Given that the human head can contain up to several hundred thousand hairs, with a maximum of about 500,000, prove that in New York City, there are two non-bald people who have the same number of hairs on their head. (b) Given that the main hall at Carnegie seats roughly 2,800, in a packed Carnegie Hall performance, there will be two people who have the same first and last initials. (c) Suppose S is a set of n + 1 integers. Prove that there exist distinct a, b ∈ S such that a − b is a multiple of n.

Jacks bank statement shows an account balance of -$25.50. which describes the magnitude, of size, of the debt in dollars

Student price tickets to a movie are $1 and non student tickets are $2. 350 tickets are sold and the total amount made is $450. how many non student tickets were sold ? a) 100 b) 150 c) 200 d)250

Someone answer this asap rn for ! a discount store’s prices are 25% lower than department store prices. the function c(x) = 0.75x can be used to determine the cost c, in dollars, of an item, where x is the department store price, in dollars. if the item has not sold in one month, the discount store takes an additional 20% off the discounted price and an additional $5 off the total purchase. the function d(y) = 0.80y - 5 can be used to find d, the cost, in dollars, of an item that has not been sold for a month, where y is the discount store price, in dollars. create a function d(c(x)) that represents the final price of an item when a costumer buys an item that has been in the discount store for a month. d(c(x)) =