Consider the following statement: For all real numbers r, if r^3 is irrational then r is irrational.
(a) Prove the statement either by contradiction or by contraposition. Clearly indicate which method you are using.
(b) If you used proof by contradiction in part (a), write what you would “suppose” and
what you would “show” to prove the statement by contraposition. If you used proof by
contraposition in part (a), write what you would “suppose” and what you would “show”
to prove the statement by contradiction.
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Solve the problem.Under a certain apportionment method State X receives 51 seats and State Y receives 19 seats. Ten years later, the population of State X has increased by 3%, while the population of State Y remains unchanged. Under the same apportionment method, State X now receives 50 seats and State Y receives 20 seats. This is called
A. the population paradox. B. the Alabama paradox. C. the new states paradox. D. a violation of the quota rule. E. none of these
Solve.If a tree 17.5 feet tall casts a shadow that is 7 feet long, find the height of a tree casting a shadow that is 19 feet long. Round to the nearest tenth of a foot, if necessary.
A. 6.4 ft B. 47.5 ft C. 7.6 ft D. 29.5 ft
Solve the equation by using the square root property. Simplify all radicals.4p2 + 2 = 5
A. 
B. 
C. {-5, 1}
D. 
Provide an appropriate response.Assume a is positive, b is negative, and c is positive for the expression a + ( b ? c).Tell whether the value of the given expression is positive, negative or cannot be determined.
A. Positive B. Negative C. Cannot be determined