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A jar contains four blue marbles and two red marbles. Suppose you choose a marble at random, and do not replace it. Then you choose a second marble. Find the probability of each event. One of the marbles you select is blue and the other is red.

Tests A multiple-choice test has four choices for each answer. a. What is the probability that a random guess on a question will yield the correct answer? b. Suppose you need to make a random guess on three of the ten test questions. What is the probability that you will answer all three correctly?

Use this information for Exercises \(53-58\) . Bag 1 contains 5 red marbles, 1 blue marble, 3 yellow marbles, and 2 green marbles. Bag 2 contains 1 red pencil, 3 red pens, 2 blue pencils, and 5 blue pens. One marble is drawn from bag 1 . What is the probability that the marble is red or yellow?

Writing. Explain why 0 cannot be in the domain of an inverse variation.

Open-Ended. The height \(h\) of a cylinder varies directly with its volume \(V\) and inversely with the square of its radius \(r .\) Find at least four ways to change the volume and radius of a cylinder so that its height is quadrupled.

An automatic pitching machine can pitch all its baseballs in 1\(\frac{1}{4}\) hours. One attendant can retrieve all the baseballs pitched by one machine in 3\(\frac{1}{2}\) hours. At least how many attendants working at the same rate should be hired so that the baseballs from 10 machines are all retrieved in less than 8 hours?

Which data set shows inverse variation: \((24.4,4.8)\) and \((9.6,12.2),\) or \((24.0,4.5)\) and \((18.0,6.5) ?\) Explain.

Multiply. \((3 \sqrt{5}+2 \sqrt{10})(2 \sqrt{5}+\sqrt{10})\)