a school gave some of its students an assessment on two subjects: language and math. each students score was…

a school gave some of its students an assessment on two subjects: language and math. each students score was classified as at grade level, above grade level, or below grade level for each subject.\nhere is a summary of the data the school got after assessing 225 students.\n| language | math | number of students |\n|--|--|--|\n| at grade level | at grade level | 20 |\n| at grade level | above grade level | 45 |\n| at grade level | below grade level | 21 |\n| above grade level | at grade level | 34 |\n| above grade level | above grade level | 11 |\n| above grade level | below grade level | 25 |\n| below grade level | at grade level | 44 |\n| below grade level | above grade level | 13 |\n| below grade level | below grade level | 12 |\nsuppose the school will assess 150 more students.\nhow many of these 150 students will score at grade level in exactly one subject? use the data to make a prediction.

a school gave some of its students an assessment on two subjects: language and math. each students score was classified as at grade level, above grade level, or below grade level for each subject.\nhere is a summary of the data the school got after assessing 225 students.\n| language | math | number of students |\n|--|--|--|\n| at grade level | at grade level | 20 |\n| at grade level | above grade level | 45 |\n| at grade level | below grade level | 21 |\n| above grade level | at grade level | 34 |\n| above grade level | above grade level | 11 |\n| above grade level | below grade level | 25 |\n| below grade level | at grade level | 44 |\n| below grade level | above grade level | 13 |\n| below grade level | below grade level | 12 |\nsuppose the school will assess 150 more students.\nhow many of these 150 students will score at grade level in exactly one subject? use the data to make a prediction.

Answer

Explanation:

Step1: Calculate number of students scoring at - grade level in exactly one subject in the first sample

We sum up the relevant cells in the table. Students who are at - grade level in language and above or below in math: (45 + 21=66). Students who are at - grade level in math and above or below in language: (34 + 44 = 78). The total number of students scoring at - grade level in exactly one subject in the sample of 225 students is (66+78 = 144).

Step2: Set up a proportion

Let (x) be the number of students out of 150 who score at - grade level in exactly one subject. We set up the proportion (\frac{144}{225}=\frac{x}{150}).

Step3: Solve the proportion for (x)

Cross - multiply: (225x=144\times150). Then (x=\frac{144\times150}{225}). Calculate (144\times150 = 21600) and (\frac{21600}{225}=96).

Answer:

96