1. The graph shows the distance a ghost crab can run over time.
A graph is shown in the xy-plane. The x-axis is labeled as Time in seconds and the y-axis is labeled as Distance in Meters. The values on the x-axis ranges from 0 to 9 in increments of 1 and the values on the y-axis ranges from 0 to 45 in increments of 5. A line starts from the origin, goes up, and passes through the points (3, 5), (6, 10), and so on.
Let d equal the distance in meters and t equal the time in seconds. Which is a direct variation equation for this relationship?
A. d= 3/5t
b. d=5/3t
c. t=5/3d
d. t=2/5d
2.Which of the following graphs shows a direct variation?
3.Which graph displays equivalent ratios? Select all that apply.
4.The relationship between the number of girls who are in the middle school and high school jazz bands is proportional. What is the constant of proportionality?
Jazz Band Number of Girls Total Members
Middle School 6 15
High School 8 20
a. 3/10
b. 2/5
c. 8/15
d. 3/4
5.A real estate agent received a $17,500 commission on the sale of a $350,000 house on Walnut Street. The same agent received a $20,000 commission on the sale of a house on Center Avenue. What was the sale price of the house on Center Avenue?
A.
$100,000
B.
$370,000
C.
$400,000
D.
$450,000
6.The number of pages Cameron reads varies directly with time in minutes. He can read 15 pages in 60 minutes. What is the constant of proportionality for the number of minutes to read 1 page.
A. 1/4
B. 1/2
C. 2
D. 4
7.In the graph, the amount of sales tax (t) is proportional to the price (p) of an item.
A graph is shown in the xy-plane. The x-axis is labeled as Price left parenthesis dollars right parenthesis and the y-axis is labeled as Tax left parenthesis cents right parenthesis. The values on the x-axis ranges from 0 to 4 in increments of 1 and the values on the y-axis ranges from 0 to 0 decimal point 4 0 in increments of 0 decimal point 1 0. A line starts from the origin, goes up and Five points are marked on the line with coordinates (0, 0), (1, 0 decimal point 0 6), (2, 0 decimal point 1 2), (3, 0 decimal point 1 8), and (4, 0 decimal point 2 4).
Which equation represents this relationship?
A. T=0.05P
B. T=0.06P
C. T=0.96P
D. T=1.6P
8.Consider the graph shown.
A graph is shown in the xy-plane. The values on the x-axis ranges from 0 to 1 decimal point 5 in increments of 0 decimal point 5 and the values on the y-axis ranges from 0 to 800 in increments of 200. A line starts from a point 100 on the y-axis, goes up, and passes through the points (0, 100), (0 decimal point 3, 200), (0 decimal point 9, 400), and (1 decimal point 5, 600).
Determine if the graph shows two quantities that vary directly. If possible, determine the constant of proportionality. Explain your reasoning.
9.Determine the constant of proportionality for the graph.
A graph is shown in the xy-plane. The x-axis is labeled as Items and the y-axis is labeled as Profit left parenthesis dollars right parenthesis. The values on the x-axis ranges from 0 to 40 in increments of 10 and the values on the y-axis ranges from 0 to 8 in increments of 2. Five points are marked on the graph with coordinates (0, 0), (10, 2), (20, 4), (30, 6), and (40, 8).
A. 1/5
B. 2
C. 5
D.10
10.Tanya polled boys and girls in her grade to determine how many prefer math to other subjects. Her results are shown in the table.
Students Prefer Math Total Students
Boys 14 30
Girls 16 32
​Which is a true statement?
A. the relationship is prportional because
16-4=2 and 32-30=2
B. the relationship is prportional because
30-14=16 and 32-16=16
C. the relationship is not prportional because
14/16=7/8 and 30/35=15/16
D. the relationship is not prportional because
14/30=7/15 and 16/32=1/2
looks like a homework dump, or an assignment, or worse yet: a test
We don't do those. We don't do the work for you, that would be cheating.
1. To find the direct variation equation for the relationship between distance (d) and time (t), we need to see how the values of d and t are related.
Looking at the graph, we can observe that as time increases, the distance also increases. The line passes through the origin and is straight, which indicates a direct variation relationship.
