business is booming for ricks house cleaning service, clean your scene, and he needs to hire more house…
business is booming for ricks house cleaning service, clean your scene, and he needs to hire more house cleaners. this table shows the relationship between the number of new house cleaners rick hires, x, and the total number of houses his company can clean per week, y.\n|x (new house cleaners)|y (total houses)|\n|----|----|\n|6|65|\n|9|74|\n|12|83|\n|17|98|\naccording to the values in the table, do x and y have a proportional relationship?\n○ yes\n○ no
Answer
Explanation:
Step1: Recall proportional - relationship condition
For a proportional relationship between $x$ and $y$, the ratio $\frac{y}{x}$ must be constant for all pairs of $(x,y)$ values.
Step2: Calculate ratios for each pair
For the first pair $(x = 6,y = 65)$, $\frac{y}{x}=\frac{65}{6}\approx10.83$. For the second pair $(x = 9,y = 74)$, $\frac{y}{x}=\frac{74}{9}\approx8.22$. For the third pair $(x = 12,y = 83)$, $\frac{y}{x}=\frac{83}{12}\approx6.92$. For the fourth pair $(x = 17,y = 98)$, $\frac{y}{x}=\frac{98}{17}\approx5.76$.
Step3: Check constancy of ratios
Since $\frac{65}{6}\neq\frac{74}{9}\neq\frac{83}{12}\neq\frac{98}{17}$, the ratios are not constant.
Answer:
no