Question

a survey was conducted with high school students in each grade to see how many prefer math or english. some of the data are shown below. chart with rows: 9, 10, 11, 12, total; columns: math, english, total. data: 9th: math (blank), english 40, total 63; 10th: math 18, english (blank), total 26; 11th: math (blank), english 15, total 29; 12th: math (blank), english 32, total 67; total: math 90, english 95, total 185 which statements are true? check all that apply. □ twenty - three ninth graders and fifteen eleventh graders prefer math. □ fourteen eleventh graders prefer english and eight tenth graders prefer english. □ thirty - five twelfth graders prefer math and nine tenth graders prefer english. □ twenty - three ninth graders and thirty - five twelfth graders prefer math. □ eighteen tenth graders prefer english and fourteen eleventh graders prefer math.

Explanation:

To solve this, we analyze each statement using the table data:

Step 1: Analyze "Twenty - three ninth graders and fifteen eleventh graders prefer math."

• For 9th graders: Total 9th graders = 63, English preference = 40. So math preference for 9th graders = \(63 - 40=23\).
• For 11th graders: Total 11th graders = 29, English preference = 15. So math preference for 11th graders = \(29 - 15 = 14

eq15\). So this statement is false.

Step 2: Analyze "Fourteen eleventh graders prefer math and eight tenth graders prefer English."

• 11th graders math preference: As calculated above, \(29 - 15=14\).
• 10th graders: Total 10th graders = 26, Math preference = 18. So English preference for 10th graders = \(26 - 18 = 8\). This statement is true.

Step 3: Analyze "Thirty - five twelfth graders prefer math and nine tenth graders prefer English."

• 12th graders: Total 12th graders = 67, English preference = 32. So math preference for 12th graders = \(67 - 32 = 35\).
• 10th graders English preference: We calculated it as 8 \(

eq9\). So this statement is false.

Step 4: Analyze "Twenty - three ninth graders and thirty - five twelfth graders prefer math."

• 9th graders math preference: \(63 - 40 = 23\).
• 12th graders math preference: \(67 - 32=35\). This statement is true.

Step 5: Analyze "Eighteen tenth graders prefer English and fourteen eleventh graders prefer math."

• 10th graders English preference: \(26 - 18 = 8

eq18\). So this statement is false.

The true statements are: "Fourteen eleventh graders prefer math and eight tenth graders prefer English" and "Twenty - three ninth graders and thirty - five twelfth graders prefer math".

If we consider the options (assuming the check - box options are as per the statements):

• The true statements correspond to the ones with "Fourteen eleventh graders prefer math and eight tenth graders prefer English" and "Twenty - three ninth graders and thirty - five twelfth graders prefer math" (depending on the exact option labels, but from our analysis these two are true).

For example, if the options are labeled as:

• Option with "Fourteen eleventh graders prefer math and eight tenth graders prefer English"
• Option with "Twenty - three ninth graders and thirty - five twelfth graders prefer math"

These two options are true.

Answer:

To solve this, we analyze each statement using the table data:

Step 1: Analyze "Twenty - three ninth graders and fifteen eleventh graders prefer math."

• For 9th graders: Total 9th graders = 63, English preference = 40. So math preference for 9th graders = \(63 - 40=23\).
• For 11th graders: Total 11th graders = 29, English preference = 15. So math preference for 11th graders = \(29 - 15 = 14

eq15\). So this statement is false.

Step 2: Analyze "Fourteen eleventh graders prefer math and eight tenth graders prefer English."

• 11th graders math preference: As calculated above, \(29 - 15=14\).
• 10th graders: Total 10th graders = 26, Math preference = 18. So English preference for 10th graders = \(26 - 18 = 8\). This statement is true.

Step 3: Analyze "Thirty - five twelfth graders prefer math and nine tenth graders prefer English."

• 12th graders: Total 12th graders = 67, English preference = 32. So math preference for 12th graders = \(67 - 32 = 35\).
• 10th graders English preference: We calculated it as 8 \(

eq9\). So this statement is false.

Step 4: Analyze "Twenty - three ninth graders and thirty - five twelfth graders prefer math."

• 9th graders math preference: \(63 - 40 = 23\).
• 12th graders math preference: \(67 - 32=35\). This statement is true.

Step 5: Analyze "Eighteen tenth graders prefer English and fourteen eleventh graders prefer math."

• 10th graders English preference: \(26 - 18 = 8

eq18\). So this statement is false.

The true statements are: "Fourteen eleventh graders prefer math and eight tenth graders prefer English" and "Twenty - three ninth graders and thirty - five twelfth graders prefer math".

If we consider the options (assuming the check - box options are as per the statements):

• The true statements correspond to the ones with "Fourteen eleventh graders prefer math and eight tenth graders prefer English" and "Twenty - three ninth graders and thirty - five twelfth graders prefer math" (depending on the exact option labels, but from our analysis these two are true).

For example, if the options are labeled as:

• Option with "Fourteen eleventh graders prefer math and eight tenth graders prefer English"
• Option with "Twenty - three ninth graders and thirty - five twelfth graders prefer math"

These two options are true.