Two-variable data: Models MCQ Quiz - Objective Question with Answer for Two-variable data: Models - Download Free PDF

Since the population decreases by a fixed percentage each month, this follows an exponential decay model, making option A (Decreasing exponential) the correct choice.

Solution:

• (A) Incorrect: The data points show that individuals weighing 65 pounds have more offspring than those weighing 50 pounds. So, this statement is false.
• (B) Correct: The number of offspring increases as weight increases, which aligns with what we observe in the graph.
• (C) Incorrect: The number of offspring is not constant—it changes with weight, so this statement is false.
• (D) Incorrect: The lowest weight (40 pounds) corresponds to the lowest number of offspring (5), not the highest.

Solution:

We need to count the days where the probability of rain is 70% or more.
From the given data:

Tuesday → 60% ( Does not qualify)
Wednesday → 90% (Qualifies)
Thursday → 30% (Does not qualify)
Friday → 70% ( Qualifies)
There are 2 favorable days (Wednesday & Friday) out of 4 total days.
Thus, the probability is: 2/4 = 1/2
​
Final Answer:
Option B) 1/2 (or 50%)

A linear model with a negative slope.

When the technician tests components at a constant rate (40 per hour), the number of untested components will decrease at this same constant rate. This creates a linear relationship between time and the number of remaining components, where the slope is negative (-40 components per hour).

If we let:

• N(t) = number of untested components remaining after t hours
• Initial batch = 500 components
• Rate of testing = 40 components per hour

Then the model would be: N(t) = 500 - 40t

This is a linear function with a slope of -40, indicating that for each hour that passes, the number of untested components decreases by 40.

Hence, The Correct Answer is option 2.

Explanation:

 Option A: "The product sales were at their lowest point at around 5 days."
At 5 days, the sales were 4, which is the lowest value on the graph.
This statement is true.
Option B: "The highest sales were recorded around the 30th day of March."
On the 30th day, sales reached 20, which is the highest value on the graph.
This statement is true.
 Option C: "The sales consistently increased without any decline."
Sales decreased multiple times:
From 6 → 4 (0 to 5 days).
From 20 → 15 (30 to 35 days).
Since sales do not increase consistently, this statement is false.
This is the correct answer to the question (NOT true statement).
Option D: "The sales initially fluctuated before showing a rising trend."
Sales decreased initially (0-5 days), then fluctuated between 8 and 10 before finally increasing to 20.
 This statement is true.

Choice B is correct. Since the work is done at a constant rate, a linear model best models the situation. The number of shirts remaining is dependent on the length of time the inspector has worked; therefore, if the relationship were graphed, time would be the variable of the horizontal axis and the number of remaining shirts would be the variable of the vertical axis. Since the number of shirts decreases as the time worked increases, it follows that the slope of this graph is negative. 
Choice A is incorrect and may result from incorrectly reasoning about the slope. Choices C and D are incorrect and may result from not identifying the constant rate of work as a characteristic of a linear model. 

Option 2 is correct. Since the farmer is harvesting apples at a constant rate, the situation is best modeled by a linear function. As time progresses, the number of apples remaining in the orchard decreases. Thus, the graph of this situation would have a negative slope. Option 1 is incorrect because a positive slope would indicate an increase in the number of apples, which does not match the scenario. Options 3 and 4 are incorrect because exponential models are used for rates of change that are not constant.

Since the population decreases by a fixed percentage each month, this follows an exponential decay model, making option A (Decreasing exponential) the correct choice.

Solution:

• (A) Incorrect: The data points show that individuals weighing 65 pounds have more offspring than those weighing 50 pounds. So, this statement is false.
• (B) Correct: The number of offspring increases as weight increases, which aligns with what we observe in the graph.
• (C) Incorrect: The number of offspring is not constant—it changes with weight, so this statement is false.
• (D) Incorrect: The lowest weight (40 pounds) corresponds to the lowest number of offspring (5), not the highest.

Solution:

We need to count the days where the probability of rain is 70% or more.
From the given data:

Tuesday → 60% ( Does not qualify)
Wednesday → 90% (Qualifies)
Thursday → 30% (Does not qualify)
Friday → 70% ( Qualifies)
There are 2 favorable days (Wednesday & Friday) out of 4 total days.
Thus, the probability is: 2/4 = 1/2
​
Final Answer:
Option B) 1/2 (or 50%)

A linear model with a negative slope.

When the technician tests components at a constant rate (40 per hour), the number of untested components will decrease at this same constant rate. This creates a linear relationship between time and the number of remaining components, where the slope is negative (-40 components per hour).

If we let:

• N(t) = number of untested components remaining after t hours
• Initial batch = 500 components
• Rate of testing = 40 components per hour

Then the model would be: N(t) = 500 - 40t

This is a linear function with a slope of -40, indicating that for each hour that passes, the number of untested components decreases by 40.

Hence, The Correct Answer is option 2.

Explanation:

 Option A: "The product sales were at their lowest point at around 5 days."
At 5 days, the sales were 4, which is the lowest value on the graph.
This statement is true.
Option B: "The highest sales were recorded around the 30th day of March."
On the 30th day, sales reached 20, which is the highest value on the graph.
This statement is true.
 Option C: "The sales consistently increased without any decline."
Sales decreased multiple times:
From 6 → 4 (0 to 5 days).
From 20 → 15 (30 to 35 days).
Since sales do not increase consistently, this statement is false.
This is the correct answer to the question (NOT true statement).
Option D: "The sales initially fluctuated before showing a rising trend."
Sales decreased initially (0-5 days), then fluctuated between 8 and 10 before finally increasing to 20.
 This statement is true.

Explanation:

Option 1: This is incorrect because it lacks a linear component to better fit the data
Opton 2: 

• This equation includes a linear term ($-10x$)
• The -10x term shifts the parabola slightly, adjusting the fit for the data.
• From the scatterplot, the points do not perfectly align with a purely symmetrical curve, which suggests that the data is slightly skewed.
• The best-fit curve should include a linear term for proper alignment.

Option 3: The smaller coefficient (8 vs. 10) means this equation may not capture the steepness of the observed data.
Option 4: 

• The quadratic term ($10x^2$) is fine.
• However, the linear term ($-25x$) is too large.
• This would cause a much stronger shift, which does not match the observed data trend.

Hence, The Correct Answer is option 2.

Explanation :

As you can see from the Graph at x = 3.3 The Actual Value of y is 10 

and The Predicted Value of y is 6.2
So, The Difference between the Actual and Predicted Value is 10 - 6.2 = 3.8 

The function $k(x)=1.05x$ features a constant positive multiplier, $1.05$, which indicates a linear relationship where $k(x)$ increases consistently as $x$ increases. This consistent rate of increase characterizes $k(x)$ as an increasing linear function.

Option 1 is incorrect as it describes a function decreasing in an exponential manner, which is not applicable. Option 2 is incorrect since it suggests a decrease, not present here. Option 3 is incorrect because exponential growth would require $x$ to be in an exponent position, which is absent in this function.