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A function that depicts depreciation can be represented as equations, graphs and tables.
<h3>The yearly value of each car for the first five years</h3>The functions are given as:
Where:
C = 5895 --- the initial value of the car
r = 22% --- the rate of depreciation
For the first 5 years, the values of t = 1, 2, 3, 4 and 5
For the first function, we have:
For the second function, we have
So, the table of values is:
See attachment for the graphs of the two functions
<h3>Interpreting the graphs</h3>The graph of car 1 increases up to C(t) = 5895, and then remains constant as the value of t increases while the graph of car 2 follows an exponential pattern.
This means that, the graph 2 that follows an exponential pattern is more realistic
<h3>The worth of the cars after 5 years</h3>From the table, the worth of car 1 is $5892.0, while the worth of car 1 is $1702.0
Read more about graphs and functions at:
Using the normal distribution, it is found that 2.64% of all the nails produced by this machine are unusable.
In a <em>normal distribution</em> with mean and standard deviation
, the z-score of a measure X is given by:
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
In this problem:
- The mean is of 3 inches, hence
.
- The standard deviation is of 0.009 inches, hence
.
Nails that are <u>more than 0.02 inches</u> from the mean are unusable, hence:
The proportion is P(|Z| > 2.22), which is <u>2 multiplied by the p-value of Z = -2.22</u>.
Z = -2.22 has a p-value of 0.0132.
2 x 0.0132 = 0.0264
0.0264 x 100% = 2.64%
2.64% of all the nails produced by this machine are unusable.
You can learn more about the normal distribution at brainly.com/question/24663213