Which of the following methods can be used to construct a pattern of 10 numbers for which it would be mathematically impossible to predict the 11th term?
(more then one answer.)
A.Make a pattern, starting with 3, where each number is the next digit of pi (3.14159 . . .).
B.Make a pattern by asking each of 10 friends what their favorite number is.
C.Make a pattern by counting the number of letters in each word of Lincoln's Gettysburg Address, starting with the first word.
D.Make a pattern based upon values assigned to the current weather.
E.Make a pattern where each number is the square of the number before it, plus 7 times the cube of the number before that.
A store mixes Kentucky bluegrass worth $11 per pound and ryegrass worth $14 per pound. The mixture is to sell for $13 per pound. Find out how much of each should be used to make a 588 pound mixture. How many pounds of the Kentucky bluegrass should be in the mixture?
a b
The methods that can be used to construct a pattern of 10 numbers for which it would be mathematically impossible to predict the 11th term are:
A. Make a pattern, starting with 3, where each number is the next digit of pi (3.14159...).
Explanation: Pi is an irrational number, which means it does not terminate or repeat. Therefore, it is impossible to predict the next digit of pi based on the previous digits. Thus, this method would create a pattern for which it would be impossible to predict the 11th term.
B. Make a pattern by asking each of 10 friends what their favorite number is.
Explanation: Each person's favorite number is subjective and cannot be predicted based on previous responses. Therefore, this method would create a pattern that is unpredictable for the 11th term.
C. Make a pattern by counting the number of letters in each word of Lincoln's Gettysburg Address, starting with the first word.
Explanation: The length of each word in the Gettysburg Address is predetermined and cannot be used to predict the length of subsequent words. Therefore, this method would create an unpredictable pattern for the 11th term.
D. Make a pattern based upon values assigned to the current weather.
Explanation: Weather patterns are complex and influenced by numerous factors. Predicting the exact values based on previous weather data would be challenging, if not impossible. Therefore, this method would create a pattern where the 11th term is mathematically unpredictable.
The method that does not fit the criteria is:
E. Make a pattern where each number is the square of the number before it, plus 7 times the cube of the number before that.
Explanation: This pattern is deterministic and can be calculated based on the previous terms. Each number can be determined based on the specific formula given, making it possible to predict the 11th term mathematically.