1. Given the table for x, sweater knitted, and y, money earned:%0D%0A%0D%0Ax: # of sweaters%097%096%092%099%093%0D%0Ay: $ earned%09392%09336%09112%09504%09168%0D%0A %09 %09 %09 %09 %09 (4 points)%0D%0Aa. Every sweater knitted is %0D%0A56%0D%0A dollars earned.%0D%0A%0D%0Ab. Dollars/1 sweater is called a %0D%0Aunit rate%0D%0A.%0D%0A%0D%0Ac. This relationship is %0D%0A because 0 sweaters knitted is %0D%0A dollars earned.
a. Every sweater knitted is $56 dollars earned.
b. Dollars/1 sweater is called a unit rate.
c. This relationship is linear because 0 sweaters knitted is $0 dollars earned.
a. To find the amount earned per sweater knitted, we can calculate the average value of money earned divided by the number of sweaters:
Total money earned: 392 + 336 + 112 + 504 = 1344
Total number of sweaters: 7 + 6 + 2 + 9 = 24
Average money earned per sweater = Total money earned / Total number of sweaters
Average money earned per sweater = 1344 / 24
Average money earned per sweater = 56
Therefore, every sweater knitted is 56 dollars earned.
b. The amount earned per sweater is called a unit rate, which is the rate of change for y with respect to x. In this case, the unit rate is the amount of money earned for 1 sweater knitted.
So, the unit rate is 56 dollars/1 sweater.
c. The given relationship between the number of sweaters knitted (x) and the money earned (y) can be described as a proportional relationship because the rate of change (unit rate) is constant.
When 0 sweaters are knitted, the amount earned is 0 dollars.
To find the answers to the given questions using the table:
a. To find how much money is earned per sweater knitted, we need to divide the total money earned by the total number of sweaters knitted. Looking at the table, we can see that the total number of sweaters knitted is 9 (7 + 6 + 2 + 9 + 3) and the total money earned is $1512 (392 + 336 + 112 + 504 + 168).
Therefore, the amount of money earned per sweater knitted is calculated as:
$1512 / 9 = $168
So, every sweater knitted is $168 dollars earned.
b. To find the term for "Dollars/1 sweater," we can use the concept of a unit rate. A unit rate is a comparison of two different quantities where one of the quantities is equal to 1. In this case, we need to find the dollar amount per 1 sweater.
From the previous calculation, we found that every sweater earns $168. Therefore, the term "Dollars/1 sweater" for this relationship is $168.
c. To find what happens when 0 sweaters are knitted, we can look at the table. When 0 sweaters are knitted, the corresponding value for money earned is not given. However, we can assume that no sweaters knitted would result in no money earned.
Therefore, the relationship between the number of sweaters knitted and the money earned is a direct relationship, and when 0 sweaters are knitted, 0 dollars are earned.