What does descartes rule of signs say about number of positive real roots and negative real roots of p(x) x^3+6x^2+9x+5

There are no positive roots

Step-by-step explanation:

The Descartes' rule posits that, given a polynomial with real coefficients ordered, the number of positive roots is equal to the amount of sign-changes OR to such amount minus a number multiple of 2. In you polynomial  P(x)=x^3+6x^2+9x+5 you have NO sign-changes, as every coefficient is positive. So, we can confirm that, if the polynomial has real roots, none of these are positive. As 0 can'y be a root of P(x) (replace x=0 and confirm), if there is some root, it will be a negative root. However, the rule can't confirm that there are roots.

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;