What does it mean in context of the example that alyssa’s rate of change is greater than sarah’s?

Part 1) The rate of change is the amount of money saved by week

Part 2) The amount of money saved weekly by Alyssa is greater than the amount of money saved weekly by Sarah.

Part 3) see the explanation

Step-by-step explanation:

see the attached figure to better understand the problem

The complete question is

Part 1) What does the rate of change in the example represent?

Part 2)  What does it mean in context of the example that Alyssa’s rate of change is greater than Sarah’s?

Part 3) Write ordered pairs for the initial values of each function. Tell what the initial values represent

Part 1) we know that

The rate of change is the slope or unit rate of the linear equation

The formula of slope is "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)

In this context the rate of change is the amount of money saved by week

Part 2) we know that

Alyssa’s rate of change is equal to $8 per week

Sarah’s rate of change is equal to $6 per week

That means ----> The amount of money saved weekly by Alyssa is greater than the amount of money saved weekly by Sarah.

Part 3) we know that

The initial value or y-intercept is the value of y when the value of x is equal to zero

In this context , the initial value is the amount of money available at the time of beginning to save

so

Sarah's Savings

Looking at the graph

The initial value is the point (0,8)

That means ----> At the beginning (x=0), Sarah already had $8 saved.

Alyssa's Savings

Looking at the graph

The initial value is the point (0,0)

That means ----> At the begin (x=0), Alyssa had nothing saved.

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.

answer: i think it is c