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Question: A pair of dice is loaded. The probability that a 4 appears on the first die is 2/7, and the probability that a 3 appears on the second die is 2/7. Other outcomes for each die appear with probability 1/7. What is the probability of 7 appearing as the sum of the numbers when the two dice are rolled?
Draw a network diagram for problem - Label all nodes appropriately with either numbers or town names. Note: if you use numbers, please provide a mapping guide to equate your numbers to towns.
It would normally follow on from work on sequences and fractions-Ruth was investigating fraction differences. She wrote down this sequence of fractions:
Prove that 1/(2n) is less than or equal to [ 1 * 3 * 5 *...* (2n - 1)] / (2 * 4 *...* 2n) whenever n is a positive integer.
Find the general solution of the network flow. Find the smallest possible value for x6.
An apartment is rented for $450 per month. Each month's rent is payable in advance. If money is worth 12% compounded monthly, what is the present value of the rent for one year?
How much work must be done to lift the entire cable to the top of the pole? How much work must be done to lift half the cable to the top of the pole (so that 10 m still hangs over the edge)?
The lengths of individual fish in a pond have an approximate Normal distribution with a mean of 18.6 cm and a standard deviation of 6.0 cm. A sample of 36 fish is taken. What is the standard deviation of the sampling distribution of the sample mea..
The constant of integration can be founds if you know one point on the curve. For the following problem, find the constant of integration. Find the constant on integration, C if
It usually takes John 3 hours longer to do the monthly payroll than it takes Peter. They start working on it together at 9am and at 5pm, they have 85% of it done.
The next model of a sports car will cost 14.3% more than the current model. The current model costs $53,000. How much will the price increase in dollars? What will be the price of the next model?
Basic probability problems
A volcano fills the volume between the graphs z=0 and z=1/(x^2+y^2)^23 , and outside the cylinder x^2+y^2=1. Find the volume of this volcano.
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