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Show that the system of equations
2x + y + z = -6a2x + y + (b +1)z = 4bx + 3y + 2z = 2a
Has a unique solution except when b = 0 and b = 6.
If b = 0, show that there is only one value for a for which a solution exists, and find the general solution in this case.
Discuss the case when b = 6.
Interpret your solutions in terms of the kernel and image of the linear transformation T: o^3 --> o^3 represented by the equations.
Determine whether A=B , if A is a subset of set B, if set B is a subset is a subset of A, if set A is a proper subset of set B, if set B is a proper subset of set A , or if none of these applies.
Interpret the confidence interval in a single sentence
Set up an appropriate probability space. Which is larger, (a) the probability of having a full house given that the first 2 cards you've dealt have the same denomination, or (b) the probability of having a full house given that there exist 2 cards
Suppose three fair coins are flipped. Find the probability for each of the following events. Exactly two coins are tails.
Three marbles are chosen without replacement from a box containing 12 red, 7 blue, and 8 yellow marbles. Let X be the number of blue marbles chosen.
The professor counts his midterm as 2/3 of the grade and his final as 11/3 of the grade. Wendy scored only 48 on the midterm. What range of scores on the final exam would put her average between 70 and 79 inclusive?
Find the empirical probability that an iris bulb of this type will bloom. Give answer as a fraction in lowest terms. How many of the bulbs should she plant next fall if she would like at least 52 to bloom?
In what fundamental way does the solution set of a system of linear equations differ from the solution set of a system of linear inequalities?
Hypothesis test for population mean
An IRS auditor randomly selects 3 returns from 59 returns of which 10 contain errors. What is the probability of her selecting NONE of those that contain errors?
How many different 6-letter code words can be formed from the first 8 letters of the alphabet if adjacent letters must be different?
Find the relationship between dyspnea on exertion
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