91Ó°ÊÓ

Boxes, each capable of holding 36 units, are used to ship a product from the manufacturer to a wholesaler. Express the number of boxes that would be required to ship \(n\) units of the product using either the floor or the ceiling notation. Which notation is more appropriate?

Prove those that are true and disprove those that are false.The square root of an irrational number is irrational.

Evaluate the expressionsa. 28 div 5 b. 28 mod 5

If \(0=\) Sunday, \(1=\) Monday, \(2=\) Tuesday, \(\ldots, 6=\) Saturday, then January 1 of year \(n\) occurs on the day of the week given by the following formula: \(\left(n+\left\lfloor\frac{n-1}{4}\right\rfloor-\left\lfloor\frac{n-1}{100}\right\rfloor+\left\lfloor\frac{n-1}{400}\right\rfloor\right) \bmod 7\). a. Use this formula to find January 1 of \(\begin{array}{lll}\text { i. } 2050 & \text { ii. } 2100 & \text { iii. the year of your birth. }\end{array}\)

If \(r\) is any rational number and \(s\) is any irrational number, then \(r / s\) is irrational.

State a necessary and sufficient condition for the floor of a real number to equal that number.

Find the greatest common divisor of each of the pairs of integers in \(9-12\). (Use any method you wish.) 7 and 21

Prove that every integer is a rational number.

Give a reason for your answer in each of 1-13. Assume that all variables represent integers. If \(n=4 k+1\), does 8 divide \(n^{2}-1\) ?

If an integer greater than 1 is a perfect square, then its cube root is irrational.