Question

20 multiple answer 5 points select all the true statements. (smiley faces: 6, triangles: 2, squares: 4) the ratio of triangles to squares is 2 to 4. the ratio of squares to smiley faces is 6:4. the ratio of smiley faces to triangles is 6 to 4. there are two squares for every triangle. there are two triangles for every smiley face. there are three smiley faces for every triangle (options: a, d, e, b, f)

Explanation:

First, let's count the number of each shape:
- Smiley faces: 6
- Triangles: 2
- Squares: 4

Step 1: Analyze each statement

1. **The ratio of triangles to squares is 2 to 4**: Triangles = 2, Squares = 4. So ratio 2:4. This is true.
2. **The ratio of squares to smiley faces is 6:4**: Squares = 4, Smiley faces = 6. So ratio should be 4:6, not 6:4. False.
3. **The ratio of smiley faces to triangles is 6 to 4**: Smiley faces = 6, Triangles = 2. Wait, no, 6:2? Wait, no, wait: Triangles are 2, Smiley faces 6. So smiley faces to triangles is 6:2? Wait, no, the statement says 6 to 4? Wait, no, wait, maybe I miscalculated. Wait, triangles are 2, squares 4, smiley 6. So smiley faces (6) to triangles (2) is 6:2, but the statement says 6:4? Wait, no, maybe I made a mistake. Wait, no, the third statement: "The ratio of smiley faces to triangles is 6 to 4". Wait, triangles are 2, so 6:2 simplifies to 3:1, but 6:4 simplifies to 3:2. Wait, no, maybe I miscounted. Wait, the triangles are 2, so smiley faces (6) to triangles (2) is 6:2, which is 3:1. But the statement says 6:4. Wait, maybe I made a mistake. Wait, no, let's recheck:

Wait, the first statement: triangles (2) to squares (4) is 2:4, which is correct.

Fourth statement: "There are two squares for every triangle". Triangles = 2, Squares = 4. So per triangle (2 triangles), squares are 4, so per 1 triangle, squares are 4/2 = 2. So yes, two squares per triangle. Correct.

Fifth statement: "There are two triangles for every smiley face". Smiley faces = 6, Triangles = 2. So per smiley face, triangles are 2/6 = 1/3. So no, false.

Sixth statement: "There are three smiley faces for every triangle". Triangles = 2, Smiley faces = 6. So per triangle, smiley faces are 6/2 = 3. So yes, three smiley faces per triangle. Correct.

Wait, let's re-examine the third statement: "The ratio of smiley faces to triangles is 6 to 4". Smiley faces = 6, Triangles = 2. 6:2 is 3:1, but 6:4 is 3:2. So that's false. Wait, maybe I miscounted triangles. Wait, the image shows two triangles. So triangles = 2, smiley = 6, squares = 4.

So let's re-express each statement:

1. Triangles (2) to squares (4): 2:4 ✔️
2. Squares (4) to smiley (6): 4:6, not 6:4 ❌
3. Smiley (6) to triangles (2): 6:2, not 6:4 ❌
4. Squares per triangle: 4 squares / 2 triangles = 2 squares per triangle ✔️
5. Triangles per smiley: 2 triangles / 6 smiley = 1/3 per smiley ❌
6. Smiley per triangle: 6 smiley / 2 triangles = 3 smiley per triangle ✔️

Wait, but the third statement: "The ratio of smiley faces to triangles is 6 to 4". Wait, maybe the statement has a typo, or I miscounted. Wait, no, triangles are 2, so 6:2 is 3:1, but 6:4 is 3:2. So that's false.

Wait, but maybe I made a mistake. Let's check again:

- Smiley faces: 6 (correct, as per the image: 6 smileys)
- Triangles: 2 (correct, two triangles)
- Squares: 4 (correct, four squares)

So:

1. Triangles (2) to squares (4): 2:4 ✔️
4. Two squares per triangle: 4 squares / 2 triangles = 2 per triangle ✔️
6. Three smiley per triangle: 6 / 2 = 3 ✔️

Wait, but the third statement: "The ratio of smiley faces to triangles is 6 to 4". Smiley (6) to triangles (2) is 6:2, which is 3:1, but 6:4 is 3:2. So that's false.

Wait, maybe the third statement is a mistake, but let's check the options. The options are A, D, E, B, F, but the original statements are:

First statement: let's call it Statement 1.

Fourth: Statement 4.

Sixth: Statement 6.

Wait, the options given are A, D, E, B, F, but the statements are:

1. The ratio of triangles to squares is 2 to 4. (True)
4. There are two squares for every triangle. (True)
6. There are three smiley faces for every triangle. (True)

Wait, maybe the third statement was a mistake, but let's recheck.

Wait, maybe I misread the third statement. Let me check again: "The ratio of smiley faces to triangles is 6 to 4". Smiley faces (6) to triangles (2). 6:2 is 3:1, but 6:4 is 3:2. So that's false.

So the true statements are:

- Statement 1: The ratio of triangles to squares is 2 to 4. (True)
- Statement 4: There are two squares for every triangle. (True)
- Statement 6: There are three smiley faces for every triangle. (True)

Now, looking at the options (A, D, E, B, F), but the original problem's options are the checkboxes for the statements, but the lower options are A, D, E, B, F. Wait, maybe the labels are:

- The first checkbox (triangles to squares 2:4) is A?
- The fourth checkbox (two squares per triangle) is D?
- The sixth checkbox (three smiley per triangle) is F?

Assuming:

- A: The ratio of triangles to squares is 2 to 4. (True)
- D: There are two squares for every triangle. (True)
- F: There are three smiley faces for every triangle. (True)

So the correct options are A, D, F. But let's confirm:

- A: Triangles (2) to squares (4) is 2:4. Correct.
- D: Squares (4) / Triangles (2) = 2. So two squares per triangle. Correct.
- F: Smiley (6) / Triangles (2) = 3. So three smiley per triangle. Correct.

Answer:

A. The ratio of triangles to squares is 2 to 4, D. There are two squares for every triangle, F. There are three smiley faces for every triangle