1.
Please articulate your complete rationale for, or against, linearity below (200 word limit)
2.
A recipe for oatmeal cookies calls for 2 cups of flour for every 3 cups of oatmeal. How much flour is needed to make a big batch of cookies if we have 9 cups of oatmeal?
Correct Answer
C. 6 cups
Explanation
To find out how much flour is needed, we can set up a proportion using the given ratio of flour to oatmeal. We know that 2 cups of flour is needed for every 3 cups of oatmeal. We can set up the proportion as 2/3 = x/9, where x represents the unknown amount of flour needed. By cross-multiplying and solving for x, we find that x = 6. Therefore, 6 cups of flour are needed to make a big batch of cookies with 9 cups of oatmeal.
3.
A recipe for oatmeal cookies calls for 2 cups of flour for every 3 cups of oatmeal. How much oatmeal is needed to make a big batch of cookies if we have 9.75 cups of flour?
Correct Answer
C. 14.63 cups
Explanation
To find the amount of oatmeal needed, we can set up a proportion using the given ratio of 2 cups of flour to 3 cups of oatmeal. Let x represent the amount of oatmeal needed. The proportion can be written as 2/3 = 9.75/x. Cross-multiplying gives us 2x = 29.25, and dividing both sides by 2 gives x = 14.63 cups. Therefore, 14.63 cups of oatmeal is needed to make a big batch of cookies with 9.75 cups of flour.
4.
What number is 35% of 80?
Correct Answer
B. 28
Explanation
To find 35% of 80, we can multiply 80 by 0.35. This calculation gives us 28, which means that 35% of 80 is equal to 28. Therefore, the correct answer is 28.
5.
65 is what percent of 80?
Correct Answer
D. 81.3
Explanation
To find the percentage, we divide the number we want to find the percentage of (65) by the total number (80) and multiply by 100. Therefore, 65 divided by 80 equals 0.8125. Multiplying this by 100 gives us 81.25, which is rounded to 81.3.
6.
42 is 75% of what number?
Correct Answer
A. 56
Explanation
To find the number that 42 is 75% of, we can set up the equation 42 = 0.75x, where x represents the unknown number. To solve for x, we divide both sides of the equation by 0.75, which gives us x = 56. Therefore, 42 is 75% of 56.
7.
If I found 45 gem stones when exploring 10 feet of a gravel bar, how many gemstones might I be likely to find if I explored 1 mile of the same gravel bar?
Correct Answer
C. From 20,000 to 25,000 gemstones
Explanation
If the person found 45 gemstones when exploring 10 feet of the gravel bar, it can be assumed that the density of gemstones is relatively consistent throughout the bar. Therefore, if they were to explore 1 mile (which is equivalent to 5,280 feet), they would cover a much larger area and have a higher chance of finding more gemstones. Multiplying the number of gemstones found in 10 feet (45) by the number of 10-foot sections in 1 mile (528), the estimate would be from 20,000 to 25,000 gemstones.
8.
I need to search this gemstone laden gravel bar faster... before first snowfall; so I will break my 1 mile of gravel bar into equal length sections of 176 yards each. This strategy lets me have 1 person search each section. Much faster!How many people will be required to search the entire mile?
Correct Answer
D. From 10 to 12 people
Explanation
To search the entire mile of the gemstone-laden gravel bar, the strategy is to divide it into equal length sections of 176 yards each. Since there are 1,760 yards in a mile, there will be 10 sections in total. Therefore, to search each section simultaneously, a minimum of 10 people will be required. However, since the answer range is from 10 to 12 people, it suggests that it may be beneficial to have additional people for a faster search or to account for any unforeseen circumstances.
9.
An agricultural agency is researching how much cheese people have been eating in different parts of the world.How much more cheese did Austria consume per capita in 2006 than in 1996?
Correct Answer
B. 7 kg
Explanation
In 2006, Austria consumed 7 kg more cheese per capita than in 1996. This means that there was an increase in cheese consumption over the 10-year period.
10.
How many hours will a car traveling at 65 miles per hour take to catch up with a car traveling at 55 miles per hour, if the slower car starts one hour before the faster car?
Correct Answer
A. 3 hours
Explanation
The faster car is traveling at a speed of 65 miles per hour, while the slower car is traveling at a speed of 55 miles per hour. The slower car starts one hour before the faster car. This means that when the faster car starts, the slower car has already traveled for one hour. In that one hour, the slower car has covered a distance of 55 miles. To catch up with the slower car, the faster car needs to cover this distance. Since the faster car is traveling at a speed of 65 miles per hour, it will take approximately 55/65 = 0.85 hours to cover the distance. Therefore, it will take approximately 1 + 0.85 = 1.85 hours, which is approximately 2 hours to catch up with the slower car.
