Exam 8: Sequences, Series, Induction, and Probability

Use the data in the table categorizing cholesterol levels by the ages of the individuals in a study. If one person from the study is chosen at random, find the probability of the given event. -The person is 60 or under. Normal Cholesterol Elevated Cholesterol Total 30 and under 17 4 21 31-60 49 32 81 61 or older 22 76 98 Total 88 112 200

Solve the problem. -Suppose that a student group consists of 10 females and 8 males. What is the probability that a committee of 4 people chosen at random will consist of only females?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The statement that Pk is true is called the________ hypothesis.

Find the indicated terms. -If the third and fourth terms of an arithmetic sequence are -7 and -10, what are the first and second terms?

Find the sum. - $\sum _ { n = 1 } ^ { 25 } ( 5 n - 3 )$

Write the word or phrase that best completes each statement or answers the question. Use mathematical induction to prove the given statement. - $( n + 2 ) ! > 7 ^ { n } \text { for positive integers } \mathrm { n } \geq 10 \text {. }$

Choose the one alternative that best completes the statement or answers the question. Determine whether the sequence is geometric. If so, find the value of r. - $\frac { 15 } { t ^ { 4 } } , \frac { 75 } { t ^ { 8 } } , \frac { 375 } { t ^ { 12 } } , \frac { 1,875 } { t ^ { 16 } }$

Solve the problem. -Given {A, B, C}, list all of the combinations of two elements from the set.

Write the first four terms of the arithmetic sequence with the given first term and common difference. - $a _ { 1 } = 9 , d = - 7$

Write the first five terms of the sequence defined recursively. - $a _ { 1 } = 20 ; a _ { n } = \frac { 1 } { 4 } a _ { n - 1 } + 3$

Solve the problem. -A ball drops from a height of 6 ft. With each bounce, the ball rebounds to $\frac { 2 } { 5 }$ of its height. The total vertical distanced traveled is given by $6 + ( 2 ) ( 6 ) \left( \frac { 2 } { 5 } \right) + 2 ( 6 ) \left( \frac { 2 } { 5 } \right) ^ { 2 } + 2 ( 6 ) \left( \frac { 2 } { 5 } \right) ^ { 3 } \cdots$ After the first term, the series is an infinite geometric series. Compute the total vertical distance traveled.

Solve the problem. -If $P ( E ) = 0.552$ , what is the value of $P ( \bar { E } )$ ?

Write the word or phrase that best completes each statement or answers the question. Use mathematical induction to prove the given statement. - $n ! > 2 n \text { for postive integers } \mathrm { n } \geq 4$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -In a business meeting, every person at the meeting shakes every other person's hand exactly one time. The total number of handshakes for n people at the meeting is given by $a _ { n } = \frac { 1 } { 2 } n ( n - 1 )$ Evaluate $a _ { 12 }$ and interpret its meaning in the context of this problem.

Write the repeating decimal as a fraction. - $0 . \overline { 6 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If n items are arranged in order, then each arrangement is called a________ of n items.

Solve the problem. -An event in Daytona Beach brings an estimated 550,000 people to the town. Suppose that each person spends an average of $330. a.How much money is infused into the local economy during the event? b. If the money is respent in the community over and over again at a rate of 64%, determine the totalAmount spent. Assume that the money is respent an infinite number of times.

Write a nonrecursive formula for the nth term of the arithmetic sequence {an} based on the given information. - $a _ { 1 } = 6 , d = 4$

Solve the problem. -Given {A, B, C, D}, list all of the permutations of three elements from the set.

Find the indicated term of a geometric sequence from the given information. - $a _ { 1 } = 3$ and $a _ { 4 } = 81$ . Find $a _ { 10 }$ .