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

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?

A group of five friends went out to lunch. The total bill for the lunch was $53.75. Their meals all cost about the same, so they wanted to split the bill evenly. Without considering tip, how much should each friend pay?

A tangent to a conic is a line which

How many ancestors does a set of triplets have in the eleven generations before them? Assume there are no duplicates.

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

Chona, a Golden Retriever, gained 5.1 pounds this month. If Chona now weighs 65.1 pounds, what is the percent increase in Chona's weight?

Melissa is four times as old as Jim. Pat is 5 years older than Melissa. If Jim is y years old, how old is Pat?

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.

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

The centroid of the area bounded by the parabola y² = 4ax and the line x = p coincides with the focus of the parabola. Find the value of p.

In polar coordinate system, the polar angle is positive when:

When the energy/hour required in driving a boat varies as the cube of the velocity, find the most economical rate/hour when going against a current of 4 kph.

Evaluate the double integral ∫∫ 1/(x - y) dx dy, with interior limits 2y to 3y and outer limits from 0 to 2.

Find lim x→-2 |x + 2|.

Judy's English quiz scores are 56, 93, 72, 89 and 87. What is the median of her scores?

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.?

A federal agency is trying to decide which of two waste management projects to investigate as the source of air pollution. In the past, projects of the first type were in violation of air quality standards with probability 0.3 on any given day, while projects of the second type were in violation of air quality standards with probability 0.25 on any given day. It is not possible for both projects to pollute the air in one day. If the first project is violating air quality standards, what is the probability the second project is also violating federal air quality standards?

Solve the differential equation y' = y/2x.

A 6-foot pine tree is planted 15 feet from a lighted streetlight whose lamp is 8 feet above the ground. How many feet long is the shadow of that tree?

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.

In the curve y = 2x³ + 3x² - 12x + 12, find the critical points.

Mrs. Farrell's class has 26 students. Only 21 were present on Monday. How many were absent?

A ball bounces 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?

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

If the slant height if a right circular cone is 13 and the total area is 90 pi, find the base radius.

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.

Find the vector perpendicular to the vector (2, 5).

If cos A = 4/5 and A is not in Quadrant I, what is the value of sin A?

Susan's age in 20 years will be the same as Thelma's age now. Ten years from now, Thelma's age will be twice Susan's. What is the present age of Susan?

A developer of a new subdivision offers a prospective home buyer a choice of 4 designs, 3 different heating systems, a garage or carport, and a patio or screened porch. How many different plans are available to this buyer?

Find the area enclosed by the curve r = 8 sin²(θ/2)

Find approximately the difference between the areas of two spheres whose radii are 4 feet and 4.05 feet.

With a throw of 3 dice, what is the probability of getting a 9 or an 11?

The growth rate of bacteria culture is proportional to the number of bacteria present. If a population whose size is initially 100 bacteria doubles every 2 hours, how long will it take for the culture to grow to a size of 5000 bacteria?

size is initially 100 bacteria doubles every 2 hours, how long will it take for the culture to grow to a size of 5000 bacteria?

If tan A = √3 and A is in quadrant III, evaluate (1 + cos A) / (1 - cos A).

The sides of the triangle are 17, 21, and 28 m respectively. Determine the length of the line bisecting the greatest side and drawn from the opposite angle.

Find the area bounded by the curve y = x² + 2 and lines x = 0, y = 0, and x = 4.

An iron ball heated to 90 deg C is dropped into a pail of water at 25 deg C. After 15 minutes, the ball reaches a temperature of 65 deg C. Determine the temperature of the ball at the end of another 15 minutes.

A ship is sailing due east when a light is observed bearing N 62 deg 10 min E. After the ship has traveled 2250 m, the light bears N 48 deg 25 min E. If the course is continued, how close will the ship approach the light?

In general solution of a conic section whose axis are parallel to x or y, if either x squared or y squared term is missing, the graph is

Evaluate i raised to 96.

We can use SOH-CAH-TOA for

The distance between points A(2, 10, 4) and B(8, 3, z) is 9.434. What is the value of z?

In an arithmetic progression whose first term is 5, the sum of 8 terms is 208, Find the common difference.

Ship A is 70 km west of ship B and is sailing south at the rate of 25 kph. Ship B is sailing north at the rate of 45 kph. How fast is the distance between the two ships changing 2 hours later?

How many four-digit numbers can be formed with the 10 digits 0, 1, 2, 3, ..., 9 if repetitions are allowed?

If the orbit of a satellite has the polar equation r(2 + cos θ) = 4, then the path of the orbit is

A force of 500 lb is required to compress a spring whose natural length is 10 in to a length of 9 in. Find the work done to compress the spring to a length of 8 in.

A mailbox opening is 4. 5 inches high and 5 inches wide. What is the widest piece of mail able to fit in the mailbox without bending? Round answer to the nearest tenth.

A vector field which has a vanishing divergence is called as

If i = √-1, what is the value of i^i?

What is the value of each interior angle of a regular pentagon?

