Let $b$ be an integer greater than 2, and let $N_b = 1_b + 2_b + \cdots + 100_b$ (the sum contains all valid base $b$ numbers up to $100_b$). Compute the number of values of $b$ for which the sum of the squares of the base $b$ digits of $N_b$ is at most 512.

Lv beethoven software supplies customized software to a managed healthcare system. lv beethoven software's costs for the software is $1,723,000. lv beethoven software sells the software to the healthcare system for $3,816,981.10. overhead expenses are estimated at 47% of the selling price. what is lv beethoven software's net profit to the nearest dollar?

Aportion of a hiking trail slopes downward at about an 84° angle. to the nearest tenth of a flot, what is the value of x, the distance the hiker traveled along the path, if he has traveled a horizontal distance of 120 feet? a. 143.3 b. 12.5 c. 120.7 d. 130.2

(c) a vine called the mile-a-minute weed is known for growing at a very fast rate. it can grow up to 0.5 ft per day. how fast in inches per hour can the mile-a-minute weed grow up to? show your work using the correct conversion factors.