Exam 12: Sequences, Series, and Probability

Solve the problem. -Mr Johnston has 3 pairs of pants, 6 shirts, 11 ties, and 10 sports coats. Assuming that he must wear one of each, how many different outfits can he wear?

Solve the problem. -A job pays a salary of 32,000 the first year. During the next 9 years, the salary increases by 5% each year. What is the salary for the 10th year? What is the total salary over the 10-year period? (Round to the nearest cent.)

Solve the problem. -A card is selected at random from a deck of cards. Find the probability: P(selecting a card that is a black card and a 6)

Write the repeating decimal as a ratio of integers. -0.151515

Evaluate the expression. - ${ } _ { 4 } \mathrm { P } _ { 4 }$

Solve the problem. -Four different colored flags will be placed on a pole, one beneath another. The arrangement of the colors indicates the message. How many messages are possible if 4 flags are to be selected from 11 different colored Flags?

Find the common difference of the sequence. - $a _ { 1 } = 5 , a _ { 4 } = 11 ; \text { find } d$

Find the indicated sum. - $a _ { 1 } = - 5 , r = 2 ; \text { find } \mathrm { s } _ { 14 }$

Solve the problem. -In a geometric series,, $a _ { 2 } = 15 \text { and } a _ { 5 } = 405$ ; find r and ; find r anda1.

Solve the problem. -A school auditorium has 34 rows with 21 seats in the first row, 24 in the second row, 27 in the third row, and so forth. How many seats are in the auditorium?

Solve the problem. -Raul Tampas' catering service is making up trays of hors d'oeuvres. The hors d'oeuvres are categorized as inexpensive, average, and expensive. If the client must select 4 of the 5 inexpensive, 4 of the 6 average, and 6 of The 7 expensive hors d'oeuvres, how many different choices are possible?

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence. - $a _ { 1 } = 8 , d = 10 ; \text { find } \mathrm { s } _ { 5 }$

Write the word or phrase that best completes each statement or answers the question. Use mathematical induction to prove the following statement for all positive integers n. - $5 + 10 + 15 + \ldots + 5 n = \frac { 5 n ( n + 1 ) } { 2 }$

For the geometric sequence, find the common ratio, r. -2, 6, 18, 54, 162, . . .

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence. --13, -23, -33, -43, . . ., -703

Solve the problem. -John's Ice Cream Parlor has 12 different flavors. Willie orders a banana split and has to select 4 different flavors. How many different selections are possible?

Evaluate the combination. - $\left( \begin{array} { l } 7 \\1\end{array} \right)$

Write the first three terms of the expansion. - $\left( m ^ { 2 } + 6 \right) ^ { 9 }$

Evaluate the factorial. - $13 !$

Find the indicated term of the geometric sequence. -a1 = -3, r = 2; find $a _ { 10 }$