Exam 1: Equations and Inequalities

If a researcher wanted to know the mean weight (the mean is the sum of all measurements divided by the number of measurements)of women in the U.S., the weight of every woman would have to be measured, and then the mean weight calculated, an impossible task. Instead, researchers find a representative sample of women and find the mean weight of the sample. Because the entire population of women is not used, there is a possibility that the calculated mean weight is not the true mean weight. For one study, researchers used the formula where m is the true mean weight, in pounds, of all women, to be 98% sure of the range of values for the true mean weight. Using this inequality, what is the range of mean weights of women in the U.S.? Round to the nearest tenth of a pound.

The range of a projectile is directly proportional to the square of its velocity. If a motorcyclist can make a jump of 188.5 feet by coming off a ramp at 67 mph, find the distance the motorcyclist could expect to jump if the speed coming off the ramp were increased to 72 mph. Round to the nearest tenth of a foot.

Solve the quadratic equation below by factoring and applying the zero product principle.

Solve the following compound inequality. Write the solution set using set-builder notation.

Find the solution of the following equation containing a rational exponent on the variable.

Jordan is driving along a highway that passes through Moyock. His distance, d , in miles, from Moyock is given by the equation where t is the time, in hours, since the start of his trip and . Determine when Jordan will be exactly 85 miles from Moyock. Round to the nearest minute.

The height, h , in feet, of a baseball above the ground t seconds after it is hit is given by . Use this equation to determine the number of seconds, to the nearest tenth of a second, from the time the ball is hit until the ball hits the ground.

Find all the real solutions of the following equation by first rewriting the equation as a quadratic equation.

Solve the following equation.

A veterinarian wishes to use 162 feet of chain-link fencing to enclose a rectangular region and subdivide the region into two smaller rectangular regions, as shown below. If the total enclosed area is 1092 square feet, find the dimensions of the enclosed area.

A solid silver sphere has a diameter of 14 millimeters, and a second silver sphere has a diameter of 16 millimeters. The spheres are melted down and recast to form a single cube. What is the length of each edge of the cube? Round your answer to the nearest tenth of a millimeter.

On a ship, the distance d that you can see to the horizon is given by , where h is the height of your eye measured in feet above sea level and d is measured in miles. How high is the eye level of a navigator who can see 16 miles to the horizon? Round your answer the nearest foot.

At the present time a company manufactures rectangular solid candy bars the measure 4.5 inches by 1.5 inches by 0.5 inch. Due to financial times, the company has decided to keep the price of the candy bar fixed and reduce its volume by 15%. What should be the dimensions, to the nearest tenth of an inch, of the new candy bar if it is decided to keep the height at 0.5 inch and to make the length on the candy bar 2.25 times as long as its width?

The SMOG (Simplified Measure of Gobbledygook)readability formula estimates the reading grade level required by a person if he or she is to fully understand the written material assessed. The SMOG formula is defined as where w is the number of words that have three or more syllables that should appear in a sample of 30 sentences. A writer of children s books has decided to write a book that can be fully understood by children at the 7th-grade level. What is the maximum number of words with three or more syllables that should appear in any sample of 30 sentences of the book?

A square piece of cardboard is formed into a box by cutting out 3-inch squares from each of the corners and folding up the sides. If the volume of the box needs to be 126.75 cubic inches, what size square piece of cardboard is needed?

The amount of juice in a grapefruit is directly proportional to the cube of its diameter. A grapefruit with a 4-inch diameter contains 5 fluid ounces of juice. How much juice is contained in a grapefruit with a 6-inch diameter? Round to the nearest tenth of a fluid ounce.

Solve the following absolute value equation for p.

A professional painter can paint a kitchen in 10 hours. His apprentice can paint the same kitchen in 20 hours. If they worked together, how long would it take for them to paint the kitchen?

Write the equation that expresses the relationship between the variables, and then use the given data to solve for the variation constant. T varies jointly as r and and the cube of s and when and .

Find all the real solutions of the following equation by first rewriting the equation as a quadratic equation.