The slope of the line can be calculated using the formula: slope = (change in y)/(change in x).
Taking two points on the line, (3, 5) and (6, 10), we can calculate the slope:
Slope = (10 - 5) / (6 - 3) = 5 / 3
Therefore, the direct variation equation for this relationship is: d = (5/3)t
Answer: B. d = (5/3)t
2. The question asks which of the following graphs shows a direct variation relationship. To determine this, we need to analyze the graphs and see if they have a straight line passing through the origin.
Without the actual graphs, it is difficult to provide a specific answer. However, a direct variation relationship is represented by a straight line passing through the origin in a graph. So, you need to look for a graph that depicts a straight line through the origin.
3. The question asks which graph displays equivalent ratios. To determine this, we need to analyze the graphs and see if the ratios of the y-values to the x-values are equal. Equivalent ratios have the same value when simplified.
Without the actual graphs, it is difficult to provide a specific answer. However, you need to look for graphs where the ratios of the y-values to the x-values are equal.
4. To find the constant of proportionality for the proportional relationship between the number of girls in the middle school and high school jazz bands, we divide the number of girls in the high school jazz band by the number of girls in the middle school jazz band when the ratio is in the simplest form.
The ratio of the number of girls in the high school to the number of girls in the middle school is: 8/6, which simplifies to 4/3.
Therefore, the constant of proportionality is 4/3.
Answer: None of the given options. The correct answer is 4/3.
5. To find the sale price of the house on Center Avenue, we need to use the information about the commission and the sale price of the other house.
We know that the agent received a $17,500 commission for the sale of a $350,000 house. Dividing the commission by the sale price, we get: $17,500 / $350,000 = 0.05 (or 5%).
Now, using the same percentage, we can determine the sale price of the other house by dividing the commission by the percentage: $20,000 / 0.05 = $400,000.
Therefore, the sale price of the house on Center Avenue is $400,000.
Answer: C. $400,000
6. To find the constant of proportionality, we need to divide the number of pages Cameron can read by the time in minutes for reading those pages when the ratio is in the simplest form.
The ratio of the number of pages to the time in minutes is: 15/60, which simplifies to 1/4.
Therefore, the constant of proportionality for the number of minutes to read 1 page is 1/4.
Answer: A. 1/4
7. To determine the equation that represents the relationship between the sales tax (t) and the price (p), we can use the information given in the graph to see how the values of t and p are related.
Looking at the graph, we can observe that as the price increases, the sales tax also increases. The line passes through the origin and is straight, indicating a direct variation relationship.
The slope of the line can be calculated using the formula: slope = (change in y)/(change in x).
Taking two points on the line, (2, 0.12) and (4, 0.24), we can calculate the slope:
Slope = (0.24 - 0.12) / (4 - 2) = 0.12 / 2 = 0.06
Therefore, the equation representing this relationship is: t = 0.06p
Answer: B. t = 0.06p
8. To determine if the graph shows two quantities that vary directly, we need to see if the graph represents a straight line passing through the origin.
Looking at the given graph, we can see that the line starts from a point on the y-axis and passes through the points (0, 100), (0.3, 200), (0.9, 400), and (1.5, 600). Since the line is not straight, it does not represent a direct variation relationship.
Therefore, the graph does not show two quantities that vary directly.
Answer: The graph does not show two quantities that vary directly.
9. To find the constant of proportionality for the given graph, we need to divide the profit (y-values) by the number of items (x-values) when the ratio is in the simplest form.
Taking two points on the graph, (10, 2) and (20, 4), we can calculate the ratio of profit to items:
Ratio = (4 - 2) / (20 - 10) = 2 / 10 = 1 / 5
Therefore, the constant of proportionality is 1/5.
Answer: A. 1/5
10. To determine if the relationship between the number of students who prefer math and the total number of students is proportional, we need to see if the ratios of the number of students who prefer math to the total number of students are equal.
Considering the boys' data, the ratio is: 14 / 30, which simplifies to 7 / 15.
Considering the girls' data, the ratio is: 16 / 32, which simplifies to 1 / 2.
Since the ratios are not equal, the relationship is not proportional.
Answer: D. the relationship is not proportional because 14/30=7/15 and 16/32=1/2.