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4) Find each of the two areas bounded by the curves y=x³-4x and y = x² + 21.
You are taking a test to see if you have supernatural abilities that involves a deck of five cards that each show one of five symbols (which we will call (A, B, C, D, E)). The cards are placed in a sequence so that each card appears exactly once; no repeats are allowed. Your job is to guess the correct sequence. (a) How many different sequences are possible? (b) What is the probability that you guess all five cards in the sequence correctly? (c) What is the probability that the letters AB occur consecutively and in that order some where in the sequence?
You are taking a test to see if you have supernatural abilities that involves a deck of five cards that each show one of five symbols (which we will call (A, B, C, D, E)). The cards are placed in a sequence so that each card appears exactly once; no repeats are allowed. Your job is to guess the correct sequence. (a) How many different sequences are possible? (b) What is the probability that you guess all five cards in the sequence correctly? (c) What is the probability that the letters AB occur consecutively and in that order some where in the sequence?
Each time you visit the state fair, you play some games at the Midway. One game has four prizes (A, B, C, D). (a) How many different four letter sequences are possible if each letter is chosen from {A, B, C, D} with repeats allowed? (b) How many different four letter sequences have each letter occurring exactly once? (c) How many different four letter sequences don't contain B? (d) How many different four letter sequences have two letters, each of which occurs twice?
Each time you visit the state fair, you play some games at the Midway. One game has four prizes (A, B, C, D). (a) How many different four letter sequences are possible if each letter is chosen from {A, B, C, D} with repeats allowed? (b) How many different four letter sequences have each letter occurring exactly once? (c) How many different four letter sequences don't contain B? (d) How many different four letter sequences have two letters, each of which occurs twice?
Find the area bounded by the curve x=y²+2y and the line x=3.
Find the area of the region bounded by the curves X= Y³ and Y= X²
2. Consider all samples of size 2 from this population:
2 5 6 8 10 12
a. Compute the mean () and variance () of the population.
b. List all samples of size 2 and compute the mean for each sample.
c. Construct the sampling distribution of the sample means.
d. Calculate the mean of the () of the sampling distribution of the sample means.
e. Calculate the variance of the () of the sampling distribution of the sample means.
) Solve the area bounded by the curve y = 4x-x² and the lines x = -2 and y = 4.
Find the area, take the elements of the area parallel to the x-axis. y= 2x³-3x³-9x; y=x²-2x²-3x.