11.
Josie takes up jogging. On the first week she jogs for 10 minutes per day, on the second week she jogs for 12 minutes per day. Each week, she wants to increase her jogging time by 2 minutes per day. If she jogs six days each week, what will be her total jogging time on the sixth week?
Correct Answer
C. 540
Explanation
In the first week, Josie jogs for 10 minutes per day, and in the second week, she jogs for 12 minutes per day. Each week, she increases her jogging time by 2 minutes per day. So, in the third week, she will jog for 14 minutes per day, in the fourth week, she will jog for 16 minutes per day, and so on. Since she jogs six days each week, her total jogging time on the sixth week will be 16 minutes per day multiplied by 6 days, which equals 96 minutes. Therefore, the total jogging time on the sixth week will be 96 minutes, not 540.
12.
Analyze and complete the table to determine the ratio of “the total minutes per day : total minutes per week”, for week 6
Correct Answer
C. 60 minutes/200 minutes
Explanation
The ratio of "the total minutes per day : total minutes per week" for week 6 is 60 minutes/200 minutes. This means that for every day in week 6, there were 60 minutes out of a total of 200 minutes in that week.
13.
Analyze the table to determine if the ratio of “the total minutes per day : total minutes per week”, is a linear relationship? If so why?
Correct Answer
D. Yes, but I can (and will) explain why (my rationale) on the next screen after I submit this question.
14.
In what time interval (eg. t=[4,6]) does this scenario have NO acceleration?
Correct Answer
A. T = [3,6] and [8,11] seconds
Explanation
In the given scenario, acceleration is defined as the rate of change of velocity. If the velocity remains constant over a given time interval, then there is no acceleration during that interval. Therefore, the time intervals [3,6] and [8,11] seconds have no acceleration because the velocity remains constant throughout these intervals.
15.
In what time interval (eg. t=[4,6]) does this scenario have positive acceleration?
Correct Answer
D. T = [1,4] seconds
16.
In what time interval (eg. t=[4,6]) does this scenario have the greatest negative acceleration?
Correct Answer
C. T = [6,8] seconds
Explanation
In the given scenario, the greatest negative acceleration occurs during the time interval t = [6,8] seconds. This means that the object is slowing down the most during this time period.
17.
If in the above graphed chemical reaction: g(x) represent the presence of constituent A, and f(x) represent the amount of product P created from said reaction, answer the following:What word could be used to describe the relationship between g(x) and f(x)?
Correct Answer
B. Reflected
Explanation
The word "reflected" could be used to describe the relationship between g(x) and f(x) because the graphed chemical reaction shows that as the presence of constituent A (g(x)) increases, the amount of product P created (f(x)) decreases. This is a reflection of the relationship between the two variables.
18.
If in the above graphed chemical reaction: g(x) represent the presence of constituent A, and f(x) represent the amount of product P created from said reaction, answer the following:When is the quantity of product P in this reaction equal to the quantity of constituent A?
Correct Answer
C. (2,1)
Explanation
In the given graphed chemical reaction, the quantity of product P is equal to the quantity of constituent A at point (2,1). This means that there is a specific point in the reaction where the amount of product P matches the amount of constituent A. At any other point in the reaction, the quantities of product P and constituent A do not align. Therefore, the quantity of product P in this reaction is never equal to the quantity of constituent A except at point (2,1).
19.
If in the above graphed chemical reaction rates are shown for two known chemicals (green and blue lines) and one unknown chemical (red line), please answer the following questions:How might we write the expression for the function f(x) in this picture?
Correct Answer
A. Y = 4^{x}
Explanation
Based on the graph, the red line (representing the unknown chemical) has a slope of 4, which means that for every unit increase in x, there is a corresponding increase of 4 units in y. Therefore, the expression for the function f(x) can be written as y = 4x.
20.
If in the above graphed chemical reaction rates are shown for two known chemicals (green and blue lines) and one unknown chemical (blue line), please answer the following questions:At what value are ALL functions equivalent?
Correct Answer
D. (0,1)
Explanation
The correct answer is (0,1). In the graphed chemical reaction rates, the green and blue lines represent the rates of two known chemicals, while the blue line represents the rate of an unknown chemical. The question asks at what value are ALL functions equivalent. Since the blue line is the rate of the unknown chemical, it is equivalent to itself, meaning that the rate of the unknown chemical is always equivalent to itself, or in other words, it is always equivalent to (0,1).