If you are interested in comparing variation in sales for small and large stores selling similar goods, which of the following is the most appropriate measure of dispersion?

What is the determinant of the following 2x2 matrix? [ 5 & 9 \ 7 & 6 ]

If sin α = x, what is sec α?

Edward purchased a house for $70,000. Five years later, he sold it for an 18% profit. What was his selling price?

At approximately what time between the hours of 12:00 noon and 1:00 p. m. would the angle between the hour hand and the minute hand of a continuously driven clock be exactly 180°?

A recent survey asked respondents about their monthly purchases of raffle tickets. The monthly expenditures, in dollars, of ten people who play the raffle are 23, 15, 11, 20, 28, 35, 13, 10, 20, and 24. Which of the following statements is NOT true?

The kitchen in Dexter's old house contains a circular stone inset with a radius of 3 feet in the middle of the floor. The room is square; each wall is 11. 5 feet long. Dexter wants to retile the kitchen, all except for the stone inset. What is the approximate square footage of the area Dexter needs to buy tiles for?

Which of the following statement is TRUE?

Find the equation of the line that passes through the points (0, 0) and (2, -2).

If a school buys three computers at a, b, and c dollars each, and the school gets a discount of 90%, which expression would determine the average price paid by the school?

x² - 6x + 8 > 0 is true for all values of x where

Thirty percent of all households have a DVD player. Suppose you select 20 houses at random. On average, how many houses of the twenty would you expect to have a DVD?

The low temperature in Anchorage, Alaska today was -4°F. The low temperature in Los Angeles, California was 63°F. What is the difference in the two low temperatures?

The graph of |x| + |y| = 8 consists of

What is the probability a randomly selected consumer had either seen an advertisement or tried the new soap?

How many even numbers greater than 40,000 may be formed using the digits 3, 4, 5, 6, and 9, if each digit must be used exactly once in each number?

Suppose you know that the number of complaints coming into a phone center averages 3 every ten minutes. Assume that the number of calls follows the Poisson distribution. What is the probability that there are exactly three calls during the next ten minutes?

If log₄ y = 3, then y is equal to

It is known that 70% of the customers in a sporting goods store purchase a pair of running shoes. A random sample of 25 customers is selected. Assume that customers' purchases are made independently, and let X represent the number of customers who purchase running shoes. What is the probability that between 17 and 21 customers, inclusively, purchase running shoes?

A pipe has a diameter of 2.5 inches. Insulation that is 0.5 inches thick is placed around the pipe. What is the diameter of the pipe with the insulation around it?

The intensity of illumination, I, on the page of a book varies inversely as the square of the distance, d, between the book and the source of light. If I = 6 when d = 4, then the value of I when d = 8 is

A university in Alabama has 1000 employees. Four hundred of the employees have at least 20 years of experience, 100 are African American, and 300 with a background in Microsoft Office 2003. Assume events A, B, and C are independent. What is the probability of finding an employee who meets all three of these criteria?

The product of (a + bi)(2a - 3bi) equals

Which of the following is equivalent to tan(θ/2) + cot(θ/2)?

Michael scored 260 points during his junior year on the school basketball team. He scored 20% more points during his senior year. How many points did he score during his senior year?

Carla can plant a garden in 3 hours and Charles can plant the same garden in 4.5 hours. If they work together, how many hours will it take them to plant the garden?

Find the power series of tan⁻¹(t²).

What is the value of x in Arctan 2x + Arctan x = π/4?

Evaluate the lim (n→∞) |(n² + 3i)(n - 1) / (in³ - 3n + 4 - i)|.

A sinking ship makes a distance signal seen by three observers all 20 m inland from the shore. The first observer is perpendicular to the ship, the second observer 100 m to the right of the first observer and the third observer is 125 m to the right of the first observer. How far is the ship from the shore?

Find the general solution of y' = y sec x.

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?

There is a vector v = 7j, another vector u starts from the origin with a magnitude of 5 rotates in the xy plane. Find the maximum magnitude of u × v.

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

Kevin has a spherical ball with a diameter of 20 centimeters. To the nearest square centimeter, what is the surface area of the ball?

The cost of operating a vehicle is given by C(x) = 0.25x + 1600, where x is in miles. If Jam just bought a vehicle and plan to spend between ₱5350 to ₱5600. Find the range of distance she can travel.

Two similar cones have heights 8 cm and 10 cm. What is the ratio of their surface areas?

What is the integral of e^(sin x) cos x dx?

Obtain the differential equation of the family of straight lines with slope and y-intercept equal.

60% of 390

What is the angle between two vectors A and B? A = 4i + 12j + 6k B = 24i - 8j + 6k

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

The area bounded by the curve y = sin x + 1 from x = 0 to x = π is revolved about the x-axis. What is the volume generated?

A car is travelling at a rate of 36 m/s toward a statue of height 6 m. What is the rate of change of a distance of the car towards the top of the statue when it is 8 m from the statue?

The area enclosed by the ellipse 9x² + 16y² = 144 on the first quadrant is revolved about the y-axis. What is the volume generated?

If φ = xy²z³, then grad φ is