If a population of yeast cells grows from 10 to 320 in a period of five hours, what is the rate of growth?

Find the sum of the first five terms of the geometric progression if the third term is 144 and the sixth term is 456.

Obtain the differential equation of the family of circles with center on the y-axis.

For health reasons, Amir wants to drink eight glasses of water a day. He has already had six glasses. What fraction is Amir left with?

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

The number of red blood corpuscles in one cubic millimeter is about 5,000,000, and the number of white blood corpuscles in one cubic millimeter is about 8,000. What, then, is the ratio of white blood corpuscles to red blood corpuscles?

Which of the following numbers can be divided evenly by 19?

A rectangular tract of land measures 860 feet by 560 feet. Approximately how many acres is this? (one acre = 43,560 square feet)

A movie is scheduled for two hours. The theatre advertisements are 3.8 minutes long There are two previews; one is 4.6 minutes long, and the other is.2.9 minutes long. The rest of time is devoted to the feature film. How long is the feature film?

Twelve is 20% of what number?

The product of two and four more than three times a number is 20. What is the number

Find the Area of a square whose side is (2n - 3).

The position vectors of two points A and B are (2a + b) and (a - 3b) respectively. Find the position vector of a point C which divides AB externally in the ratio 1:2. Also, show that A is NIE the mid-point of the line segment CB.

Find three consecutive odd integers whose sum is 117.

Find the equation of a line with slope 3 and y-intercept - 2.

On a particular morning the temperature went up 1 ° every two hours. If the temperature was 53° at 5 A.M., at what time was it 57°?

On a particular morning the temperature went up 1 ° every two hours. If the temperature was 53° at 5 A.M., at what time was it 57°?

A weight of 49 kg falls from rest. If the air resistance is proportional to the speed and if limiting speed is 30 m/s, what is the speed at the end of 3 seconds?

The time x a student spends computer learning a software package is normally distributed with a mean of 8 hours and a standard deviation of 1.5 hours. What is the probability that the average learning time for 5 students exceeds 8.5 hours?

From past experience, it is known that 90% of one-year-old children can distinguish their mother's voice from the voice of a similar sounding female. A random sample of 25 one year-old children are given this voice recognition test. Find the probability that all 25 children recognize their mother's voice.

Three randomly chosen senior high school students was administered a drug test. Each student was evaluated a s positive to the drug test (P) or negative to the drug test (N). Assume the possible combination 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 all three students get positive results?

Find the area of the first octant part of the plane x/a + y/b + z/c = 1, where a, b and c are positive.

At the city park, 32% of the tress are oaks, if there are 400 trees in the park, how many trees are NOT oak.

It is estimated that the annual cost of driving a certain new car is given by the formula: C = 0.25 m + 1,600 where m represents the number of miles driven per year and C is the cost in dollars. Jane purchases such a car and determines between $5,350 and $5,600 for next year's driving cost. What is the corresponding range of miles that she can drive her new car.

At exactly what time after 5 O'lock wil the hour hand and the minute hand be perpendicular for the first time?

Find the equation of the line passing through the intersection of x - y = 0 and 3x - 2y = 2 cutting from the first quadrant a triangle whose area is 9

Find the area of the region enclosed by the triangle with vertices (1, 1), (3, 2) and (2, - 4).

Hotels, like airlines, often overbook, counting on the fact that some people with reservations will cancel at the last minute. A certain hotel chain finds 20% of the reservations will not be used if four reservations are made, what is the chance fewer than two will cancel?

A chord of a circle of a diameter 10 ft is decreasing in length 1 ft/min. Find the rate of change of the smaller arc subtended by the chord when the chord is 8 ft. long.

Parcel charges of a courier company are follows. P40 for the first 2 kilograms P15 for each of the succeeding kilogram weight of parcels. With these rates, what amount would be charged on a parcel weighing 30kg?

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

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?

Fred walks 0.75 miles to school; Raffy walks 1.3 miles; Fely walks 2.8 miles; and Beth walks 0.54 miles. What is the total distance the four walk to school?

Find the volume generated by revolving the area bounded by y = 12x and x = 3 about the line x= 3

Joey will be x years old y years from now. How old is she now?

A rectangle with sides parallel to the coordinate axes has one vertex at the origin, one on the positive x-axis and its fourth vertex in the first quadrant on the line with equation 2x + y = 100. What is the maximum possible area of rectangle?

Find the volume generated by revolving the area bounded by y = 12x and y = 3 about the line y = 3

Find the equation of the line passing 3 units from the origin and parallel to 3x + 4y - 10 = 0.

Patrick has a rectangular patio whose length is 5m less than the diagonal and a width that is 7m less than the diagonal. If the area of his patio is 195 m 2, what is the length of the diagonal?

Find | u x v | correct to three decimal places where | u | = 9 , | v | = 3, LO = 85 deg Select the correct answer.

If 1 is added to the difference when 10x is subtracted from -18x, the result is 57. What is the value of x?

Joseph gave ¼ of his candies to Joy and Joy gave 1/5 of what she got to Tim. If Tim received 2 candies, how many candies did Joseph have?

