Basic operations and concepts - math word problems - page 318 of 332
Number of problems found: 6633
- Triangle Geometry Proof
On side AB of triangle ABC, points D and E are given such that |AD| = |DE| = |EB|. Points A and B are the midpoints of segments CF and CG. Line CD intersects line FB at point I, and line CE intersects line AG at point J. Prove that the intersection of lin - Square ABCD
Construct a square ABCD with center S [3,2] and the side a = 4 cm. Point A lies on the x-axis. Construct a square image in the displacement given by oriented segment SS'; S` [-1 - 4]. - Probability
A restaurant always counts the cash register at the end of the day so that the employees can divide their tips. It has been found that the daily tips follow a normal distribution with a mean of €130 and a standard deviation of €60. What is the probability - Water current
John is swimming upstream. After a while, he passes a floating bottle. From that moment, he continues swimming upstream for 20 minutes. He then turns around and swims downstream. From the point where he first passed the bottle, he swims 2 km before meetin - Vectors 5
The position vector of a material point moving in a plane can be expressed in the introduced reference frame by the relation: r(t) = (2t + 3t²; 6t + 3), where t is time in seconds and the coordinates of the vector are in metres. Calculate: a) what is the - Hexagon = 8 parts
Divide the regular hexagon into eight equal parts. - Construction
Construct the triangle ABC if you know: the size of the side AC is 6 cm, the size of the angle ACB is 60°, and the distance of the center of gravity T from the vertex A is 4 cm. (Sketch, analysis, notation of construction, construction) - Lines
How many points will intersect 27 different lines where no two are parallel? - Wimbledon finals
Serena Williams made a successful first serve 67% of the time in a Wimbledon finals match against her sister Venus. If she continues to serve at the same rate the next time they play and serves six times in the first game, determine the probability that: - Position vector The position vector of a point mass moving in a plane can be expressed in the established reference frame by the relation: r(t) = (1 + 5t + 2t² ; 3t + 1), where t is time in seconds and the vector coordinates are in meters. Calculate: a) What is the posit
- Safe key locks
We have to distribute the keys to the safe among four people so that no two of them can open the safe but in such a way that any three can open the safe. How many minimum keys do we need? How to divide them? How many minimum locks must be on the safe? All - Probability
A man had 4 coins, some worth $2 and some worth $1. Each coin had a number on one side and a picture on the other. The man flipped them, and the sum of the numbers showing on top was 1. The probability of this happening was 1/8. What was the probability t - Parallelogram diagonal construction
Construct a parallelogram ABCD if a=5 cm, height to side a is 5 cm, and angle ASB = 120 degrees. S is the intersection of the diagonals. - Uphill and downhill
The cyclist moves uphill at a constant speed of v1 = 10 km/h. When he reaches the top of the hill, he turns and passes the same track downhill at a speed of v2 = 40 km/h. What is the average speed of a cyclist? - Three-day trip
George went on a moped for a three-day trip. He drove 90 km on the first day, 30 km on the second day, and 60 km on the third day. He always drove at the same average speed and always the whole number of hours. Calculate the average speed if George drove - Four pavers
Four pavers would pave the square in 18 days. How many pavers do you need to add to the done work in 12 days? - Graphic solution
Solve the system by the graphical method: x + y = 8 2x-y = 1 - Line point division
Draw a point x on the line, which divides it in the given ratio: a) 2:3 b) 1:5 c) 6:2 - Triangle circle proof
Given is an acute-angled triangle ABC. On the half lines opposite to BA and CA lie successively the points D and E such that |BD| = |AC| and |CE| = |AB|. Prove that the center of the circle circumscribing triangle ADE lies on the circle circumscribing tri - Two cities
The car goes from city A to city B at an average speed of 70 km/h and back at an average speed of 50 km/h. If it goes to B and back at an average speed of 60 km/h, the whole ride will take 8 minutes less. What is the distance between cities A and B?
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