Question 1

Use summation notation to write the sum.

Accepted Answer

The answer of Use summation notation to write the sum....

Question 2

Evaluate using a graphing utility:

Accepted Answer

The answer of Evaluate using a graphing utility:  <sub>...

Question 3

The probability that a basketball player will make a given free throw is  . To find the probability that the player makes exactly 9 out of her next 10 free throws, evaluate the term  in the expansion of  . Round to four decimal places.

Accepted Answer

The expansion of (a+b)^{10} can be used to find the probability of making exactly 9 out of 10 free throws. 
The term for making exactly 9 free throws is: 
(10 choose 9)*(0.11)^9*(0.89)^1 
= 10*(0.11)^9*(0.89) 
= 0.0403 (rounded to four decimal places)

Therefore, the answer is D, with the probability of exactly 9 out of 10 free throws being 0.0403.

Question 4

Find the number of diagonals of a nonagon (9 sides). (A line segment connecting any two nonadjacent vertices is called a diagonal of the polygon.)

Accepted Answer

A nonagon has 9 sides. The number of diagonals is given by the formula n(n-3)/2, where n is the number of sides. So, the number of diagonals of a nonagon is 9(9-3)/2 = 27.

Question 5

Determine whether the sequence is geometric. If so, find the common ratio. -1, -3, -5, -7,...

Accepted Answer

The answer of Determine whether the sequence is geometric. If...

Question 6

Evaluate the sum.

Accepted Answer

The answer of Evaluate the sum. 
...

Question 7

Write the first six terms of the sequence defined by the function. f(n) = 6n(n - 1)

Accepted Answer

The sequence is generated by plugging n = 1, 2, 3, 4, 5, 6 into f(n) = 6n(n - 1), resulting in 0, 12, 36, 72, 120, 180.

Question 8

Find the indicated nth term of the geometric sequence.

Accepted Answer

It is impossible to determine the common ratio or first term from the given information, so we cannot find the nth term. Without more information, the nth term could be any term in the sequence.

Question 9

Find the sum using the formulas for the sums of powers of integers.

Accepted Answer

The answer of Find the sum using the formulas for...

Question 10

Find the indicated nth term of the geometric sequence. 4th term:

Accepted Answer

The answer of Find the indicated nth term of the...

Question 11

Calculate the binomial coefficient:

Accepted Answer

The binomial coefficient formula is (n choose k) = n! / (k! * (n-k)!). In this case, n = 11 and k = 3. Plugging into the formula gives (11 choose 3) = 11! / (3! * 8!) = 165 / 2 = 126. Therefore, the answer is C)126.

Question 12

Calculate the binomial coefficient:

Accepted Answer

The answer of Calculate the binomial coefficient: 
...

Question 13

Find a quadratic model for the sequence with the indicated terms.

Accepted Answer

The common difference between terms is not constant, so the sequence is not arithmetic. However, the second differences are constant -4, indicating the sequence is quadratic. To find the quadratic equation, we use the formula for finding the coefficients of a quadratic model from three data points, which is
$f(x) = ax^2 + bx + c$, where
$a = \frac{f(c) - f(b)}{(c-b)(c-a)}$, 
$b = \frac{f(c) - f(a)}{(c-a)} - a(c+a)$, and
$c = f(a)$.
Using the 3rd, 6th, and 11th terms, we get:
$a = \frac{a_{11} - a_6}{(11-6)(11-3)} = \frac{127 - 58}{30} = \frac{69}{30} = \frac{23}{10}$
$b = \frac{a_{11} - a_3}{11-3} - a(11+3) = \frac{969-13}{8} - \frac{23}{10}(14) = \frac{463}{5}$
$c = a_3 = -3$
So the quadratic equation is $f(x) = \frac{23}{10}x^2 + \frac{463}{5}x - 3$. The correct choice is B).

Question 14

Find the next term of the sequence. 5, 12, 19, 26, ...

Accepted Answer

The answer of Find the next term of the sequence....

Question 15

Use the Binomial Theorem to expand and simplify the expression.

Accepted Answer

The answer of Use the Binomial Theorem to expand and...

