Question

a group of 55 football players was polled about which synthetic grass they like to play on, chemgrass or chemstrand. the data from the survey is shown in the venn diagram. use the venn diagram to find the missing values in the frequency table. synthetic grass preference venn diagram with chemstrand (15), overlap (13), chemgrass (17), and 10 outside both synthetic grass preference frequency table with columns likes chemstrand, does not like chemstrand, total what are the values of x, y, and z? \\(\bigcirc\\) \\(x = 17, y = 15,\\) and \\(z = 13\\) \\(\bigcirc\\) \\(x = 13, y = 15,\\) and \\(z = 17\\) \\(\bigcirc\\) \\(x = 15, y = 13,\\) and \\(z = 17\\) \\(\bigcirc\\) \\(x = 13, y = 17,\\) and \\(z = 15\\)

Explanation:

Step1: Analyze Venn Diagram

The Venn diagram has Chemstrand (15 only), overlap (13), Chemgrass (17 only), and outside both (10). Total players: 55. Let's relate to the frequency table (assuming columns: Likes Chemgrass, etc., but from options, we can match x, y, z.

Step2: Match Values

From Venn:

• x (maybe Likes Chemstrand only? Wait, no. Wait, the options: Let's see the total. Wait, the Venn parts: Chemstrand only (15), overlap (13), Chemgrass only (17), neither (10). Total: 15+13+17+10=55, which matches. Now, the frequency table: Let's assume the rows/columns. But the options have x, y, z. Let's see the options:

Looking at the Venn, the overlap is 13 (maybe x), Chemstrand only 15? No, wait the options: Let's check the correct option. Wait, the Venn has Chemstrand (15) only, overlap (13), Chemgrass (17) only, and 10 outside. So if x is the number who like both? No, overlap is 13. Wait, the options: Let's see the correct one. Wait, the option with x=13, y=17, z=15? No, wait no. Wait, maybe x is the number who like Chemstrand only? No, 15. Wait, no, let's re-express. Wait, the Venn:

• Number who like Chemstrand: 15 (only) +13 (both) =28
• Number who like Chemgrass:13 (both)+17 (only)=30
• Number who don't like Chemstrand:17 (only Chemgrass) +10 (neither)=27
• Number who don't like Chemgrass:15 (only Chemstrand)+10 (neither)=25

But the options: Let's check the values. The correct option should be x=13 (overlap), y=17 (Chemgrass only), z=15 (Chemstrand only)? Wait no, the options:

Wait the options are:

1. x=17, y=15, z=13 → No
2. x=13, y=15, z=17 → No
3. x=15, y=13, z=17 → No
4. x=13, y=17, z=15 → Wait, no, wait the Venn: Chemstrand only is 15, overlap 13, Chemgrass only 17. So if x is overlap (13), y is Chemgrass only (17), z is Chemstrand only (15)? Wait no, the option D: x=13, y=17, z=15? Wait no, the option is "x=13, y=17, and z=15"? Wait no, the last option is x=13, y=17, z=15? Wait no, the options:

Wait the options are:

• x=17, y=15, z=13
• x=13, y=15, z=17
• x=15, y=13, z=17
• x=13, y=17, z=15

Wait, from Venn, the overlap is 13 (x), Chemgrass only 17 (y), Chemstrand only 15 (z)? No, wait z would be 15. Wait, the correct option is x=13, y=17, z=15? Wait no, the last option is x=13, y=17, z=15? Wait, no, let's check the total. Wait, maybe the frequency table has:

• Likes Chemgrass: y (17) +13 (both) =30
• Likes Chemstrand: x (15) +13 (both)=28? No, wait I think I messed up. Wait the correct option is x=13, y=17, z=15? No, wait the Venn has Chemstrand only 15, overlap 13, Chemgrass only 17. So the correct option is x=13 (overlap), y=17 (Chemgrass only), z=15 (Chemstrand only)? Wait, the option is "x=13, y=17, and z=15" (the last option? Wait no, the options are:

Wait the user's options:

1. x=17, y=15, and z=13

1. x=13, y=15, and z=17

1. x=15, y=13, and z=17

1. x=13, y=17, and z=15

Ah, the fourth option: x=13, y=17, z=15. Wait, but Chemstrand only is 15, overlap 13, Chemgrass only 17. So if x is the number who like both (13), y is the number who like Chemgrass only (17), z is the number who like Chemstrand only (15), then the fourth option is correct.

Answer:

D. \( x = 13 \), \( y = 17 \), and \( z = 15 \) (assuming the last option is D, but as per the options given, the correct one is \( x = 13 \), \( y = 17 \), and \( z = 15 \))