Question

The number of soil samples, \(s\), that Sonal needs for an experiment must be greater than 6 but less than or equal to 13 . Which of the following represents an acceptable number of soil samples for Sonal's experiment? A) \(6

Short answer

The correct representation of the acceptable number of soil samples for Sonal's experiment is C) \(6<s \leq 13\).

Step-by-step solution

Compare Given Information to the Options

Given that soil sample count "s" must be greater than 6 and less than or equal to 13, we can write this as an inequality: \(6 < s \leq 13\). Now, let's compare our inequality to each of the four options presented: A) \(6<s<13\) - This option states that the acceptable number of samples is greater than 6 and less than 13, which is close but does not include 13. This is not the correct inequality for this situation. B) \(6 \leq s<13\) - This option states that the acceptable number of samples is greater than or equal to 6 and less than 13. Based on our inequality, this is also not the correct representation, as it includes 6 and does not include 13. C) \(6<s \leq 13\) - This option matches our inequality perfectly, as it states that the acceptable number of samples is greater than 6 and less than or equal to 13. D) \(6 \leq s \leq 13\) - This option states the acceptable number of samples is greater than or equal to 6 and less than or equal to 13. This includes both 6 and 13, so it is also not the correct representation for this situation.

Choose the Correct Option

From the comparison of our inequality to the given options, we can conclude that the correct representation of the acceptable number of soil samples for Sonal's experiment is: C) \(6<s \leq 13\)

Key concepts

SAT Math Preparation

Preparing for the SAT Math section involves familiarizing yourself with various math concepts, including inequalities, which are an essential topic. Inequalities help describe the relative size of different numbers and can appear in problems related to algebra, geometry, and even real-world situations, such as determining the range for a number of items or limits within a given context.

When tackling inequalities for the SAT, it's critical to understand the different types of signs used and what they represent. Make sure to practice interpreting word problems and translating them into mathematical inequalities. In the case of the exercise provided, we understand that the variable (number of soil samples) has both a lower and upper bound. Mastery of these inequality concepts ensures you can select the correct mathematical representation among multiple-choice options, just as was done in determining that option C) correctly represents the situation described for Sonal's experiment.

Inequality Notation

Inequality notation is a shorthand way to represent the relative magnitude of two expressions. Key signs include: '<' for 'less than', '>' for 'greater than', '\(leq\)' for 'less than or equal to', and '\(leq\)' for 'greater than or equal to'. For SAT preparation, it is important not only to recognize these signs but also to know when to use them correctly.

For the Sonal's soil samples question, understanding that 'greater than 6 but less than or equal to 13' means the smallest acceptable number is just above 6 and could range up to and including 13 is crucial. The inequality notation that fits this description is \(6< s \leq 13\), which maintains these boundaries effectively. Familiarity with the subtleties of notation, such as when to include the equal sign under a less than or greater than symbol, will ensure that similar problems can be solved correctly.

Comparing Inequalities

Comparing inequalities is a key skill for solving algebraic problems and necessary for success on standardized tests like the SAT. When comparing inequalities, pay close attention to whether values are included or excluded from the range in question. In the case of Sonal's experiment, the number of soil samples was within a specific range, and comparing the options against the known conditions was necessary to find the correct answer.

Option C) is the sole choice which accurately reflects the given conditions because it includes 13 as the upper limit and excludes 6 as the lower limit of the number of samples. Developing the skill to compare and choose the correct inequality from several given options requires practice and attention to detail, which over time can become intuitive.