Exam 1: Equations and Inequalities

The percent of a file that remains to be downloaded using an Internet connection is given by the equation Percent Remaining where N is the size of the file in bytes and t is the number of seconds since the download began. In how many minutes will 20% of a 264,000-byte file remain to be downloaded? Round your answer to the nearest minute.

The load L that a horizontal beam can safely support varies jointly as the width w and the square of the depth d . If a beam with width 2 inches and depth 12 inches safely supports up to 798 pounds, how many pounds can a beam of the same length that has a width of 4 inches and depth 10 inches be expected to support? Round to the nearest pound. Assume the two beams are made of the same material.

Write the equation that expresses the relationship between the variables described below, then use the given data to solve for the variation of constant. w varies directly as q, and when

How many liters of a 42% acid solution should be mixed with 5 liters of a 30% acid solution to produce a 39% solution?

Solve the rational equation below.

The load L a horizontal beam can safely support varies jointly as the width w and the square of the depth d and inversely as the length l . If a 16-foot beam with width 7 inches and depth 15 inches safely supports 272 pounds, how many pounds can a 20-foot beam that has width 8 inches and depth 9 inches be expected to support? Round to the nearest pound. Assume the two beams are made of the same material.

Solve the following equation.

The price of a computer fell 30% this year. If the computer now costs $525, how much did it cost last year?

The volume V of a right circular cone varies jointly as the square of the radius r and the height h . Tell what happens to V when r is doubled.

Solve the following formula for the specified variable.

The SMOG (Simplified Measure of Gobbledygook)readability formula is often used to estimate the reading grade level required by a person if he or she is to fully understand the written material being assessed. The formula is given by where w is the number of words that have three or more syllables in a sample of 30 sentences. A sample of 30 sentences from a given book shows a total of 75 words that have three or more syllables. Use the SMOG reading grade level formula to estimate the reading grade level required to fully understand this novel. Round your answer to the nearest tenth.

Hooke s Law states that the distance a spring stretches varies directly as the weight on the spring. A weight of 70 pounds stretches a spring 9 inches. How far will a weight of 110 pounds stretch the spring? Round to the nearest tenth of an inch.

You can rent a car for the day from Company A for $28 plus $0.11 a mile. Company B charges $22.00 plus $0.22 a mile. Find the number of miles m (to the nearest mile)per day for which it is cheaper to rent from Company A.

Use interval notation to express the solution set for the inequality below.

The pressure a liquid exerts at a given point on a submarine is directly proportional to the depth of the point below the surface of the liquid. If the pressure at a depth of 4 feet is 250 pounds per square foot, find the pressure at a depth of 14 feet.

An investment adviser invested $100,000 in two accounts. One investment earned 9% annual simple interest, and the other investment earned 8.5% annual simple interest. The amount of interest earned for 1 year was $8700 How much was invested in each account?

Solve the absolute value equation below for x .

Five people decide to share the cost of a yacht. By bringing in an additional partner, they can reduce the cost to each person by $7000. What is the total cost of the yacht?

Solve the following formula for the specified variable.

Use the square root procedure to solve the quadratic equation below.