Uncountable Basis

It can be shown that R (the set of all real numbers) is an infinite-dimensional vector space over Q (field of rationals). Is it true that any basis (by basis I mean algebraic basis or Hamel basis) of R over Q has to be uncountable ?

uniformly continuous

Suppose that f:(0,1)-->R is uniformly continuous. Show that lim f(x) exists. x->0

What was the annual interest rate?

A business invests $10,000 in a savings account for two years. At the beginning of the second year, an additional $3500 is invested. At the end of the second year, the account balance is $15,569.75. What was the annual interest rate?

wide can the path be if there is enough gravel for 516 square feet?

A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet?

Find the number of characters used by the designer.

A designer attempts to arrange the characters of his artwork in the form of a square grid with equal numbers of rows and columns, but finds that 24 characters are left out. When he tries to add one more row and column, he finds that he has 25 too few characters. Find the number of characters used by the designer.