10. Make Sense and Persevere A 12-sided solid has equal-sized faces numbered 1 to 12.
a. Find P(number greater than 10).
b. Find P(number less than 5).
c. If the 12-sided solid is rolled 200 times, how many times would you
expect either a 4, 6, or 9 to be rolled?

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

Suppose that the price p, in dollars, and the number of sales, x, of a certain item follow the equation 4 p plus 4 x plus 2 pxequals56. suppose also that p and x are both functions of time, measured in days. find the rate at which x is changing when xequals2, pequals6, and startfraction dp over dt endfraction equals1.5.

If you have 12 feet of string and you cut it into equal length of 5 inches each how much string will be left