Find the domain for which the functions f (x) = 2x2 – 1 and g (x) = 1 – 3x are equal.

f(x) = g(x)

2x^2 - 1 = 1 - 3x

2x^2 + 3x - 1 = 1

2x^2 + 3x - 2 = 0

x^2 + 3/2*x - 1 = 0

x = - 3/4 ± √(9/16 + 1)

x1 = -2

x2 = 0.5

L = {-2 ; 0.5}

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;