Exam 11: Sequences, Series, and Probability

Solve the problem using the idea of labeling. -In how many ways can 11 volunteers be assigned to work in the governor's reelection campaign with 3 assigned to stuffing envelopes, 2 assigned to making phone calls, and 6 assigned to making signs?

Use mathematical induction to prove the statement is true for all positive integers n. -

Write the repeating decimal number as a fraction. -0.92929292 . . .

Solve the problem using the idea of labeling. -How many permutations are there of the letters in the word GIGGLE?

Solve the problem. -The distribution of B.A. degrees conferred by a local college is listed below, by major. What is the probability that a randomly selected degree is not in Mathematics? Round to the nearest thousandth.

Find the first six terms of the sequence. -

Solve the problem. -A piece of cardboard is 0.04 in. thick. The cardboard is cut in half, with one half being placed on top of the other so that its thickness doubles for 7 times in a row. How thick would the final stack of cardboard be? Round to Two decimal places.

Find the sum of the geometric series. -2 + 6 + 18 + 54 + 162

Solve the problem. -A collection of dimes is arranged in a triangular array with 12 coins in the base row, 11 in the next, 10 in the next, and so forth with 1 dime in the last row. Find the value of the collection.

Write a recursion formula for the sequence. --3, 7, 17, 27, . . .

Identify the sequence as arithmetic, geometric, or neither. --8, 8, -9, 9, -10, 10, . . .

Find the probability of the event. -A bag contains 6 red marbles, 4 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue when one marble is drawn from the bag?

Solve the problem. -How many 5-card poker hands consisting of 2 aces and 3 kings are possible with an ordinary 52-card deck?

Provide an appropriate response. -Consider the selection of seven apples from a barrel of 75 apples. Is this a combination, a permutation, or neither?

Write the series in summation notation. Use the index i and let i begin at 1 in each summation. -4 + 7 + 10 + 13 + 16

Evaluate the expression. -C(9, 9)

Write a formula for the nth term of the arithmetic sequence. Do not use a recursion formula. -0.23, 0.26, 0.29, 0.32, 0.35, . . .

Evaluate the expression. -P(4, 0)

Solve the problem. -A woman borrowed $20,000 at 8% interest compounded annually. If the loan was paid off in one lump sum at the end of 4 years, how much did she pay?

Write the geometric series in summation notation. -