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 are given this voice recognition test. Find the probability that all 20 children recognize their mother’s voice.

Determine the differential equation of the family of lines passing through (h, k).

A Statistics Department is contacting alumni by telephone asking for donations to help fund a new computer laboratory. Past history shows that of the alumni contacted in this manner will make a contribution of at least P50. A random sample of 20 alumni is selected. What is the probability that less than 17 alumni will make a contribution of at least P50?

Find the value of sin (arc cos 15/17).

Find two numbers whose sum is 50 and with largest possible product.

The curve which has an eccentricity equals to zero

A line segment is a side of a square and also the hypotenuse of an isosceles right triangle. What is the ratio of the area of the square to the area of the triangle?

Describe the locus represented by |z + 2i| + |z – 2i| = 6.

From past experience it is known 90 percent of one year old children can distinguish their mother’s voice of a similar sounding female. A random sample of one year’s old are given this voice recognize test. Find the probability that at least 3 children did not recognize their mother’s voice.

A line that is perpendicular to the y-axis has a slope equal to .

During his major league career, Hank Aaron hit 38 more home runs than Babe Ruth hit during his career. Together they hit 1,524 home runs. How many home runs did Babe Ruth hit?

Find the length of arc of the parabola x^2 = 4y from x = −2 to x = 2.

What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis?

A man is driving a car at the rate of 30 km/hour towards the foot of monument 6 m high. At what rate is he approaching the top when he is 36 m from the foot of the monument?

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

Oscar sold 2 glasses of milk for every 5 sodas he sold. If he sold 10 glasses of milk, how many sodas did he sell?

A point is chosen at random inside a circle having a diameter of 8 inches. What is the probability that the point is at least 1.5 in away from the center of the circle?

The equation of a limacon is

Each of the question on a quiz is a five-part multiple choice question with exactly one correct answer. A student, totally unprepared for the quiz, guesses on each of 15 questions. If at least 11 questions must be answered correctly to pass the quiz, what is the chance the student passes?

What conic section is described by the equation 4x2 – y2 + 8x + 4y = 15?

A fencing is limited to 20 ft. length. What is the maximum rectangular area that can be fenced in using two perpendicular corner sides of an existing wall?

42% of 997 =

Find the value of x for which f(x) = x^2 + 5x + 2 is maximum.

Water is running out of a conical funnel at a rate of 1 cu. in / sec. If the radius of the base of the funnel is 4 in and the altitude is 8 in, find the rate at which the water level is dropping when it is 2 in from the top.

A laboratory keeps two acid solutions on hand. One is 20% acid and the other is 35% acid. How many liters of distilled water should be added to a liter of 35% acid solution in order to dilute it to a 20% acid solution?

A car consumes 16 gallons of gasoline to travel 448 miles. How many miles/gallon is the car’s consumption?

Find the radius of curvature of the curve y^2 = 4x at P(4, 4).*

A normal to a given plane is

Find ∫ (3x – 4)^3 dx.

Find the area of the polygon with vertices at: 2 + 3i, 3 + i, -2 - 4i, -4 -i, -1+ 2i.

B^2 - 4AC < 0 describes a/an

Find the point on the line 3x + y + 4 = 0 that is equidistant from the points (-5, 6) and (3, 2).

In an arithmetic series, the terms of the series are equally spread out. For example, in 1 + 5 + 9 + 13 + 17, consecutive terms are 4 apart. If the first term in an arithmetic series is 3, the last term is 136, and the sum is 1,390, what are the first 3 terms?

Evaluate lim ( 1 + 2x )^( 1 + 2x ) / x

x --> 0

When a metallic ball bearing is placed inside a cylindrical container of radius 2 cm, the height of the water inside the container increases by 0.6 cm. What is the radius of the ball bearing?

What is the area bounded by the curve y = 0, y = 3x^2, x = 0, and x = 2?

Find the domain of the following function: f(x) = 3x, −6 ≤ x ≤ 8.

A container is in the form of a right circular cylinder with an altitude of 6 in and a radius of 2 in. If an asbestos of 1 in thick is inserted inside the container along its lateral surface, find the volume capacity of the container.

