How do you explain this function?

Hello from MrBillDoesMath!

For  0 <= x < =40 the function is that of the straight line 15x which has slope 15. Note that at x = 40 the value of the function is 15(4) =600

For x > 40 , the function is another straight line but with slope 20. This line is steeper than the 15x line but for x near, but slightly greater than  40, the value is close to 600 + 20 (40-40)  or 600 + 20(40-40) = 600.  This is the same value as the first line, 15x, at x = 40.

In summary, the graph of p(x), from   0 <= x <=40, is a line of slope 15 and for x>40 is a line of slope 20.  p(x) has a removable discontinuity at x = 40 because  p(x) approaches 600 as x approaches 40, regardless of the method of approach (i.e. whether x  approaches 40 from values less than 40 or from values greater than 40)

Thank you,

MrB

according to egenuity the answer is

step-by-step explanation:

d. 344.22

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;