TWO-VARIABLE DATA: MODELS AND SCATTERPLOTS 2 — Problem-Solving and Data Analysis

Questions in this quiz (7)

1. A music teacher recorded the number of hours, $$h$$, each of their $$15$$ students practiced the piano in a week and the number of mistakes, $$m$$, each student made during a recital at the end of the week. The teacher found that the data were well represented by the line of best fit with the equation $$m=-2.5h+30$$. One of the students, Kendra, practiced for $$8$$ hours and made $$12$$ mistakes. The number of mistakes Kendra made was how many more than the number of mistakes predicted by the line of best fit for her number of practice hours?

   • $$0$$
   • $$2$$
   • $$10$$
   • $$18$$

2. The growth models for the number of subscribers for two online video channels are shown in the table. Which of the following statements best describes the monthly gain in subscribers for the two channels?

   • Channel $$A$$ always gains more subscribers per month than Channel $$B$$.
   • Channel $$A$$ always gains fewer subscribers per month than Channel $$B$$.
   • Channel $$A$$ gains more subscribers per month than Channel $$B$$ at first, but eventually gains fewer
   • Channel $$A$$ gains fewer subscribers per month than Channel $$B$$ at first, but eventually gains more

3. Two savings plans were chosen, as shown in the table above. The interest in Savings Plan $$A$$ is compounded once per year. Which of the following is true about the growth of these savings?

   • Savings Plan $$A$$ always grows slower per year than Savings Plan $$B$$.
   • Savings Plan $$A$$ always grows faster per year than Savings Plan $$B$$.
   • Savings Plan $$A$$ grows slower per year than Savings Plan $$B$$ at first but eventually grows faster.
   • $$D$$ Savings Plan $$A$$ grows faster per year than Savings Plan $$B$$ at first but eventually grows slower.

4. A market analyst studied the average cost of a $$16$$-gigabyte computer RAM kit. The analyst determined that there was a linear relationship between the average cost, $$C$$, in dollars, and the number of years, $$t$$, after the year $$2010$$. A line of best fit for the data is given by the equation $$C=-6.5t+115$$. Which of the following is the best interpretation of the number $$115$$ in this context?

   • The estimated average cost of a $$16$$-gigabyte RAM kit in $$2010$$ was $$115$$ dollars.
   • The estimated average cost of a $$16$$-gigabyte RAM kit in $$2020$$ was $$115$$ dollars.
   • The estimated average cost of a $$16$$-gigabyte RAM kit decreased by $$115$$ dollars each year.
   • The estimated average cost of a $$16$$-gigabyte RAM kit increased by $$115$$ dollars each year.

5. The population of a certain species of tree in a city park was recorded over a period of time. A scatterplot of the data showed a positive linear relationship between the number of trees, $$N$$, and the number of years, $$t$$, since the study began. A line of best fit is modeled by the equation $$N=40t+850$$. Which of the following is the best interpretation of the slope of this line?

   • The predicted number of trees in the park at the start of the study.
   • The predicted number of trees in the park after $$40$$ years.
   • The predicted increase in the number of trees in the park each year.
   • The predicted number of years for the population to increase by $$850$$ trees.

6. For $$w$$ > $$0$$, the function $$g$$ is defined as follows:$$g(w)$$ is the value obtained by subtracting $$45\%$$ of $$w$$ from $$500$$.Which of the following could describe this function?

   • Decreasing exponential
   • Decreasing linear
   • Increasing exponential
   • Increasing linear

7. Two service plans are offered as shown in the table below. Which of the following is true about the annual increase in cost for the two plans?

   • The annual increase for Plan $$X$$ is always greater than the annual increase for Plan $$Y$$.
   • The annual increase for Plan $$X$$ is always less than the annual increase for Plan $$Y$$.
   • The annual increase for Plan $$X$$ is greater than the annual increase for Plan $$Y$$ at first but eventually is less.
   • The annual increase for Plan $$X$$ is less than the annual increase for Plan $$Y$$ at first but eventually is greater.