91Ó°ÊÓ

Write the first four terms of the arithmetic sequence with the given first term and common difference. $$a_{1}=\frac{3}{4}, d=-\frac{1}{8}$$

Identify the first term and the common difference, then write the expression for the general term \(a_{n}\) and use it to find the 6 th, 10 th, and 12 th terms of the sequence. $$7,4,1,-2,-5, \dots$$

Determine the number of three-letter permutations of the letters given, then use an organized list to write them all out. How many of them are actually words or common names? $$\mathrm{T}, \mathrm{R}, \text { and } \mathrm{A}$$

Determine the number of three-letter permutations of the letters given, then use an organized list to write them all out. How many of them are actually words or common names? $$\mathrm{P}, \mathrm{M}, \text { and } \mathrm{A}$$

Find the indicated term using the information given. $$a_{1}=5, d=4 ; \text { find } a_{15}$$

The local chapter of Mu Alpha Theta will soon be electing a president, vice- president, and treasurer. In how many ways can the positions be filled if the chapter has 15 members?

Two fair dice are rolled. What is the probability the sum of the dice is a. a multiple of 3 and an odd number b. a sum greater than 5 and a 3 on one die c. an even number and a number greater than 9 d. an odd number and a number less than 10

Identify \(a_{1}\) and \(r,\) then write the expression for the \(n\) th term \(a_{n}=a_{1} r^{n-1}\) and use it to find \(a_{6}, a_{16},\) and \(a_{12}.\) $$0.2,0.08,0.032,0.0128, \ldots$$

Batting averages: Tony Gwynn (San Diego Padres) had a lifetime batting average of 0.347 ranking him as one of the greatest hitters of all time. Suppose he came to bat five times in any given game. a. What is the probability that he will get exactly three hits? b. What is the probability that he will get at least three hits?

Opinion polls: From past experience, a research firm knows that \(20 \%\) of telephone respondents will agree to answer an opinion poll. If 20 people are contacted by phone, what is the probability that a. exactly 18 refuse to be polled b. exactly 19 refuse to be polled c. at least 18 refuse to be polled d. none of them agree to be polled