1.a Let this two-digit number be AB, 10A+B+9B= 100, and A+B= 10.
2.c 25×0.4×0.4×0.4×0.4×0.4 & lt； 0.5
3.b Original formula =1-1/4+1/8-1/8+1/6-1/65438.
4. four rounds of dabcd repetition, three rounds of EFG repetition and two rounds of HI repetition. So all three groups are repeated once, and the number of rounds should be their common multiple, that is, the first repetition is the least common multiple: 12 rounds. Repeat for the second time 13 rounds.
Obviously, everyone's peaches should be even.
6.a wrote 589 Chinese characters in the whole month, with an average of 589÷3 1= 19 (pieces) per day, which means that 19 Chinese characters were written on 16. According to arithmetic progression's formula for finding the nth item, the tolerance is = (19-4) ÷ (16-1) =1(pieces).
Second, fill in the blanks
1. Original formula = 2009× 2008×1000/-2008× 2009×10001= 0.
It takes 800,000 people to move 800,000 tons of mountains.
First generation: 1
Second generation: 2
Third Generation: 2×2=4
Fourth Generation: 2×2×2=8
、、、、、、、
Generation 13: 2×2×, × 2 = 4096 (02 times of 65438+2)
1+2+4+8+,,, +4096=S (when calculating, the formula is written backwards once, and the two formulas are aligned and subtracted).
It can be found that: S=2×2×, ×2( 13 quadratic)-1= 8191>; 8000 (person)
So it can be moved to 13 generation.
As can be seen from the title, the family in this town is divided into three parts, one of which has a child; The rest are divided into two parts on average: half have two children and the other half have no children. If a family with two children is given to a family without children, so that all families in this town have one child, there will be 5,000 children.
Draw a picture, we can see that it takes 9 hours to go back and forth in the middle, and the distance is the same. Downstream is twice as fast as countercurrent. It can be concluded that the ship has been retrograde for 6 hours and sailed forward for 3 hours, and the forward speed is 400÷20=20 km/h, so the forward distance is 20×3=60 km, and it will go back and forth.
5. As can be seen from the question, the average score of admission is 24+6=30 points more than that of non-admission, and all the average scores are 60 points, which means that all the extra points of admission are distributed to everyone, and finally they are 60 points; There are three applicants, of whom 1 applicants were admitted, and 30× 1÷3 = 10, and everyone got 10, that is, the original average score of those who were not admitted was 60- 10 = 50. Then, the admission score is 50+24=74 (points)
6. Hong Tailang's journey is half walking and half running, while Grey Wolf is walking and half running. It is certain that running is longer than walking, that is, Big Wolf can't walk half, but runs more than half, and the two wolves walk the same distance. Big Wolf runs more distances than Kotaro, and naturally takes less time.
7. The first situation can be understood as: A walked 2+2.5=4.5 hours, and B walked 2.5 hours, and the two met.
The second situation can be understood as: A walks for 3 hours, and B walks for 2+3=5 hours, and the two meet.
Let A drive X kilometers per hour, then B should be: (36-4.5x) ÷ 2.5 =14.4-0.18x (km) per hour.
According to the second case, the equation can be listed as 3x+(14.4-0.18x) × 5 = 36.
X=6 km/h, B =3.6 km/h.
8. The first number must be 7, so we will not consider it.
(1) The second to fifth digits only take numbers from 0 to 5. According to the principle of multiplication, * * * has 6×5×4×3=360 cases.
② Numbers from 0 to 5 are used in the 2nd and 4th digits, and only 6, 7 and 9 are used in the 3rd and 5th digits. There are 6×5×3×2= 180 cases * *.
③ Numbers from 0 to 5 are used in the 2nd, 3rd and 4th digits, and only 6, 8 and 9 are used in the 5th digit. * * * There are 6×5×4×3=360 cases.
④ Numbers from 0 to 5 are used in the 2nd, 4th and 5th digits, and only 6, 8 and 9 are used in the 3rd digit. There are 6×5×4×3=360 cases * *.
To sum up, there are 360+180+360+360 =1260 cases where the five numbers of this expression are different.
9. Start with the sum of numerator and denominator, and put the same in a box.
The first box: sum is 2.
The second box: the total is 3.
By analogy, the sum of 7/ 19 is 26, which means it is in the 25th box.
In each box, the denominator is sum, and this fraction is a number, so 7/ 19 should be the number 19 in the 25th box.
So 1+2+3+, +25+ 19=344 (pieces).
10 had two draws. B, and you can get 2 points. B You have to win one game to make the total score odd. If you win A, A must win the remaining two games to get the first place in the total score, but you got 6 points, which doesn't matter. It means that B won D and tied with A. Because A scored first, there are only two wins and one draw, and B..D has lost to A and B. If you want to be singular, you can only win C or draw C. If D and C are tied, then C and D.
Third, answer questions.
The prime numbers within 1.37 are: 2, 3, 5, 7,1,13, 17, 19, 23, 29, 3/kloc-.
(1), if two numbers add up to 37, there is no (odd+odd = even, 37 is odd, so there is no).
(2) If three numbers are added, odd+odd+odd =37.
37=3+5+29=3+ 1 1+23=5+ 13+ 19=7+ 1 1+ 19=7+ 13+ 17
(3) If four numbers are added, odd+odd+even =37.
37=2+5+7+23=2+5+ 1 1+ 19=2+3+ 13+ 19=2+ 17+7+ 1 1=2+ 17+5+ 13
(4) When five numbers are added, odd+odd+odd =37 (none).
There are 10 kinds of * *. If the product is the smallest, the multiplier is the least and the distance is the largest, it is obvious that only 37=3×5×29 is satisfied.
2. Two more than three, four more than five and six more than seven can be understood as: one less than three, one less than five and one less than seven. Therefore, the common multiple of 3, 5 and 7 should be one less, and the common multiple of 3, 5 and 7 is only 2 10 between 200 and 300, so the number of chess pieces is 2 10- 1=209.
3. Number of triangles: (4+3+2+ 1)×4=40.
The number of trapezoid: (4+3+2+ 1)×6=60.
Difference: 60-40=20
4. Method (1) In profit and loss problem, suppose a company takes one pill every day.
The two conditions in the question can be translated into: if you transfer to a company, you can eat the existing six-day grain and eat six more days;
If you transfer out of a company, the existing grain can be eaten for 10 days, and the grain is eaten less for 10 days.
(10+6)÷( 10-6)=4 (company) (Understanding: Why is there a difference between 16? Because you ate four more days, you can see that you ate four servings of food a day. There are four companies because one company eats a portion of grain every day. Thinking: If it is assumed that a company eats something other than one pill every day, will it affect the final result? )
(4+ 1)×6=30 portions of grain, enough for one person to eat for 30 days.
Method (2) Solve the equation
There are x companies.
(x+ 1)×6 =(x- 1)× 10
X=4