To determine which statements are true regarding the ratio of Pitchers cards to Infield cards, let's carefully examine the data provided and the correct ratio between Pitchers and Infield cards.
1. Determine the given quantities:
- Outfield cards: 3
- Infield cards: 4
- Catcher cards: 1
- Pitchers cards: 2
2. Identify the ratio we need to find:
- The ratio of Pitchers cards to Infield cards.
3. Calculate the ratio:
- The number of Pitchers cards is 2.
- The number of Infield cards is 4.
- The ratio of Pitchers to Infield cards is given by dividing the number of Pitchers cards by the number of Infield cards:
[tex]\[
\text{Ratio} = \frac{\text{Pitchers}}{\text{Infield}} = \frac{2}{4} = 0.5
\][/tex]
Using the ratio of [tex]\( 0.5 \)[/tex], we can analyze the following possible statements to determine which are true:
1. Statement 1: The ratio of Pitchers to Infield cards is 0.5.
- This statement is true because we calculated that the ratio is indeed [tex]\( 0.5 \)[/tex].
2. Statement 2: There are twice as many Infield cards as there are Pitchers cards.
- This statement is true because if you take the number of Pitchers cards ([tex]\(2\)[/tex]) and double it, you get [tex]\(4\)[/tex], which is exactly the number of Infield cards.
3. Statement 3: The number of Infield cards is half the number of Pitchers cards.
- This statement is false because the number of Infield cards ([tex]\(4\)[/tex]) is not half but double the number of Pitchers cards ([tex]\(2\)[/tex]).
4. Statement 4: The ratio of Infield to Pitchers cards is 2.
- This statement is true because if we take the inverse of the ratio of Pitchers to Infield cards ([tex]\( \frac{1}{0.5} \)[/tex]), we get [tex]\(2\)[/tex], which is the ratio of Infield to Pitchers cards.
Conclusion:
The true statements are:
- The ratio of Pitchers to Infield cards is 0.5.
- There are twice as many Infield cards as there are Pitchers cards.
- The ratio of Infield to Pitchers cards is 2.
