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Population Growth

Which of the following would be best to use for population growth with known upper limit?

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Effectiveness of Hand Wash

Bacteria such as V. cholerae are known to follow an exponential growth curve rate, and will double their number every 15 minutes. Fortunately, anti-bacterial hand wash can kill 99.9% of bacteria on a surface. If a colony of 500 V. cholerae cells are left alone for 2 hours, then anti-bacterial handwash is applied thoroughly, how many bacterial cells are left?

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Bocce Ball

There are 5 white, 7 red and 8 black balls in a box. If you are blindly picking up balls from the box, what is the minimum number of balls you need to take out of the box to ensure that you have at least 2 balls of the same color?

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Length of the Hypotenuse

If the area and perimeter of a right triangle are 30 cm2 and 30 cm, respectively, what is the length of the hypotenuse (the side opposite the right angle)?

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Perimeter of a Square

What is the maximum perimeter of a square that can fit inside a circle of radius 5 cm?

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Grading Policies

In a certain course, the Professor has two different grading policies, from which he picks the best. The first policy is to put 40% and 60% weights, respectively, on the midterm and final exams. Under the second grading policy, these weights are 50% each. A student has scored 85% on the midterm, and needs to score at least x% on the final to make a B (a total of 82%). What is the value of x?

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Smallest Variance

Which of the following data sets contains the smallest variance?

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Filling Cylinders

How many cubic centimeters of water will approximately be required to fill a cylinder with a 3 cm radius and 7 cm height?

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Predict Number of Lions

A researcher is attempting to predict the number of lions in an African habitat based on previous data. He has formed a regression equation which is: Y = 25 + 0.5X – 2ZX, where X is the number of years since the first population sample, and Z is the death rate of the lions. If it has been 10 years, and the death rate is 1 lion per year, what is the predicted number of lions in the habitat?

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The Matrix

It takes 6 minutes and 12 minutes, respectively, to run two computer programs when they are run one at a time. However, their speeds are reduced by 50% and 40%, respectively, if running in parallel. If a PC starts running the two programs together, how long will it take for them to finish?

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