Write a (formal) proof of the following statement: "If 4 does not divide an integer n, then does not divide n²-3n+ 5."

Smoking 2009, women and men In Exercise 2, we ex-amined the percentage of men aged 18–24 who smoked from 1965 to 2009 according to the Centers for DiseaseControl and Prevention. How about women? Here’s ascatterplot showing the corresponding percentages forboth men and women:a) In what ways are the trends in smoking behaviorsimilar for men and women?b) How do the smoking rates for women differ fromthose for men?c) Viewed alone, the trend for men may have seemed toviolate the Linearity Condition. How about the trendfor women? Does the consistency of the two patternsencourage you to think that a linear model for thetrend in men might be appropriate? (Note: there is nocorrect answer to this question; it is raised for you tothink about.)

Weight Gain of Athletes A researcher wishes to see whether there is any difference in the weight gains of athletes following one of three special diets. Athletes are randomly assigned to three groups and placed on the diet for 6 weeks. The weight gains (in pounds) are shown here. At a=0.005, can the researcher conclude that there is a difference in the diets?   Diet A: 3, 4, 5, 6   Diet B: 12, 13, 14, 6, 7, 8   Diet C: 3, 4, 5 ,6   Part 2. State the hypotheses and identify the claim with the correct hypothesis.       Part 3. Compute the test value. Always round score values to two decimal places.       Part 4. Find the -value. Round the answer to four decimal places.       Part 5. Reject or not to reject the null hypothesis.

(8) X and Y are independent events. P(X)=0.3; P(Y)=0.4. Find (a) P(X and Y) (b) P(X | Y) (c) P(Y | X) (d) P(X or Y)