A farmer stocked a newly dug pond with 1000 fish fingerlings. It is known that each year, the number of fish in the pond increases by $x$ times the initial number, and x is constant. By changing the farming techniques and fish feed, after two years, the number of fish in the pond is 36000. What is the annual growth rate of the fish population in the pond? Assume the growth rate each year is constant.
The supplied key prints correct-answer weights of 4 and 6 points. Wrong-answer and blank-answer scoring are not stated; no penalties or blank credit are inferred.
An wants to buy some notebooks and pens to prepare for the new school year. The price of 1 notebook is 5,000 VND, and the price of 1 pen is 3,000 VND. An has a total of 76,000 VND. An wants to buy a total of 18 items (including both notebooks and pens). How many notebooks and how many pens did An buy?
A publishing house needs to print at most 500 books with two printing options: • Printer A: Fixed cost is 2,000,000 VND, and each book costs an additional 10,000 VND. • Printer B: Fixed cost is 4,000,000 VND, and each book costs an additional 8,000 VND. How many books should the publishing house print to minimize the total cost, and what is that optimal cost?
A rectangular football field has an area of 600 m\$^2\$. It is known that if the length is decreased by 5 m and the width is increased by 5 m, the field becomes a square. What was the original length of the football field (round the result to the first decimal place)?
In an archaeological excavation of an ancient tomb, archaeologists found a broken ancient circular disk. The archaeologists want to restore the shape of this disk. To determine the radius of the disk, the archaeologists took 3 points on the disk and measured them, obtaining the results as shown in the figure (AB=4.3 cm, BC=3.7 cm, CA=7.5 cm). What is the radius of this disk?
Nam has the following schedule: • Motorbike maintenance is done once every 15 days, with the first maintenance on January 5, 2025 (Sunday). • Health check-ups are done once every 20 days, with the first check-up on January 10, 2025 (Friday). Today is December 25, 2025 (Thursday). What is the next closest day after today when An has both the maintenance and the health check-up on the same day? What day of the week is that?
Below is a chart of the exploitation and cultivation output of our country from 2000 to 2016. From what year did the cultivation output exceed the exploitation output?
Below is a chart of the structure of planted areas for different crop groups in our country in 1990 and 2002. From 1990 to 2002, which of the following statements is true?
Food crops increased; industrial crops increased
Food, fruit and other trees increased; food crops decreased
Industrial crops increased; food crops increased
Food crops decreased; food, fruit and other trees decreased
In a meeting room, there are 6 chairs arranged in a row. There are 4 people (A, B, C, D) and 2 empty chairs. How many ways are there to arrange the seating such that all of the following conditions are satisfied: A and B must not sit next to each other. C and D must sit next to each other. No two empty chairs are next to each other.
Nam rolls a fair 6-sided die (with numbers from 1 to 6) and flips a fair coin. Calculate the probability that: “The number rolled on the die is a prime number and the coin lands on heads (H), OR the number rolled on the die is a multiple of 3 and the coin lands on tails (T).”
You need to open a 3-digit lock (from 000 to 999). The code contains no digit 0. Exactly 1 digit is in the correct position compared to the real code. Exactly 1 digit is correct but in the wrong position compared to the real code. You tried the three codes and received the feedback in the table. What is the exact code?
There are 45 students who took a test. No one scored below 2, and only 4 students scored 10. What is the minimum number of students who could have the same test score (test scores are integers from 1 to 10)?
In an exam, each correct answer earns 4 points, each incorrect answer deducts 2 points, and not answering deducts 1 point. Minh took the exam consisting of 30 questions and scored 88 points. It is known that the number of questions Minh answered incorrectly is half the number of questions not answered. How many questions did Minh answer correctly?
Mr. Nam has two options for borrowing 100 million VND from a bank for 12 months: • Option 1: Pay interest monthly on the original principal with an interest rate of 0.8%/month. • Option 2: Loan with decreasing principal balance and an interest rate of 1%/month (both principal and interest paid monthly). After 12 months, which payment method is cheaper?
A production facility can produce two types of goods, I and II, from raw materials A and B. The daily supply of raw materials A and B is at most 12 and 18 units, respectively. To produce one unit of good I, 2 units of raw material A and 3 units of raw material B are required. To produce one unit of good II, 3 units of raw material A and 4 units of raw material B are required. The selling prices of goods I and II are 7 and 5 million VND, respectively. Furthermore, it is known that the daily consumption of good I does not exceed 3 units; the consumption of good II does not exceed 1 unit. The problem is to determine how many units of each good should be produced daily to maximize total revenue.
Consider a cross $Aa\times aa$ resulting in $F_1$. From $F_1$, 3 individuals are randomly selected. What is the probability that all 3 individuals are genetically different?
The following chemical equation is not balanced: $a\mathrm{CuO}+b\mathrm{NH}_3\to c\mathrm{Cu}+d\mathrm{N}_2+e\mathrm{H}_2\mathrm O$. Use a system of linear equations to determine the smallest positive integer coefficients $a,b,c,d,e$ that balance it. Calculate $P=a+b+c+d+e$.
A car intends to travel a certain distance at an initial speed of v (km/h). If the car increases its speed by 10 km/h, it will arrive 3 hours earlier. If the car decreases its speed by 10 km/h, it will arrive 5 hours later. Calculate the original speed v (km/h) of the car.