Find the equation of the circle tangent to 4x – 3y + 12 = 0 at (−3, 0) and tangent also to 3x + 4y – 16 = 0 at (4, 1).

Matthew had 200 baseball cards. He sold 5% of the cards on Saturday and 10% of the remaining cards on Sunday. How many cards are left?

Liza thought she had the exact money to buy 10 chocolate bars. However the price per bar had increased by 50 centavos. Consequently, she was able to buy only 8 bars and had P2 left. How much money did Liza have?

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.

If the average value of a periodic function over one period is zero, and it consists of only odd harmonics, then it must be possessing ____ symmetry.

Approximately how many liters of water will a 10-gallon container hold?

A steel girder 8 m long is moved on rollers along a walkway 4 m wide and into a corridor perpendicular to the walkway. How wide must the corridor be to successfully move the girder?

Solve for z: 5z^2 + 2z + 10 = 0

Find the area bounded by the parabolas x2 – 2x + 2y + 5 = 0 and x2 – 2x + y + 1 = 0.

A transmitter with a height of 15 m is located on top of a mountain, which is 3.0 km high. What is the farthest 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.

The axis of the hyperbola through its foci is known as:

Larry finds the angle of elevation of the top of a tower to be 30 degrees. He walks 85 m nearer the tower and finds its angle of elevation to be 60 degrees. What is the height of the tower?

Three randomly chosen senior high school students was administered a drug test. Each student was evaluated as positive to the drug test (P) or negative to the drug test (N). Assume the possible combinations of the three students’ drug test evaluation as PPP, PPN, PNP, NPP, PNN, NPN, NNP, NNN. Assuming each possible combination is equally likely, what is the probability that at least one student gets a negative result?

Radium decomposes at a rate proportional to the amount at any instant. In 100 years, 100 mg of radium decomposes to 96 mg. How many mg will be left after 100 years?

Which ratio best express the following: five hours is what percent of a day?

In a pile of logs, each layer contains one more log than the layer above and the top contains just one log if there are 105 logs in the pile, how many layers are there?

Evaluate cos(arc sin 2/3 – arc sin (−1/3)).

A square has a side 5 cm shorter than the side of a second square. The area of the larger square is four times the area of the smaller square. Find the side of each square.

Find the sum of a geometric progression if there are 4 geometric means between 3 and 729.

Find the radius of curvature at any point in the curve y + ln cos x = 0.

The area in the second quadrant of the circle x2 + y2 = 36 is revolved about the line y + 10 = 0. What is the volume generated?

Which of the following is a disadvantage of using the sample range to measures of spread or dispersion?

A group consists of n engineers and n 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.

Find the equation of the normal line to x2 + y2 at the point (2, 1).

A statue 3 m high is standing on a base of 4 m high. If an observer’s eye is 1.5 m above the ground, how far should he stand from the base in order that the angle subtended by the statue is a maximum?

If a rock is dropped, its distance below the starting point at the end of t sec is given by s = 16 t square, where s is in ft. Find the rate of change of distance after 1.5 minutes.

A pebble dropped into a lake creates an expanding circular ripple. If the radius of the ripple is increasing at the rate of 2 in/sec, at what rate is its area increasing  when its radius is 10 in.?

Find the maximum area of a rectangle which can be inscribed in an ellipse having the equation x^2 + 4y^2 = 4.

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 are 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 mean of x.

Find the volume generated when the area bounded by the curve y = cosh x and the x-axis from x  = 0 to x = 1 is revolved about the x-axis.

What is the graph of the curve whose equation is 5x2 + 5y2 – 5x – 10y – 33 = 0.

If 10^x = 4, find the value of 10^2x + 1.

Solve the differential equation 7yy’ = 5x.

Find the sum of the first five terms of the geometric progression if the third term is 144 and the sixth term is 486. 

A cone shaped icicle is dripping from the roof. The radius of the icicle is decreasing at a rate of 0.2 cm/hr, while the length is increasing at a rate of 0.8cm/hr. If the icicle is currently 4 cm in radius and 20 cm long, is the volume of the icicle increasing or decreasing, and at what rate?

In an ellipse a chord which contains a focus and is in a line perpendicular to the major axis is a: