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Mathematical problem column
1. The radius and height of the bottom of the cone are equal to the side length of the rectangle. It is known that the volume of this rectangle is 30 cubic centimeters and the volume of this cone is (10 cubic centimeters).

2. Cuboid and cone have the same volume. If the base area of a rectangle is two-fifths of the base area of a cone, then the height of the rectangle is (5/6) of the height of the cone.

3. A four-digit decimal is accurate to 5.00 after the percentile, so the maximum value of this four-digit decimal is (5.0049) and the minimum value is (4.9950).

4. The store sells shoes for a shoe factory, and both parties agree that the quantity shall not exceed 200 pairs, and the royalty shall be 8% of the total sales; If it exceeds 200 pairs, the commission will be 65,438+00% of the total sales. It is known that the commission is 9990 yuan after the first-stage entrustment. If the price of each pair is a two-digit prime number, then the price of each pair is (37 yuan).

5. Three sticks in the fifth group. (b) cannot be connected end to end to form a triangle. (Unit: cm)

A.7, 13, 19 d.25, 30, 42.

The following problem solving process

1. The original * * members of Class 3, Grade 8 were a quarter of the non-* * members, and then four people joined the league. At this time, the number of * * * members accounts for 30% of the class. How many people are there in Class Three, Grade Eight? (The question number is wrong and has been revised. )

4÷30%- 1/( 1+4)

=4÷ 10%

=40 people

2。 A project can be completed by one person in Team A 15 days, which is 5 days more than that of Team B. If two teams work together, can it be completed from July 26th to the end of July?

1÷ 1/ 15+ 1/( 15-5)

= 1÷ 1/6

=6 days

It will be finished by the end of the month.

3. At a party, 100 students won the lottery ticket with the label 1 to 100. According to the lottery ticket number, the moral principles for giving rewards are as follows:

(1) If the tag number is a multiple of 2, 2 notebooks will be awarded.

(2) The number of tags is a multiple of 3 to reward 3 notebooks.

The tag number is a multiple of 2 and a multiple of 3, and the prize can be collected repeatedly.

④ Other tag number rewards 1 notebook.

Q: How many notebooks should be prepared for this party?

100/2=50

100/3=33…… 1

100/6= 16……4

2×50+33×3+( 100-50-33+ 16)× 1

= 100+99+33

=232 copies