Find the minimum distance from the point (4,2) to the parabola y² = 8x.

From past experience, it is known 90% of one-year-old children can distinguish their mother’s voice from the voice of a similar sounding female. A random sample of 20 one-year-olds is given this voice recognition test. Let the random variable X denote the number of children who do not recognize their mother’s voice. Find the variance of X.

A group consists of n engineers and nurses. If two of the engineers are replaced by two other nurses, then 51% of the group members will be nurses. Find the value of n.

Sand is being poured into a conical pile in such a way that the height is always 1/3 of the radius. At what rate is sand being added to the pile when it is 4 ft high if the height is increasing at 2 in/min.

An unlimited number of squares are inscribed one within another by joining the midpoints of the sides of each preceding square. If the initial square is 8 cm on a side, find the sum of the perimeters of these squares.

The area enclosed by the ellipse 4x² + 9y² = 36 is revolved about the line x = 3, what is the volume generated?

Solve (x+y)dx =(x-y)dx?

If in the Fourier series of a periodic function, the coefficient a₀ = 10, then it must be having ___ symmetry.

A ball rebounds 2/3 of the altitude from which it falls. Suppose the ball is dropped from a height of 18 ft. How far will it travel at the instant it strikes the ground for the 5th time?

Find k so that a = 3i - 2j and b = i + kj are perpendicular.

A shopkeeper offers a 25 percent discount on the marked price on an item. In order to cost $48, what should the marked price be?

When two lines are perpendicular, the slope of one is:

A survey was conducted in a certain barangay in Metro Manila to find out which of the three political parties they like best. The results indicated that 350 liked PPC, 320 liked PMP and 160 liked INDEPENDENTS. But of these, 80 liked both PPC and PMP, 80 liked both PPC and INDEPENDENTS, and 120 liked both PMP and INDEPENDENTS. Only 50 said they liked all three parties and none admitted that they did not like any party. How many voters are there in the barangay?

What is the smallest angle of the triangle whose sides are 26 cm, 18 cm, and 24 cm long?

Baby’s age is three times Maria’s. If 20 is added to Maria’s age and 20 is subtracted from Baby’s, their ages will be equal. How old is Baby now?

A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there is 50 milligrams of the material present and after two hours it is observed that the material has lost 10 percent of its original mass, find the mass of the material after four hours.

The sum of the first 7 terms of an A.P. is 98 and the sum of the first 12 terms is 288. Find the sum of the first 20 terms.

Find the area inside r = cos² (θ/2).

A circular plate expands under the influence of heat so that its radius increases from 5 in to 5.06 in. Find the approximate increase in area.

Let (-4, -2) be a point on the graph y = f(x). Under the transformation y = 3f(x) + 2, the point (-4, -2) will be translated to what point?

Find the force on one face of a right triangle of sides 4 m and altitude of 3 m. The altitude is submerged horizontally with the 4 m side in the surface.

For any set of grouped or ungrouped data, which measures of central location always have only one value?

For ungrouped data, which measures of central location always have only one value?

The arch of an underpass is a semi-ellipse 60 ft wide and 20 ft high. Find the clearance at the edge of a lane if the edge is 20 ft from the middle.

The coefficient of (x - 1)⁵ in the Taylor series for xln x about x = 1 is

Simplify (1 + tan x) / (1 - tan x).

Find the area of the region between the curves y = sqrt x, y = 1, and x = 4.

The probability that A can solve a given problem is 4/5, that B can solve it is 2/3, and that C can solve it is 3/7. If all three try, compute the probability that the problem will be solved.

A hot air balloon is hovering over Valley Forge. Person A views the balloon at an angle of elevation of 25° while person B views the balloon at an angle of elevation of 40°. If A and B are 4000 feet apart, find the height of the balloon.

The sum of the interior angles of a polygon is 1080°. Find the number of sides.

Evaluate L [t sin kt].

In two intersecting lines, the angles opposite to each other are termed as:

What is the limit of [3(x cubed) - 2x + 4] / [2 - 3(x squared) - 2(x cubed)] as x approaches +infinity?

A student’s marks in five tests are 36%, 78%, 67%, 88%, and 98%. The weights for the five tests are 1, 2, 2, 3, 3, respectively. Find the weighted mean μ of the five tests.

The minute hand of a wall clock is 8 cm long. Approximate the distance (in cm) traveled by the tip of the minute hand in 10 minutes.

A hemispherical tank of radius 3 ft is full of water. Find the work done in emptying the tank through an outlet pipe 2 ft above the top of the tank.

If z₁ = i - 1 and z₂ = -2 + 4i evaluate z₁² + 2z₁ - 3.

If 8 men take 12 days to assemble 16 machines, how many days will it take 15 men to assemble 50 machines.

If the line 3x - ky - 8 = 0 passes through the point (-2, 4), then k is equal to

Solve y''' - 6y'' + 11y' - 6y = 0.

Describe the locus represented by |z - i| = 2.

A transmitter with a height of 15 m is located on top of a mountain, which is 3.0 km high. What is the furthest distance on the surface of the earth that can be seen from the top of the mountain? Take the radius of the earth to be 6400 km.

Which of the following is an exact DE?

Five cards are drawn from a pack of 52 well-shuffled cards. Find the probability that 3 are 10's and 2 are queens.

Solve for C of a triangle ABC if b = 25, c = 30, and B = 227.7 degrees.

Find the area of a quadrilateral having vertices at (2, -1), (4, 3), (-1, 2), and (-3, -2).

From a point on a level ground, the angles of elevation of the top and bottom of the tower situated on the top of the mountain are measured as 45 deg and 35 deg respectively. Find the height of the tower if the distance directly from the said point on the ground to the top of the mountain is 100 ft.

If a person is dealt 13 cards from an ordinary deck of 52 playing cards several times, how many hearts per hand can he expect?

A parabolic arch 18 m high has a horizontal beam 64 m long placed across the arch 8 m from the top. Find the width at the bottom.