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The batch with the greatest concentration has the greatest total pigment content (in grams).: False
The median concentration of the 4 highest-volume batches is less than the median concentration of the 4 lowest-volume batches.: True
The average price per liter for Cobalt batches is more than $95.: True
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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The table provides data about 15 different pigment batches currently in stock at a paint manufacturer. For each batch, the data include volume (liters), pigment concentration (grams per liter, g/L), and price per batch.
For each statement, select True if it can be verified to be true from the table, otherwise select False.
| Batch | Series | Volume (L) | Concentration (g/L) | Price |
|---|---|---|---|---|
| U1 | Ultramarine | 18 | 270 | $1,420 |
| U2 | Ultramarine | 20 | 260 | $1,360 |
| U3 | Ultramarine | 16 | 240 | $1,320 |
| U4 | Ultramarine | 26 | 280 | $1,580 |
| C1 | Cadmium | 15 | 310 | $1,590 |
| C2 | Cadmium | 12 | 290 | $1,520 |
| C3 | Cadmium | 28 | 250 | $1,480 |
| K1 | Cobalt | 14 | 240 | $1,260 |
| K2 | Cobalt | 16 | 245 | $1,600 |
| V1 | Viridian | 30 | 230 | $1,330 |
| V2 | Viridian | 10 | 235 | $1,180 |
| T1 | Titanium | 32 | 180 | $1,050 |
| T2 | Titanium | 21 | 185 | $1,080 |
| O1 | Ochre | 22 | 200 | $1,200 |
| M1 | Magenta | 19 | 260 | $1,380 |
For each statement, select True if it can be verified to be true from the table, otherwise select False.
| True | False | |
| The batch with the greatest concentration has the greatest total pigment content (in grams). | ||
| The median concentration of the 4 highest-volume batches is less than the median concentration of the 4 lowest-volume batches. | ||
| The average price per liter for Cobalt batches is more than $95. |
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Official Answer
The batch with the greatest concentration has the greatest total pigment content (in grams).: False
The median concentration of the 4 highest-volume batches is less than the median concentration of the 4 lowest-volume batches.: True
The average price per liter for Cobalt batches is more than $95.: True
15 Oct 2025, 02:30
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Bunuel
• The batch with the greatest concentration has the greatest total pigment content (in grams).
First, calculate the total pigment content in the batch with the greatest concentration. That batch is C1, with 15 liters and 310 g/L, giving 15*310 = 4650 g.
To compare, try a batch with considerably larger volume and comparable concentration. U4 has 26 liters and 280 g/L, giving 26*280 = 7280 g. Since 7280 g is greater than 4650 g, the batch with the greatest concentration does not have the greatest total pigment.
Answer: False
• The median concentration of the 4 highest-volume batches is less than the median concentration of the 4 lowest-volume batches.
For four values, the median is the average of the two middle values after sorting.
Highest volumes: T1 (32 L, 180), V1 (30 L, 230), C3 (28 L, 250), U4 (26 L, 280). Concentrations: 180, 230, 250, 280. The median is (230 + 250)/2 = 240.
Lowest volumes: V2 (10 L, 235), C2 (12 L, 290), K1 (14 L, 240), C1 (15 L, 310). Concentrations: 235, 240, 290, 310. The median is (240 + 290)/2 = 265.
Since 240 is less than 265, the statement holds.
Answer: True
• The average price per liter for Cobalt batches is more than $95.
First, calculate the price per liter for each Cobalt batch.
K1: 1260/14 = 90 dollars per liter.
K2: 1600/16 = 100 dollars per liter.
Since there are 14 liters of the first and 16 liters of the second, the overall average will be closer to the 16-liter batch’s value of 100. The midpoint between 90 and 100 is 95, so the weighted average must be greater than 95.
Answer: True
I29-210
General Discussion
1. The batch with the greatest concentration has the greatest total pigment content (in grams).
The batch with the greatest concentration (C1: 310 g/L) does not have the greatest total pigment content. The greatest total pigment content is found in batch U4 (26 L × 280 g/L = 7280 g). Therefore, False
2. The median concentration of the 4 highest-volume batches is less than the median concentration of the 4 lowest-volume batches.
The median concentration of the 4 highest-volume batches is 240 g/L, while the median concentration of the 4 lowest-volume batches is 265 g/L. So, the statement is True
3. The average price per liter for Cobalt batches is more than $95.
The average price per liter for Cobalt batches (K1 and K2) is (1260+1600)/(14+16) = 95.33, which is more than $95, so the statement is True.
The batch with the greatest concentration (C1: 310 g/L) does not have the greatest total pigment content. The greatest total pigment content is found in batch U4 (26 L × 280 g/L = 7280 g). Therefore, False
2. The median concentration of the 4 highest-volume batches is less than the median concentration of the 4 lowest-volume batches.
The median concentration of the 4 highest-volume batches is 240 g/L, while the median concentration of the 4 lowest-volume batches is 265 g/L. So, the statement is True
3. The average price per liter for Cobalt batches is more than $95.
The average price per liter for Cobalt batches (K1 and K2) is (1260+1600)/(14+16) = 95.33, which is more than $95, so the statement is True.
