Exam 12: Further Topics in Algebra

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence. Round to the nearest thousandth, if necessary. -A railroad bridge is built over a V-shaped canyon. If the supports are 8 feet long at each end, the center support is 264 feet long, and the supports increase in length by 2 feet with each support (from 8 feet to 264 feet), what is the total length of all the supports?

Find the common ratio r for the given infinite geometric sequence. -A town has a population of 10,000 people and is increasing by 10% every year. What will the 175) population be at the end of 4 years?

Solve the problem. -Cal is packing his suitcase to go on a trip. He wants to pack 3 pairs of pants chosen from the 8 pairs of pants in his closet and 4 shirts chosen from the 10 shirts in his closet. In how many ways can this Be done?

Find the probability. -A bag contains 3 red marbles, 2 blue marbles, and 8 green marbles. What is the probability of choosing a blue marble when one marble is drawn?

Solve the problem. -Give the probability that the roll of a die will show 4 or 5.

Evaluate the sum using the given information. - =-4,=1,=-2, and =-1 --1

Evaluate the expression. - $\frac { 7 ! } { 5 ! 2 ! }$

Solve the problem. -How many ways can a committee of 4 be selected from a club with 10 members?

Provide an appropriate response. - $\text { How many terms are in the expansion of } ( x + y ) ^ { 5 }$ ? 220)

Solve the problem. -In how many ways can a group of 8 students be selected from 9 students?

Provide an appropriate response. -Convert the decimal $.8262626 \ldots$ to a fraction by writing it as the infinite series $\frac { 8 } { 10 } + \frac { 26 } { 10 \cdot 100 } + \frac { 26 } { 10 \cdot 100 ^ { 2 } } + \frac { 26 } { 10 \cdot 100 ^ { 3 } } + \ldots$

Solve the problem. -A lottery game has balls numbered 1 through 15 . What is the probability of selecting an even numbered ball or a 9?

Solve the problem. -100 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows the results. If one of the 100 employees is randomly selected, Find the probability that the person does not commute by public transportation. 1. Public transportation: 7 full time, 9 part time 2) Bicycle: 3 full time, 4 part time 3) Drive alone: 29 full time, 33 part time 4) Car pool: 9 full time, 6 part time

Use the formula for $\mathrm { S } _ { \mathbf { n } }$ to find the sum of the first five terms of the geometric sequence. - $\mathrm { a } _ { 1 } = 7.543 , \mathrm { r } = 2.466$ (Round to the nearest hundredth)

Solve the problem. -In how many ways can the letters in the word PAYMENT be arranged if the letters are taken 6 at a time?

Use a calculator to evaluate the expression. - ${ } _ { 17 } \mathrm { P } _ { 4 }$

Evaluate the expression. - $\frac { 10 ! } { 5 ! 5 ! }$

Decide whether the given sequence is finite or infinite. -9, 10, 11, 12, . . .

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). -The first term is 21, and the common difference is 7; n = 5

Write the series using summation notation. - $1 + \frac { 1 } { 2 ^ { 7 } } + \frac { 1 } { 3 ^ { 7 } } + \frac { 1 } { 4 ^ { 7 } } + \frac { 1 } { 5 ^ { 7 } }$