Vermont maple sugar producers sponsored a testing program to determine the benefit of a potential new fertilizer regimen. A random sample of 27 maple trees in Vermont were chosen and treated with one of three levels of fertilizer suggested by the chemical producer. In this experimental setup, nine trees--three in each of three climatic zones--were treated with each fertilizer level and the amount of sap produced (in mL) by the trees in the subsequent season was measured.

Fertilizer Zone Sap Production
Low Southern Zone 76.2
Low Southern Zone 80.4
Low Southern Zone 74.2
Low Central Zone 79.4
Low Central Zone 87.9
Low Central Zone 86.9
Low Northern Zone 84.5
Low Northern Zone 85.2
Low Northern Zone 80.1
Medium Southern Zone 87
Medium Southern Zone 95.1
Medium Southern Zone 93
Medium Central Zone 98.2
Medium Central Zone 94.7
Medium Central Zone 96.2
Medium Northern Zone 88.4
Medium Northern Zone 90.4
Medium Northern Zone 92.2
High Southern Zone 84.2
High Southern Zone 87.5
High Southern Zone 83.1
High Central Zone 90.3
High Central Zone 89.9
High Central Zone 93.2
High Northern Zone 81.4
High Northern Zone 84.7
High Northern Zone 82.2

the number of the people going.

step-by-step explanation:

the cost to buy one movie ticket is $7. if the total cost for the movie is a function of how many people go, then the input is : the number of the people going.

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.