Which of the following is a factor of f(x) = 5x3 + 24x2 − 75x + 14?
(x + 1 over 2)
(x − 1 over 2)
(x + 2)
(x − 2)

(x-2) is a factor of the function.

Step-by-step explanation:

Given function is,

As when we equate any factor of a polynomial to zero, the value of x we get is the zero of the polynomial.

So equating all the options to 0, we get

If x is a zero of a polynomial, then after putting the value of x in the polynomial, it becomes 0.

So,

So, (x-2) is a factor of the function.

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;

the diver is 33 feet below the surface.

step-by-step explanation:

hope this