From past experience, it is known 90% of one year old children can distinguish their mother voice from the voice of a similar sounding female. A random sample of 20 one year old 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.

What percentage of 50 is 12?

Find all values of z for whichFind all values of z for which e^3z = 1

In the vicinity of a bonfire, the temperature T in degrees at distance of x meters from the center of the fire was given by; T= 762,500 / x^2 + 300 At what range of distances from the fires center was the temperature less than 500 deg C?

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?

If sinA = - 4/5 and sinB = 7/25, what is sin (A + B) if A is in the 3rd quadrant and B is in the 2nd quadrant.

Three randomly chosen senior high school students were 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 at least one student gets negative result?

A bag contains 3 red, 6 blue, 5 purple and 2 orange marbles. One marble is selected at random. What is the probability that the marble is blue?

z varies directly as x and inversely as y2. If x = 1 and y = 2 then z = 2. Find z when x = 3 and y = 4.

Which of these is equal to 6 (X - 3)?

After paying a commission of 7% of the sale price to his broker, Tess receives P103,000 for his car. How much was the car sold?

What is the general solution of the following differential equation, y"+ 5y'= 0.

If Rita can run around the block 5 times in 20 minutes, how many times can she run around the block for one hour?

Evaluate the double integral of ddy/x - y), with limits 2y to 3y and outer limits from O to 2.

Find the angle subtended by a line 10 yards long at a distance of 5,000 yards.

Marvin helps his teacher plan a field trip. There were 125 persons in the field trip and each school bus holds 48 persons. What is the minimum number of school buses are needed to be reserved for the trip?

Find the area of the triangle having the vertices at 4-i, 1+2i, 4-3i.

Evaluation the integral of sin^5 xdx from 0 to π/2.

In a room are N engineers and N nurses, if two engineers are replaced by nurses, 51% of the engineers and nurses are nurses. Find N.

If z = 6 e^πi/3 evalua e^iz

Eccentricity w/c is less than one.

Find the area bounded by the parabola x^2 - 2y eO and X + 2y - 8 = 0.

Find the arc length of a single hump of the cycloid given by the parametric equation: x = a(0 - sin@), y = a(1 - cos@).

For a given function, f(t) = f(- t) symmetry. What type of symmetry does f(t) have?

There is 5 seated bus. How many ways will the 5 students be seated if 2 students will always be in 1st and 2nd seat.

T h e cost p er hour of running a motor boat is proportional to the c u b e of t h e speed. At what speed will the boat run against a current of 4km/hr in order to go a given distance economically.

What is the solution of the linear differential equation, y(k + 1) = 15y(k).

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

A balloon 150m from the observer is rising vertically at constant rate. After 1 min. the angle of elevation is 280 29'. What is the angle after 3 min.

Area of hypocycloid, x = acos^3@, y = a sin^3@.

Find the length of a wire used to construct a circle and an equilateral triangle so that it can have a minimum area.

A certain man bought 400 hotdogs for picnic. He can make 8 hotdogs in a pack, how many packs did he make?

Three sides of a trapezoid are each 8 cm long. How long is the 4th side when the area of the trapezoid has the greatest value?

What is the radius of the circle defined by x^2 +y^2-4x +8y = 7

A pendulum of 8 ft long made a subtended angle of 34°. Find the height.

The maximum volume of the cylinder inscribed in the cone is % of the volume of the cone.

What is the general solution of the following differential equation, y’ + 5y = 0

The equation of a line is y= mx + b, what is m?

A number x is between -3 and 8 inclusive.

Find the length of the arc of the parabola x? = 4y from - 2 to +2.

What is the domain if f(x) = 3x, - 6 <=x<=8.

Point on the curve that starts to change concavity

Axis of hyperbola through its foci.

What conic section is having an equation x2 - 4y + 3x-8=0

Joy is 10% taller than Joseph and Joseph is 10% taller than Tom. How many percent is Joy taller than Tom?

A company hires 30 new employees today. It increases their workforce by 5%. How many workers are there now?

A bus leaves Manila at 12NN for Baguio 250 km away, traveling an average of 55 kph. At the same time, another bus leaves Baguio for Manila traveling 65 kph. At what time will they meet?

Inverse Laplace transforms of 1/(s + b)^2

Find the area bounded by the curve defined by the equation x?=8y and its latus rectum.

Solve (coscosy - cotx)dx-sinxsinydy = 0

Find the area of the triangle formed if the sides are given y the equations: 2x - 3y + 21 = 0, 3x - 2y - 6 = 0, 2x + 3y + 9 = 0

A ladder with the length of 32m with the bottom touching the floor and the top touching the surface of the wall. If the rate of bottom of the ladder is moving 2m/s towards the wall, what is the distance of the top of the ladder to the floor when the rate of top and bottom part are equal?

Find the relation of height and base radius of a right circular cylinder of minimum surface when volume is given.

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

Find the sum of all odd integers between 100 and 1000.

What is the value of x in arctan3x + arctan2x = 45.deg?