Suppose the sum \[ \sum_{k = 0}^{49} ( - 1)^k \binom{99}{2k}, \] where \binom{n}{j} = \frac {n! }{j! (n - j)! }, is written in the form a^b, where a and b are integers and b is as large as possible. find a+b.

Samantha is growing a garden in her back yard. she spend $90 setting up the garden bed and buying the proper garden supplies. in addition, each seed she plants cost $0.25. a. write the function f(x) that represents samantha's total cost on her garden. b. explain what x represents. c. explain what f(x) represents. d. if samantha plants 55 seeds, how much did she spend in total?

Find the area of the unshaded square

Neoli is a nurse who works each day from 8: 00 am to 4: 00 pm at the blood collection centre. she takes 45 minutes for her lunch break. on average, it takes neoli 15 minutes to collect each sample and record the patient's details. on average, how many patients can neoli see each day?