The function below models the correlation between the number of hours a plant is kept in sunlight (x) and the height (y), in mm, to which it grows:
y = 4 + 2x
What does the slope of this function represent?
The original height of the plant was 4 mm.
The original height of the plant was 2 mm.
The height of the plant increases by 2 mm for every hour of sunlight it receives.
The height of the plant increases by 4 mm for every hour of sunlight it receives.
The slope of the function represents the rate at which the height of the plant increases for every hour of sunlight it receives.
Since the function is y = 4 + 2x, the slope is 2. Therefore, the height of the plant increases by 2 mm for every hour of sunlight it receives.
Therefore, the correct answer is:
The height of the plant increases by 2 mm for every hour of sunlight it receives.
An equation was created for the line of best fit from the actual enrollment data. It was used to predict the dance studio enrollment values shown in the table below:
Enrollment Month
January February March April May June
Actual 500 400 550 550 750 400
Predicted 410 450 650 650 600 450
Residual 90 −50 −100 −100 150 −50
Analyze the data. Determine whether the equation that produced the predicted values represents a good line of best fit.
No, the equation is not a good fit because the sum of the residuals is a large number.
No, the equation is not a good fit because the residuals are all far from zero.
Yes, the equation is a good fit because the residuals are not all far from zero.
Yes, the equation is a good fit because the sum of the residuals is a small number.
To determine whether the equation that produced the predicted values represents a good line of best fit, we need to consider the residuals.
The residuals are the differences between the actual enrollment values and the predicted enrollment values. If the equation is a good fit, then the residuals should be as close to zero as possible.
Looking at the residuals in the table, we can see that they vary in magnitude and sign. Some residuals are positive (90, 150) and some are negative (-50, -100). This indicates that the predicted values are both overestimating and underestimating the actual values.
Since the residuals are not all far from zero and there is a mixture of positive and negative values, we can conclude that the equation is not a good fit.
Therefore, the correct answer is:
No, the equation is not a good fit because the residuals are all far from zero.
The display shows how much water is used in a household in a given day.
The bar chart is titled water usage per day in a household. There are five vertical bars: toilet represents 27 gallons, washer represents 32 gallons, shower represents 25 gallons, dishwasher represents 9 gallons, and tap represents 7 gallons.
Which of the following describes this data set?
Categorical and bivariate
Categorical and univariate
Numerical and bivariate
Numerical and univariate
The given data set is categorical and univariate.
Categorical because it categorizes the different sources of water usage in a household such as toilet, washer, shower, dishwasher, and tap.
Univariate because it only provides information about one variable, which is the amount of water used for each source.
The slope of the function represents the rate at which the height of the plant increases for every hour of sunlight it receives. In this case, the slope is 2, which means that the height of the plant increases by 2 mm for every hour of sunlight it receives. Therefore, the correct answer is: The height of the plant increases by 2 mm for every hour of sunlight it receives.
The slope of the function represents the rate at which the height of the plant increases for every increase in the number of hours it is kept in sunlight. In this case, the slope is 2, which means that the height of the plant increases by 2 mm for every hour of sunlight it receives.
To understand this, we can look at the mathematical representation of the function. The equation y = 4 + 2x tells us that the height of the plant (y) is equal to the original height of 4 mm plus 2 times the number of hours (x) that it is kept in sunlight.
So, for every increase of 1 unit in x (which represents 1 hour of sunlight), the y value (height of the plant) increases by 2 units. This means that the height of the plant increases by 2 mm for every hour of sunlight it receives.
Therefore, the correct statement is: "The height of the plant increases by 2 mm for every hour of sunlight it receives."