At the deli counter in the supermarket, Nigel paid $10 for 212 pounds of roast beef. The cost of deli meat is proportional to its weight. What is the equation for the graph of this proportional relationship?(1 point)
Let's represent the cost of deli meat as C and the weight of deli meat as W. According to the problem, the cost of deli meat is proportional to its weight.
We can express this relationship with the equation C = kW, where k is the constant of proportionality.
To find the value of k, we can use the given information. Nigel paid $10 for 212 pounds of roast beef. Plugging these values into our equation, we get:
10 = k(212)
To find the value of k, we divide both sides of the equation by 212:
k = 10 / 212
Simplifying this expression, we get:
k ≈ 0.04716981132
Therefore, the equation for the graph of this proportional relationship is:
C ≈ 0.04716981132W
Miley is saving for a new pair of boots. They cost $150 . Every week, she puts $25 into her savings account. Based on the graph, state the number of weeks it will take for her to save enough money to buy the boots.
To determine the number of weeks it will take for Miley to save enough money to buy the boots, we can create an equation to represent the situation.
Let's denote the number of weeks as W and the amount Miley has saved as S. The amount Miley can save each week is $25.
The equation representing the situation is:
S = 25W
Miley needs to save $150 to buy the boots. So we set up the equation:
S = 150
We substitute S = 25W into the equation:
25W = 150
To solve for W, we divide both sides of the equation by 25:
W = 150/25
Simplifying this expression, we get:
W = 6
Therefore, it will take Miley 6 weeks to save enough money to buy the boots.
The age of a dog is proportional to the age of a human. Based on the graph, determine a dog’s age if a human is 3 years old.
To determine a dog's age if a human is 3 years old, we need to look at the graph and find the corresponding dog's age.
Since the relationship between a dog's age and a human's age is proportional, we can assume that the graph is a straight line passing through the origin (0,0).
If a human is 3 years old, we can find the corresponding dog's age by reading the point on the graph where the human's age is 3. The corresponding dog's age will be the value on the graph at that point.
Without the graph or specific information, we cannot determine the dog's age. Please provide more information or refer to the given graph to find the specific dog's age for a human age of 3.
The amount of water is directly proportional to the number of cups of rice. The coordinate (1/2, 1) is on the graph of this proportional relationship. Identify another point on the graph.(1 point)
Responses
(1/4, 2)
Left Parenthesis Start Fraction 1 over 4 End Fraction comma 2 Right Parenthesis
(2/3, 4)
Left Parenthesis Start Fraction 2 over 3 End Fraction comma 4 Right Parenthesis
(3/2, 3)
Left Parenthesis Start Fraction 3 over 2 End Fraction comma 3 Right Parenthesis
(2, 6)
To determine the equation for the graph of this proportional relationship, we need to find the constant of proportionality. In this case, the constant of proportionality represents the cost per pound of roast beef.
To find the constant of proportionality, we can set up a proportion using the given information. The cost C is equal to the constant of proportionality k times the weight W:
C = kW
Using the values given in the problem, we can set up the proportion:
10 = k * 212
To solve for k, we divide both sides of the equation by 212:
10/212 = k
Simplifying the right side of the equation:
k ≈ 0.0471698
Now that we have the value of k, we can write the equation for the graph:
C = 0.0471698W
So, the equation for the graph of this proportional relationship is C = 0.0471698W.