Use De Morgan’s law for quantified statements and the laws of propositional logic to show the following equivalences: a. ¬ x(P (x) ¬Q(x)) x(¬P (x) Q(x))∀∧≡∃∨
b. ¬ x(¬P (x) = Q(x)) x(¬P (x) ¬Q(x))∀⇒≡∃∧
c. ¬ x(¬P (x) (Q(x) ¬R(x))) x(P (x) (¬Q(x) R(x)))

Recall that the owner of a local health food store recently started a new ad campaign to attract more business and wants to know if average daily sales have increased. historically average daily sales were approximately $2,700. the upper bound of the 95% range of likely sample means for this one-sided test is approximately $2,843.44. if the owner took a random sample of forty-five days and found that daily average sales were now $2,984, what can she conclude at the 95% confidence level?

Rewrite the following quadratic functions in intercept or factored form. show your work. f(t) = 20t^2 + 14t - 12

Find the distance between c and d on the number line c=3 and d=11