An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. The y-axis is titled total cost in dollars and the x-axis is titled number of markers. A solid line, labeled A, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 3 comma 6 right parenthesis. A dotted line, labeled B, passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 3 right parenthesis.
Predict what the total cost would be for buying 10 of the type A markers.
To predict the total cost for buying 10 markers of type A, we can look at the solid line A on the graph.
From the given information, we know that the line passes through the points (0,0) and (3,6). This means that when the number of markers is 0, the total cost is 0, and when the number of markers is 3, the total cost is 6.
We can calculate the slope of line A using the formula:
Slope = (change in y-coordinate) / (change in x-coordinate)
Slope = (6 - 0) / (3 - 0)
Slope = 2
Now we can use the equation of a line to find the total cost for buying 10 markers (x = 10):
Total Cost = Slope * Number of Markers
Total Cost = 2 * 10
Total Cost = 20
Therefore, the predicted total cost for buying 10 markers of type A is $20.
You are going to drive to another state for a vacation. One route will take 8 hours to drive 400 miles, and the other route will take 7 hours to drive 420 miles. You write two equations to try and figure out the average rate of speed you would travel on each route. How much higher will your average speed be on the faster route?(1 point)
To calculate average speed, we divide the total distance traveled by the total time taken.
For the first route:
Average speed = 400 miles / 8 hours = 50 miles per hour
For the second route:
Average speed = 420 miles / 7 hours = 60 miles per hour
The average speed on the second route is higher than the average speed on the first route by (60 - 50) = 10 miles per hour.
Therefore, your average speed will be 10 miles per hour higher on the faster route.
A candy store sells different types of candy by the ounce. Red Snaps cost $0.25 per ounce, and Blue Tarts cost $0.30 per ounce. You decide to buy 8 ounces of candy to share with your friends. How much more expensive would it be to get a bag of Blue Tarts instead of a bag of Red Snaps?(1 point)
To find out how much more expensive it would be to get a bag of Blue Tarts instead of a bag of Red Snaps, we need to calculate the cost difference per ounce.
For Red Snaps:
Cost per ounce = $0.25
Total cost for 8 ounces = Cost per ounce * 8 = $0.25 * 8 = $2.00
For Blue Tarts:
Cost per ounce = $0.30
Total cost for 8 ounces = Cost per ounce * 8 = $0.30 * 8 = $2.40
To find the cost difference, we subtract the cost of Red Snaps from the cost of Blue Tarts:
Cost difference = $2.40 - $2.00 = $0.40
Therefore, it would be $0.40 more expensive to get a bag of Blue Tarts instead of a bag of Red Snaps.
You are training twice a week for a race. On Monday, you go 4 miles in 40 minutes. Then on Wednesday you go 2 miles in 16 minutes. Write an equation where y is the number of miles and x is the time in minutes for the day you ran the fastest for the week.(1 point)
To write the equation, we need to compare the time and distance for each training day and find the day when the runner ran the fastest.
On Monday:
Distance = 4 miles
Time = 40 minutes
On Wednesday:
Distance = 2 miles
Time = 16 minutes
To find the fastest day, we need to compare the time and see which day has the lowest time.
Let's consider y as the number of miles and x as the time in minutes.
For Monday's run:
y = 4 miles
x = 40 minutes
For Wednesday's run:
y = 2 miles
x = 16 minutes
Based on the given information, the equation representing the day when the runner ran the fastest for the week would be:
y = (4/40)x
Simplifying this equation, we get:
y = (1/10)x
Therefore, the equation is y = (1/10)x.
Wrong.
Apologies for the incorrect response. Let's try again to write the equation for the day the runner ran the fastest for the week.
On Monday, the runner ran 4 miles in 40 minutes, and on Wednesday, the runner ran 2 miles in 16 minutes.
To compare the speeds of the two runs, we can calculate the average speed (miles per minute) for each day:
Average speed on Monday = Distance / Time = 4 miles / 40 minutes = 0.1 miles per minute
Average speed on Wednesday = Distance / Time = 2 miles / 16 minutes = 0.125 miles per minute
Since we're looking for the day with the fastest speed, we're interested in the day with the highest average speed. In this case, Wednesday has the higher average speed of 0.125 miles per minute.
Therefore, the equation representing the day the runner ran the fastest for the week is:
y = 0.125x
Where y represents the number of miles and x represents the time in minutes for the day the runner ran the fastest.
To predict the total cost for buying 10 of the type A markers, we need to determine the equation of the line A and then substitute the x-value of 10 into the equation to find the corresponding y-value.
We can determine the equation of the line A using the coordinates (0,0) and (3,6).
Step 1: Calculate the slope (m) of the line A using the formula:
m = (change in y) / (change in x)
m = (6 - 0) / (3 - 0) = 2
Step 2: Use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) is any point on the line A. Let's use (0,0) as a point on the line:
y - 0 = 2(x - 0)
Simplifying the equation, we get:
y = 2x
Now, we can substitute the x-value of 10 into the equation to find the corresponding y-value:
y = 2(10)
y = 20
Therefore, the predicted total cost for buying 10 of the type A markers is $20.