The equation y = 6x + 6 describes the relationship between quantities x and y. Are the quantities in a proportional relationship? (1 point)
A. Yes, becuase the graph of the equation is a straight line
B. Yes, becuase the graph of the equation passes through the origin
C. No, becuase the graph of the equation is not a straight line
D. No, becuase the graph of the equation does not pass through the origin
A. Yes, because the graph of the equation is a straight line.
Which two ratios form a proportion?(1 point)
A. 1/2 and 8/4
B. 2/1 and 16/ 8
C. 1/2 and 4/2
D. 2/1 and 4/8
A. 1/2 and 8/4
Use proportional relationships to solve this mixture problem. The incoming 6th-grade class has a choice between band or choir as an elective. There are four times as many seats in choir as there are in band. How many students can choose band if there is a total of 250 students?(1 point) Responses 124 students 124 students 200 students 200 students 250 students 250 students 50 students
Let's call the number of seats in band as 'x' and the number of seats in choir as 'y'. According to the problem, y = 4x.
We are also given that the total number of students is 250. So, the number of students in band plus the number of students in choir should add up to 250.
Therefore, x + y = 250.
Substituting y = 4x, we can rewrite the equation as x + 4x = 250.
Simplifying this equation, we get 5x = 250.
Dividing both sides by 5, we find x = 50.
So, the number of students that can choose band is 50.
Therefore, the correct answer is 50 students.
Rafael is making punch and needs a gallon of raspberry sorbet and 2 liters of lemon-lime soda to make 12 cups. He pays $3.00 for a 2-liter container of lemon-lime soda and $4.00 for a quart of sorbet. What is the minimum amount he should charge per cup of punch to make a $10 profit? (Remember there are 4 quarts in a gallon.) Your answer should be a dollar amount rounded to the nearest hundredth.(1 point)
To determine the minimum amount Rafael should charge per cup of punch, we need to calculate his total cost and then add the desired profit.
1 gallon is equal to 4 quarts. So, Rafael needs 4 quarts of raspberry sorbet.
The cost of 4 quarts of sorbet is $4.00.
Rafael needs 2 liters of lemon-lime soda, which costs $3.00.
To calculate the total cost, we need to convert the cost of the soda to the same unit as the sorbet. Since there are 3.78541 liters in a gallon, we can convert 2 liters to gallons:
2 liters * (1 gallon / 3.78541 liters) = 0.528344 gallons
So, Rafael needs 0.528344 gallons of soda.
The total cost Rafael incurs is the cost of sorbet + cost of soda:
$4.00 + $3.00 = $7.00
Now, Rafael needs to add his desired profit to the total cost.
The desired profit is $10.00, and Rafael is making 12 cups of punch. So, the profit per cup of punch is:
$10.00 / 12 cups = $0.833333 (rounded to the nearest hundredth)
To determine the minimum amount he should charge per cup of punch, Rafael needs to add the profit per cup to the total cost per cup:
$7.00 / 12 cups + $0.833333 = $0.583333 (rounded to the nearest hundredth)
Therefore, Rafael should charge at least $0.58 per cup of punch to make a $10 profit.