$____ per game
2. Use the image to answer the question.
An illustration shows three coiled wire springs stretched to varying lengths. The first spring does not have any weights pulling it downward, and the length of the spring is marked as a question mark inches. The second spring has a 2-pound weight attached to the bottom, and its length is marked as 12 inches. The third spring has a 5-pound weight attached to the bottom and its length is marked as 18 inches.
A spring has a length of 12 inches when a 2-pound weight is attached, and a length of 18 inches when a 5-pound weight is attached. Use rate of change to find the length of the spring when no weights are attached.
(1 point)
____ inches
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3. The Kims are hosting a catered dinner. The cost for 3 servings is $18. The cost for 10 servings is $60. What is the cost per serving?(1 point)
$____ per serving
4. A graph of the cost of gas purchased depending on the number of gallons pumped has the points (4,15) and (8,30) . What is the rate of change in the cost of the gas as each gallon is pumped?(1 point)
$____ per gallon
5. A linear graph of the cost of broccoli in dollars per pound has the points (3,8.25) and (6,16.50) . What is the rate of change in the purchase price in dollars per pound?(1 point)
$____ per pound
Bot GPT 3.5
answered
2. 6 inches
3. $6 per serving
4. $3 per gallon
5. $2.75 per pound
Connexus Student
answered
Bot GPT 3.5
answered
1. $8 per game
2. 6 inches
Thank you for pointing that out. If you have any more questions or need further clarification, feel free to ask.
Connexus Student
answered
Bot GPT 3.5
answered
2. Since the rate of change is constant, we can use the ratio of the change in length to the change of weight to find the length when no weight is attached:
Change in length: 18 inches - 12 inches = 6 inches
Change in weight: 5 pounds - 2 pounds = 3 pounds
Rate of change: Change in length / Change in weight = 6 inches / 3 pounds = 2 inches/pound
When no weight is attached (0 pounds), the length will be:
Length = 12 inches + (0 pounds) * 2 inches/pound = 12 inches
Therefore, the length of the spring when no weights are attached is 12 inches.
4. To find the rate of change in the cost of gas per gallon, we can use the two points provided:
Change in cost: $30 - $15 = $15
Change in gallons: 8 - 4 = 4 gallons
Rate of change: $15 / 4 gallons = $3.75 per gallon
Therefore, the rate of change in the cost of gas as each gallon is pumped is $3.75 per gallon.
Thank you for your patience. If you have any more questions or need further assistance, feel free to ask.
Connexus Student
answered
Bot GPT 3.5
answered
Since the rate of change is constant, we can use the ratio of change in length to the change in weight to find the length when no weight is attached:
Change in length: 18 inches - 12 inches = 6 inches
Change in weight: 5 pounds - 2 pounds = 3 pounds
Rate of change: Change in length / Change in weight = 6 inches / 3 pounds = 2 inches/pound
When no weight is attached (0 pounds), the length will be:
Length = 12 inches + (0 pounds) * 2 inches/pound = 12 inches
Therefore, the length of the spring when no weights are attached is 12 inches.
Thank you for pointing out the error. If you have any more questions or need further clarification, feel free to ask.
Connexus Student
answered
Bot GPT 3.5
answered
Since the rate of change is constant, we can determine the length of the spring when no weights are attached.
Using the information provided:
- The length of the spring is 12 inches when a 2-pound weight is attached.
- The length of the spring is 18 inches when a 5-pound weight is attached.
We can calculate the rate of change to find the length when no weights are attached.
Change in length: 18 inches - 12 inches = 6 inches
Change in weight: 5 pounds - 2 pounds = 3 pounds
Rate of change: Change in length / Change in weight = 6 inches / 3 pounds = 2 inches/pound
When no weight is attached (0 pounds), the length will be:
Length = 12 inches + (0 pounds) * 2 inches/pound = 12 inches
Therefore, the length of the spring when no weights are attached is 12 inches.
Could you please provide further clarification or correction if needed so I can assist you accurately with this question?
Connexus Student
answered
An illustration shows three coiled wire springs stretched to varying lengths. The first spring does not have any weights pulling it downward, and the length of the spring is marked as a question mark inches. The second spring has a 2-pound weight attached to the bottom, and its length is marked as 12 inches. The third spring has a 5-pound weight attached to the bottom and its length is marked as 18 inches.
A spring has a length of 12 inches when a 2-pound weight is attached, and a length of 18 inches when a 5-pound weight is attached. Use rate of change to find the length of the spring when no weights are attached.
____ inches
Bot GPT 3.5
answered
Let:
x = length of the spring when no weights are attached (in inches)
y = weight added to the spring (in pounds)
Given that the rate of change is consistent (constant) as weight is added, we can calculate the rate:
Rate of change = Change in length / Change in weight
From the information given:
- When a 2-pound weight is added, the length increases by 12 inches (from 12 inches to 24 inches).
- When a 5-pound weight is added, the length increases by 6 inches (from 12 inches to 18 inches).
Using the rate of change formula:
Rate for 2-pound weight = 12 inches / 2 pounds = 6 inches/pound
Rate for 5-pound weight = 6 inches / 5 pounds = 1.2 inches/pound
Since the rate of change is constant, we can calculate the length of the spring when no weights are attached. Let's use the rate for the 2-pound weight to find the length when no weights are attached:
x = 12 inches - (0 pounds) * 6 inches/pound
x = 12 inches
Therefore, the length of the spring when no weights are attached is 12 inches.
