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 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 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 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 ago
The Department of Health encourages elderly people to have a flu vaccination each year.
4 years 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 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 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 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 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 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 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 ago
At what time between 7 and 8 o’clock will the hands of the clock be directly opposite each other?
4 years 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 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 ago
In how many ways can 4 couples be seated at a round table with the men and women alternating?
4 years ago
In the figure, $AB = BC$. The value of $\theta$ is:
4 years 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 ago
Convert $5\pi / 6$ into degree measure.
4 years ago
Find the area of a sector of a circle of radius 6 cm and a central angle of 60°.
4 years ago
When the population growth of a certain city was first studied, the population was 22,000.
4 years 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 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 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 ago
Find $y'$ if $x = 2 \arccos (2t)$ and $y = 4 \arcsin (2t).
4 years ago
A contractor bought a concrete mixer at P120,000.00 if paid in cash.
4 years ago
There are five harmonic means between 4/3 and 4/11. What is the fourth term?
4 years ago
How far apart are the foci of the curve $9x^2 + 25y^2 - 18x + 100y - 116 = 0$.
4 years ago
The map shows 5 cm representing 450 km. What actual distance is represented by a map distance of 2.8 cm?
4 years 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 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 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 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 ago
Find the volume of the tetrahedron bounded by the coordinate planes and the plane $8x + 12y + 4z - 48 = 0$.
4 years 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 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 ago
Find the radius of curvature of the curve $y = x^3 - 2x^2 + 5x - 3$ at $x = 5$.
4 years ago
A 3-degree simple curve has an external distance of 23 m. What is the length of the long chord?
4 years ago
The area under the curve $y = x^2 between the values $x = 1$ and $x = 7$ is closest to:
4 years ago
Company A has a fixed expense of P1.5M monthly and each unit is produced at P20.
4 years ago
A vertical summit curve has tangent grades of +2.6% and -1.5%. Using h1 = 1.37 m and h2 = 0.1 m, calculate the minimum length of curve if the required sight distance is 140 m.
4 years ago
A circle of radius 15 cm is revolved about a line tangent to it. What is the surface area of the resulting by the solid?
4 years ago
A car travels with an initial velocity of 10 m/s or 36 km/hr. If it is decelerating at a rate of 3 m/sec-sec, how far, in meters, does it travel before stopping?
4 years ago
Find the area enclosed by the curve $r^2 = 64 \cos 2\theta$.
4 years ago
MSTE-00 Welcome Message and General Instructions
4 years ago
I need guidance in designing a beam supporting specified ultimate moment of 1100 kN.m (doubly reinforced beam)
4 years ago
One number is 25 greater than a second number. If the lesser number is subtracted from 3 times the greater number, the difference is 195. Find the product of two numbers.
4 years ago
Find two consecutive positive even integers such that the square of the second, decreased by twice the first is 124. Find the smaller number.
4 years ago
The sum of the digits of a two-digit number is 11. When the digits are reversed, the new number exceeds the original number by 9. From the original number, calculate the product of tens digit to the square of the units digit.
4 years ago
Three times Dick's age plus Tom's age equals twice Harry's age. Double the cube of Harry's age is equal to three times the cube of Dick's age added to the cube of Tom's age. Their respective ages are relatively prime to each other. How old is Harry?
4 years ago