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Two urns contain both black and white marbles. Urn 1 contains 5 white marbles and 8 black marbles. Urn 2 contains 6 white marbles and 10 black marbles.
a. In one experiment, one marble is selected at random from Urn 1 and one marble is selected at random from Urn 2 at the same time. What is the probability that both marbles are white?
b. In a second experiment, one marbles is selected at random from Urn 1 and placed into Urn 2, and then a marble is randomly selected from Urn 2. What is the probability that the marble selected from Urn 2 is white given that the marble selected from Urn 1 was also white?
c. In the second experiment, what is the probability that both marbles selected are white?
d. In the second experiment, what is the probability that the marble selected from Urn 1 was black given that the marble selected from Urn 2 is white?
Find the directional derivative at P(-2,2,-1) in the direction of Q(18,-2,4). Find the direction of maximum decrease at P. (your answer does not have to be unit vector.) What is the maximum rate of decrease?
A pizza pan is removed at 8:00 PM from an oven at a fixed temperature of 400 degrees into a room that is a constant 72 degrees. After 5 minutes, the pan is at at 300 degrees F. At what time is the pan 135 degrees?
Write the fraction. There are 100 centimeters in a meter. What fractional part of a meter does 7 centimeters represent?
A light bulb company knows the lifetime of 10,000 bulbs is normally distributed. The mean lifetime of a bulb is 8 months, and the standard deviation is 1.5 months. Approximately, how many bulbs will last more than 10 months?
Estimate the number of replications needed to reduce the half width of each con?dence interval by 25 percent. Run the additional replications for each system and compute new con?dence intervals using a 0.10 level of signi?cance.
A rectangular trench is to be dug which is to be 210 ft long, 90 ft wide and 12 ft deep. A large dump truck can carry 20 cubic yards in a load. How many truck loads will be required to remove the dirt from this trench?
John invested $15,000 into two accounts paying 6% and 8% intreset. His total return at the end of the year was $1,112.55, how much did he invest in each account?
A target heart rate T that is half a person's maximum heart rate is given by T=110 - 1/2A where A is a person's age.
Using the readings discussed in this course, provide one real-world application of the information learned that has been the most valuable to you. Why has it been valuable?
What then is the chance that there will be a need for exactly 2 ambulances during that time slot on any given Wednesday morning?
Carl wants to construct three rectangular dog-trainig arenas side-by-side, as shown, using a total of 340 feet of fencing. What should the overall length and width be in order to maximize the area of the three combined arenas?
Model each situation with a linear function and graph. Is it reasonable to include negative numbers in the range?
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