (1-40 × 1 / 120) = 2 / 3
SO 2 / 3 ÷ (1 / 100 + 1 / 120) = 400 / 11 (days)
Typing is so tiring
I think I can understand

How many natural numbers can be taken from 1.2.3.2004, so that the difference between each two numbers is not equal to 4

Up to 670 numbers can be taken out. 4 is a multiple of 1 and 2, not 3, 5, 6, 7 Take a group of arithmetic sequence with tolerance of 3: 1, 4, 7, 10 There are 668 numbers in 1996, 1999 and 2002. Obviously, the difference between any two numbers in this group is not equal to 4, because 2 + 4 = 6 and 2004-4 = 2010 are not in the above series

The speed of a passenger car is 60 km / h, and that of a freight car is 45 km / h. The freight car is 135 meters longer than the passenger car. If two cars are running opposite each other on parallel tracks, and the time they spend in the process of meeting is 30 seconds, the lengths of the passenger car and the freight car are______ ．

① Total length of two cars: (60 + 45) △ 60 × 0.5 = 0.875 (km) = 875 (m); length of freight car: (875 + 135) △ 2 = 505 (m); length of passenger car: 505-135 = 370 (m); answer: length of passenger car: 370 m, length of freight car: 505 M

If a, B and C are all integers and ABC = 21, what are the maximum and minimum values of a + B + C?

Maximum a + B + C = 21 + 1 + 1 = 23
Minimum a + B + C = - 21-1 + 1 = - 21

Xiaoqiao's father is a pastry maker, and her mother is a cook. & nbsp; & nbsp; & nbsp; & nbsp; (1) on January 3, both father and mother have a rest, so which day is the same rest day for father and mother in January? (2) What are the rest days for mom and dad in February?

Please help me answer a question about inequality Let a > 0, b > 0, then the following inequality is not always true: A. (a + b) (1 / A + 1 / b) > = (greater than or equal to) B.a3+b3>=2a+2b C.a2+b2+2>=2a+2b D. A-B | > = a-b A.(a+b)(1/a+1/b)>=4

The distance between a and B is 360 km. The passenger cars and freight cars are facing each other at the same time. They meet three hours later. The passenger cars travel 6 km more per hour than the freight cars, and there are more cars per hour Less kilometers? (equation)