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Sagot :
Let's analyze each statement one by one according to the information given in the table:
| Person | Mangos Used | Smoothie Size |
|---------|--------------|---------------|
| Angela | 1 | 90 oz |
| Kim | 3 | 27 oz |
| Bri | 4 | 36 oz |
Step 1: Calculating the Ratios
1. Angela's Ratio: Smoothie size to mangos used
[tex]\[ \text{Ratio (Angela)} = \frac{\text{Smoothie Size}}{\text{Mangos Used}} = \frac{90 \text{ oz}}{1} = 90.0 \][/tex]
2. Kim's Ratio: Smoothie size to mangos used
[tex]\[ \text{Ratio (Kim)} = \frac{\text{Smoothie Size}}{\text{Mangos Used}} = \frac{27 \text{ oz}}{3} = 9.0 \][/tex]
3. Bri's Ratio: Smoothie size to mangos used
[tex]\[ \text{Ratio (Bri)} = \frac{\text{Smoothie Size}}{\text{Mangos Used}} = \frac{36 \text{ oz}}{4} = 9.0 \][/tex]
Step 2: Analyzing Each Statement
1. Statement 1: "The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela."
- Kim's Ratio = 9.0
- Angela's Ratio = 90.0
- These ratios are not the same, so this statement is false.
2. Statement 2: "The ratio of smoothie size to mangos used for Kim is 19, and the ratio of smoothie size to mangos used for Bri is [tex]\(\frac{4}{27}\)[/tex]."
- Kim's Ratio = 9.0, not 19.
- Bri's Ratio = 9.0, not [tex]\(\frac{4}{27}\)[/tex] (4 divided by 27 is approximately 0.148).
- Both parts of this statement are incorrect, so this statement is false.
3. Statement 3: "The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim."
- Angela's Ratio = 90.0
- Kim's Ratio = 9.0
- 90.0 (Angela) is indeed higher than 9.0 (Kim), so this statement is true.
4. Statement 4: "The ratio of smoothie size to mangos used for Bri is [tex]\(\frac{9}{1}\)[/tex], and the ratio of smoothie size to mangos used for Angela is [tex]\(\frac{4}{36}\)[/tex]."
- Bri's Ratio = 9.0, which is [tex]\(\frac{9}{1}\)[/tex]
- Angela's Ratio = 90.0, but [tex]\(\frac{4}{36}\)[/tex] is approximately 0.111
- Only the first part of this statement is correct, so this statement is false.
Based on the analysis:
- Correct Statement: "The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim."
| Person | Mangos Used | Smoothie Size |
|---------|--------------|---------------|
| Angela | 1 | 90 oz |
| Kim | 3 | 27 oz |
| Bri | 4 | 36 oz |
Step 1: Calculating the Ratios
1. Angela's Ratio: Smoothie size to mangos used
[tex]\[ \text{Ratio (Angela)} = \frac{\text{Smoothie Size}}{\text{Mangos Used}} = \frac{90 \text{ oz}}{1} = 90.0 \][/tex]
2. Kim's Ratio: Smoothie size to mangos used
[tex]\[ \text{Ratio (Kim)} = \frac{\text{Smoothie Size}}{\text{Mangos Used}} = \frac{27 \text{ oz}}{3} = 9.0 \][/tex]
3. Bri's Ratio: Smoothie size to mangos used
[tex]\[ \text{Ratio (Bri)} = \frac{\text{Smoothie Size}}{\text{Mangos Used}} = \frac{36 \text{ oz}}{4} = 9.0 \][/tex]
Step 2: Analyzing Each Statement
1. Statement 1: "The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela."
- Kim's Ratio = 9.0
- Angela's Ratio = 90.0
- These ratios are not the same, so this statement is false.
2. Statement 2: "The ratio of smoothie size to mangos used for Kim is 19, and the ratio of smoothie size to mangos used for Bri is [tex]\(\frac{4}{27}\)[/tex]."
- Kim's Ratio = 9.0, not 19.
- Bri's Ratio = 9.0, not [tex]\(\frac{4}{27}\)[/tex] (4 divided by 27 is approximately 0.148).
- Both parts of this statement are incorrect, so this statement is false.
3. Statement 3: "The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim."
- Angela's Ratio = 90.0
- Kim's Ratio = 9.0
- 90.0 (Angela) is indeed higher than 9.0 (Kim), so this statement is true.
4. Statement 4: "The ratio of smoothie size to mangos used for Bri is [tex]\(\frac{9}{1}\)[/tex], and the ratio of smoothie size to mangos used for Angela is [tex]\(\frac{4}{36}\)[/tex]."
- Bri's Ratio = 9.0, which is [tex]\(\frac{9}{1}\)[/tex]
- Angela's Ratio = 90.0, but [tex]\(\frac{4}{36}\)[/tex] is approximately 0.111
- Only the first part of this statement is correct, so this statement is false.
Based on the analysis:
- Correct Statement: "The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim."
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