Prove that for all real numbers a and b 2. negate the following statements (a) there exists a rational number q such that for all positive real mumbers ax,2 0 and ys = 43 3. prove that for all real numbers a, b, and c, we have be+ ac+aba2 + b? + c2. 4. let x and y be integers. prove that if is even and y is odd then x +y is odd. and y such that 2- y = 1 5. show that there are no natural numbers 6. using a proof by cases, show that, for all real numbers a and b la lalbl

Anormally distributed data set has a mean of 176.3 and a standard deviation of 4.2. what is the approximate z-score for the data value of 167.9? 2.00 −2.00 8.4 −8.4

On the way home from visiting his family, vincent’s plane cruised at an altitude of 3.2 × 10^4 feet. he had heard that a man named felix baumgartner skydived from an altitude of 1.28 × 10^5 feet. vincent wants to know how much higher felix went on his skydiving trip. question 1 you have already seen how adding numbers works in either scientific notation or standard notation. but can you subtract numbers in scientific notation and get the same results as subtracting in standard notation? to find out, first solve vincent’s problem in standard notation. part a write the cruising altitude of vincent’s plane in standard notation.

16x^2-16x=5 solve the equation by completing the square