The total surface area of a regular tetrahedron is 339.482 cm2. Find the measure of the edge of this tetrahedron.
4 years 11 months ago
The sides of a triangle measure 10 cm, 14 cm, and 8 cm, respectively. What is the smallest interior angle of this triangle?
4 years 11 months ago
A certain lotto game consists of 30 different balls numbered 1 to 30. If five balls are drawn at random without replacement, how many possible winning combinations can be made?
4 years 11 months ago
A hemispherical dome is 16 meters in diameter. If the bottom 1-meter strip of the dome’s surface painted, what is the total painted area?
4 years 11 months ago
A polygon has 104 diagonals. How many sides have this polygon?
4 years 11 months ago
A circle having a radius of 18 cm is cut by a chord 5 cm from the center. What is the area of the of the smaller segment?
4 years 11 months ago
Closed right circular cylinder 2 meter in diameter and 2-meter tall is partially filled with water. When lying in a horizontal position, the depth of water is 2/3 the diameter. When the cylinder is in the vertical position, what is the depth of water?
4 years 11 months ago
If a certain soccer game ended 3:2, what is the probability that the side that lost scored first? Assume that all scoring scenarios are equiprobable.
4 years 11 months ago
The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability that exactly two will buy a pack of candy?
4 years 11 months ago
A furniture manufacturer has two machines, but only one can be used at a time.
4 years 11 months ago
At what angle do the lines $y = 2x + 2$ and $y = x - 4$ intersect?
4 years 11 months ago
If the power of an engine grows by 10% when the number of its cylinders is increased by one, which of the following is closest to the ratio of the power of a 9-cylinder engine to that of a 12-cylinder engine?
4 years 11 months ago
The box contains 10 tablets of medicine A and 15 tablets of medicine B. N tablets are taken from the box at random. What is the least possible N that ensures that at least two tablets of each kind are among the extracted?
4 years 11 months ago
9. Two cities A and B are 30 km apart. From both of these cities, simultaneously, two hikers start their journeys towards each other.
4 years 11 months ago
Pass a plane through a cube so that the section formed will be a regular hexagon. If the edge of the cube is 2 units, find the area of this section.
4 years 11 months ago
Eight books are to be arranged on a bookshelf. Three of the books are by the same author. In how many ways can the book be arranged on the bookshelf if the books by the same author are to stay together?
4 years 11 months ago
The Department of Health encourages elderly people to have a flu vaccination each year.
4 years 11 months ago
Five men and three women are arranged randomly in a row. What is the probability that there are not two women standing together anywhere in the row?
4 years 11 months ago
There are four red, three green and five blue discs in a bag. Find the probability that two discs of the same color are drawn.
4 years 11 months ago
A disease is known to affect 1 in 10,000 people. It can be fatal, but it is treatable if it is detected early.
4 years 11 months ago
Water evaporates at the rate of two liters per hour per one square meter of surface. How long will it take to evaporate 30 liters of water from a cylindrical swimming pool full of water with 6 m in diameter and 2 m depth?
4 years 11 months ago
A strip of 640 m2 is sold from a triangular field whose sides are 96 m, 72 m, and 80 m. The strip is of uniform width h and has one of its sides parallel to the longest side of the field. Find the width of the strip.
4 years 11 months ago
Stations A and B are placed 1000 m apart on a straight road running East and West. From A, the bearing of the tower C is 32° West of North and from B the bearing of C is 26° North of East. Find the shortest distance of the tower from the road.
4 years 11 months ago
A man drives from station A to station B 60 km away at an average speed of 30 kph and return to A at an average speed of 20 kph. What was the average speed of the man in the whole journey?
4 years 11 months ago
At what time between 7 and 8 o’clock will the hands of the clock be directly opposite each other?
4 years 11 months ago
Mary was 4 times as old as Ann 4 years ago and if Mary will be twice as old as Ann 4 years hence, how old is Ann?
4 years 11 months ago
A circle of radius 1 unit is shown. AD is the diameter of the circle and O is the center. Find the length of arc BC.  
4 years 11 months ago
In how many ways can 4 couples be seated at a round table with the men and women alternating?
4 years 11 months ago
In the figure, $AB = BC$. The value of $\theta$ is:
4 years 11 months ago
A sector of a circle with radius 10 cm has a central angle of 120°. Find the arc length of the sector.
4 years 11 months ago
Convert $5\pi / 6$ into degree measure.
4 years 11 months ago
Find the area of a sector of a circle of radius 6 cm and a central angle of 60°.
4 years 11 months ago
When the population growth of a certain city was first studied, the population was 22,000.
4 years 11 months ago
If an arc length is 12 m subtends a central angle $\phi$ in a circle of radius 3, find the measure of $\phi$ in terms of radians.
4 years 11 months ago
A and B can finish the job in 8 days and the working speed of A is twice that of B. How many days would it take A to finish the job alone?
4 years 11 months ago
A group of dancers consists of x boys and x girls. If two of the boys are replaced by two girls, then 48% of the group members will be boys. Find the original value of the boys.
4 years 11 months ago
Find $y'$ if $x = 2 \arccos (2t)$ and $y = 4 \arcsin (2t).
4 years 11 months ago
A contractor bought a concrete mixer at P120,000.00 if paid in cash.
4 years 11 months ago
There are five harmonic means between 4/3 and 4/11. What is the fourth term?
4 years 11 months ago
How far apart are the foci of the curve $9x^2 + 25y^2 - 18x + 100y - 116 = 0$.
4 years 11 months ago
The map shows 5 cm representing 450 km. What actual distance is represented by a map distance of 2.8 cm?
4 years 11 months ago
A company invests P10,000 today to be repaid in five years in one lump sum at 12% compounded annually. If the rate of inflation is 3% compounded annually, how much profit in present day pesos is realized over five years?
4 years 11 months ago
A dog is tied with a chord 3 m long to the edge of a circular tank 8 m in diameter. The point where the cord is attached to the tank is at the same elevation as the dog’s collar. Determine the total area about which the dog can move, in square meter...
4 years 11 months ago
Line AB has point A(4, 5) and point B(-3, -2). Find point C along line AB if distance BC is three times the distance AC.
4 years 11 months ago
At 6:00 A.M., a fighter plane took off at 410 kph from an aircraft carrier, maintaining the direction of N 50° E.
4 years 11 months ago
Find the volume of the tetrahedron bounded by the coordinate planes and the plane $8x + 12y + 4z - 48 = 0$.
4 years 11 months ago
To determine the area of a triangular lot ABC, a surveyor set-up a transit at point P inside the lot and recorded the following bearing and distances of each corners of the lot from P.
4 years 11 months ago
In how many days will the original gang of pipe layers, under the supervision of foreman B, finish the original pipe-laying job?
4 years 11 months ago
Find the radius of curvature of the curve $y = x^3 - 2x^2 + 5x - 3$ at $x = 5$.
4 years 11 months ago
A 3-degree simple curve has an external distance of 23 m. What is the length of the long chord?
4 years 11 months ago