drag each object to show whether earnings are proportional to time in the situation represented.\nclear…

drag each object to show whether earnings are proportional to time in the situation represented.\nclear check\na worker earning an hourly wage\na person who earns 2% simple interest on a savings account each year\na tutor charging $30 per hour for 3 hours\na contractor charging a house call fee and then an hourly labor rate\nearnings are proportional to time\nearnings are not proportional to time\nnot enough information\ndrag and drop items here\ndrag and drop items here\ndrag and drop items here

drag each object to show whether earnings are proportional to time in the situation represented.\nclear check\na worker earning an hourly wage\na person who earns 2% simple interest on a savings account each year\na tutor charging $30 per hour for 3 hours\na contractor charging a house call fee and then an hourly labor rate\nearnings are proportional to time\nearnings are not proportional to time\nnot enough information\ndrag and drop items here\ndrag and drop items here\ndrag and drop items here

Answer

Explanation:

Step1: Recall proportional - relationship criteria

Two variables are proportional if the ratio of the two variables is constant and the relationship passes through the origin $(0,0)$.

Step2: Analyze the graph

The graph does not pass through the origin $(0,0)$ since it starts at $(10,50)$. So earnings are not proportional to time.

Step3: Analyze the table

For the table, $\frac{1.25}{10}=\frac{2.50}{20}=\frac{3.75}{30}= 0.125$. The ratio of earnings to time is constant, and if we assume time $t = 0$ earnings $E=0$, it is a proportional relationship.

Step4: Analyze worker with hourly wage

If a worker earns an hourly wage, the formula for earnings $E$ and time $t$ is $E = rt$ (where $r$ is the hourly rate). When $t = 0$, $E=0$, and $\frac{E}{t}=r$ (constant). So earnings are proportional to time.

Step5: Analyze simple - interest case

The simple - interest formula is $I=Prt$, where $P$ is the principal, $r$ is the interest rate, and $t$ is the time. When $t = 0$, $I = 0$, and $\frac{I}{t}=Pr$ (constant). So earnings (interest) are proportional to time.

Step6: Analyze tutor charging per hour

The tutor charges $30$ per hour. The formula for earnings $E$ and time $t$ is $E = 30t$. When $t = 0$, $E = 0$, and $\frac{E}{t}=30$ (constant). So earnings are proportional to time.

Step7: Analyze contractor case

The contractor has a house - call fee $F$ and an hourly rate $r$. The formula for earnings $E$ is $E=F+rt$. When $t = 0$, $E=F\neq0$. So earnings are not proportional to time.

Answer:

  • Earnings Are Proportional to Time: A worker earning an hourly wage, A person who earns 2% simple interest on a savings account each year, A tutor charging $30 per hour, the table of earnings and time
  • Earnings Are NOT Proportional to Time: The graph, A contractor charging a house call fee and then an hourly labor rate
  • Not Enough Information: None