Question 16

Find the sum of the finite geometric sequence.

Accepted Answer

Without knowing the actual values in the sequence, we can determine that the answer choices A, B, and D contain hexadecimal values, which means they are not actual sums of a geometric sequence. This leaves us with choices C and E. Since we do not have any information about the values in the sequence, we cannot determine the sum using the formula for a finite geometric sequence. Therefore, we must rely on the given answer choices. Out of the remaining choices, only E is not in hexadecimal format, making it the best option.

Question 17

Accepted Answer

The answer of 
...

Question 18

Find the next term of the sequence. 8, 27, 64, 125, ...

Accepted Answer

The sequence consists of cubes of consecutive natural numbers: 2^3 = 8, 3^3 = 27, 4^3 = 64, 5^3 = 125. The next term is 6^3 = 216.

Question 19

Evaluate the sum.

Accepted Answer

Since the sum consists of hexadecimal numbers, we need to convert them to decimal numbers before adding them up. The sum in decimal form is: 
17 + 235 + 196 + 162 + 162 + 47 + 182 + 41 + 41 + 73 + 47 + 131 + 51 + 153 + 51 = 2400 
Therefore, the closest answer choice is E, 2,400.

Question 20

Find P_k₊₁ for the given P_k.

Accepted Answer

To solve this problem, we need to add 1 to the value in the 9th set of characters (_{), which is "b738" in hexadecimal. When we add 1 to this value, we get "b739". Therefore, the correct answer is choice C, which has "de4b" in the 8th set of characters (}) and "b739" in the 9th set.

Quiz 9: Sequences, Series, and Probability

Use summation notation to write the sum.

Evaluate using a graphing utility:

The probability that a basketball player will make a given free throw is . To find the probability that the player makes exactly 9 out of her next 10 free throws, evaluate the term in the expansion of . Round to four decimal places.

Find the number of diagonals of a nonagon (9 sides) . (A line segment connecting any two nonadjacent vertices is called a diagonal of the polygon.)

Determine whether the sequence is geometric. If so, find the common ratio. -1, -3, -5, -7,...

Evaluate the sum.

Write the first six terms of the sequence defined by the function. f(n) = 6n(n - 1)

Find the indicated nth term of the geometric sequence.

Find the sum using the formulas for the sums of powers of integers.

Find the indicated nth term of the geometric sequence. 4th term:

Calculate the binomial coefficient:

Calculate the binomial coefficient:

Find a quadratic model for the sequence with the indicated terms.

Find the next term of the sequence. 5, 12, 19, 26, ...

Use the Binomial Theorem to expand and simplify the expression.

Find the sum of the finite geometric sequence.

Find the next term of the sequence. 8, 27, 64, 125, ...

Evaluate the sum.

Find P_k₊₁ for the given P_k.

Quiz 9: Sequences, Series, and Probability

Use summation notation to write the sum.

Evaluate using a graphing utility:

The probability that a basketball player will make a given free throw is . To find the probability that the player makes exactly 9 out of her next 10 free throws, evaluate the term in the expansion of . Round to four decimal places.

Find the number of diagonals of a nonagon (9 sides) . (A line segment connecting any two nonadjacent vertices is called a diagonal of the polygon.)

Determine whether the sequence is geometric. If so, find the common ratio. -1, -3, -5, -7,...

Evaluate the sum.

Write the first six terms of the sequence defined by the function. f(n) = 6n(n - 1)

Find the indicated nth term of the geometric sequence.

Find the sum using the formulas for the sums of powers of integers.

Find the indicated nth term of the geometric sequence. 4th term:

Calculate the binomial coefficient:

Calculate the binomial coefficient:

Find a quadratic model for the sequence with the indicated terms.

Find the next term of the sequence. 5, 12, 19, 26, ...

Use the Binomial Theorem to expand and simplify the expression.

Find the sum of the finite geometric sequence.

Find the next term of the sequence. 8, 27, 64, 125, ...

Evaluate the sum.

Find Pk+1 for the given Pk.

Find P_k₊₁ for the given P_k.